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.gitignore

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+__pycache__
+.ipynb_checkpoints
+.streamlit
+wandb/
+*.egg-info/
+jax_cache/

CITATION.cff

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+# YAML 1.2
+---
+abstract: "DALL·E mini is a JAX/Flax reimplementation of OpenAI's DALL·E that requires much smaller hardware resources. By simplifying the architecture and model memory requirements, as well as leveraging open-source code and pre-trained models, we were able to create a model that is 27 times smaller than the original DALL·E and train it on a single TPU v3-8 for only 3 days. DALL·E mini achieves impressive results, albeit of a lower quality than the original system. It can be used for exploration and further experimentation on commodity hardware."
+authors: 
+  -
+    family-names: Dayma
+    given-names: Boris
+  -
+    family-names: Patil
+    given-names: Suraj
+  -
+    family-names: Cuenca
+    given-names: Pedro
+  -
+    family-names: Saifullah
+    given-names: Khalid
+  -
+    family-names: Abraham
+    given-names: Tanishq
+  -
+    family-names: "Lê Khắc"
+    given-names: "Phúc"
+  -
+    family-names: Melas
+    given-names: Luke
+  -
+    family-names: Ghosh
+    given-names: Ritobrata
+cff-version: "1.1.0"
+date-released: 2021-07-29
+identifiers: 
+keywords: 
+  - dalle
+  - "text-to-image generation"
+  - transformer
+  - "zero-shot"
+  - JAX
+license: "Apache-2.0"
+doi: 10.5281/zenodo.5146400
+message: "If you use this project, please cite it using these metadata."
+repository-code: "https://github.com/borisdayma/dalle-mini"
+title: "DALL·E Mini"
+version: "v0.1-alpha"
+...

Docker/Dockerfile

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+FROM nvidia/cuda:11.6.2-cudnn8-devel-ubuntu20.04
+
+RUN apt-get update && apt-get install -y \
+  git \
+  python3 \
+  python3-pip \
+  && rm -rf /var/lib/apt/lists/*
+
+RUN pip install --upgrade "jax[cuda]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html \
+  && pip install -q \
+  git+https://github.com/borisdayma/dalle-mini.git \
+  git+https://github.com/patil-suraj/vqgan-jax.git
+
+RUN pip install jupyter
+
+WORKDIR /workspace
+

Docker/README.md

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+# Running Dalle-mini With Docker
+
+This folder contains the Dockerfile needed to build a Docker image that can easily run Dalle-mini.
+
+## Inference
+
+Steps to run inference with Dalle-mini are as follows:
+
+1. Build the docker image with ```dalle-mini/Docker/build_docker.sh```
+2. Run the container with ```dalle-mini/run_docker_image.sh```
+3. Navigate to ```/workspace/tools/inference/``` and run ```run_infer_notebook.sh```
+4. Click the Jupyter Notebook link and run through the notebook.
+
+### Inference Video Tutorial
+
+Alteratively check out a video tutorial on how to run Dalle-mini on [Linux](https://www.youtube.com/watch?v=eWpzLIa6v9E) and [Windows](https://www.youtube.com/watch?v=OqEuEe-xSKk)

Docker/build_docker.sh

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+docker build . -t dalle-mini:latest

LICENSE

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+   9. Accepting Warranty or Additional Liability. While redistributing
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+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
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+   Copyright 2021 The DALL·E mini Authors
+
+   Licensed under the Apache License, Version 2.0 (the "License");
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+
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Makefile

@@ -0,0 +1,5 @@
+.PHONY: style
+
+style:
+	black .
+	isort .

README.md

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+# DALL·E Mini
+
+<a href="https://www.craiyon.com/"><img src="https://www.craiyon.com/thumbnail.png" width="300"></a>
+
+## How to use it?
+
+You can use the model on [🖍️ craiyon](https://www.craiyon.com/)
+
+## How does it work?
+
+Refer to our reports:
+
+* [DALL·E mini - Generate Images from Any Text Prompt](https://wandb.ai/dalle-mini/dalle-mini/reports/DALL-E-mini-Generate-images-from-any-text-prompt--VmlldzoyMDE4NDAy)
+* [DALL·E mini - Explained](https://wandb.ai/dalle-mini/dalle-mini/reports/DALL-E-Mini-Explained-with-Demo--Vmlldzo4NjIxODA)
+* [DALL·E mega - Training Journal](https://wandb.ai/dalle-mini/dalle-mini/reports/DALL-E-Mega-Training-Journal--VmlldzoxODMxMDI2)
+
+## Development
+
+### Dependencies Installation
+
+For inference only, use `pip install dalle-mini`.
+
+For development, clone the repo and use `pip install -e ".[dev]"`.
+Before making a PR, check style with `make style`.
+
+You can experiment with the pipeline step by step through our [`inference pipeline notebook`](tools/inference/inference_pipeline.ipynb)
+
+[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/borisdayma/dalle-mini/blob/main/tools/inference/inference_pipeline.ipynb)
+
+### Training of DALL·E mini
+
+Use [`tools/train/train.py`](tools/train/train.py).
+
+You can also adjust the [sweep configuration file](https://docs.wandb.ai/guides/sweeps) if you need to perform a hyperparameter search.
+
+## FAQ
+
+### Where to find the latest models?
+
+Trained models are on 🤗 Model Hub:
+
+* [VQGAN-f16-16384](https://huggingface.co/dalle-mini/vqgan_imagenet_f16_16384) for encoding/decoding images
+* [DALL·E mini](https://huggingface.co/dalle-mini/dalle-mini) or [DALL·E mega](https://huggingface.co/dalle-mini/dalle-mega) for generating images from a text prompt
+
+### Where does the logo come from?
+
+The "armchair in the shape of an avocado" was used by OpenAI when releasing DALL·E to illustrate the model's capabilities. Having successful predictions on this prompt represents a big milestone for us.
+
+## Contributing
+
+Join the community on the [LAION Discord](https://discord.gg/xBPBXfcFHd).
+Any contribution is welcome, from reporting issues to proposing fixes/improvements or testing the model with cool prompts!
+
+You can also use these great projects from the community:
+
+* spin off your own app with [DALL-E Playground repository](https://github.com/saharmor/dalle-playground) (thanks [Sahar](https://twitter.com/theaievangelist))
+
+* try [DALL·E Flow](https://github.com/jina-ai/dalle-flow) project for generating, diffusion, and upscaling in a Human-in-the-Loop workflow (thanks [Han Xiao](https://github.com/hanxiao))
+
+  [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/jina-ai/dalle-flow/blob/main/client.ipynb)
+
+* run on [Replicate](https://replicate.com/borisdayma/dalle-mini), in the browser or via API
+
+## Acknowledgements
+
+* 🤗 Hugging Face for organizing [the FLAX/JAX community week](https://github.com/huggingface/transformers/tree/master/examples/research_projects/jax-projects)
+* Google [TPU Research Cloud (TRC) program](https://sites.research.google/trc/) for providing computing resources
+* [Weights & Biases](https://wandb.com/) for providing the infrastructure for experiment tracking and model management
+
+## Authors & Contributors
+
+DALL·E mini was initially developed by:
+
+* [Boris Dayma](https://github.com/borisdayma)
+* [Suraj Patil](https://github.com/patil-suraj)
+* [Pedro Cuenca](https://github.com/pcuenca)
+* [Khalid Saifullah](https://github.com/khalidsaifullaah)
+* [Tanishq Abraham](https://github.com/tmabraham)
+* [Phúc Lê Khắc](https://github.com/lkhphuc)
+* [Luke Melas](https://github.com/lukemelas)
+* [Ritobrata Ghosh](https://github.com/ghosh-r)
+
+Many thanks to the people who helped make it better:
+
+* the [DALLE-Pytorch](https://discord.gg/xBPBXfcFHd) and [EleutherAI](https://www.eleuther.ai/) communities for testing and exchanging cool ideas
+* [Rohan Anil](https://github.com/rohan-anil) for adding Distributed Shampoo optimizer and always giving great suggestions
+* [Phil Wang](https://github.com/lucidrains) has provided a lot of cool implementations of transformer variants and gives interesting insights with [x-transformers](https://github.com/lucidrains/x-transformers)
+* [Katherine Crowson](https://github.com/crowsonkb) for [super conditioning](https://twitter.com/RiversHaveWings/status/1478093658716966912)
+* the [Gradio team](https://gradio.app/) made an amazing UI for our app
+
+## Citing DALL·E mini
+
+If you find DALL·E mini useful in your research or wish to refer, please use the following BibTeX entry.
+
+```text
+@misc{Dayma_DALL·E_Mini_2021,
+      author = {Dayma, Boris and Patil, Suraj and Cuenca, Pedro and Saifullah, Khalid and Abraham, Tanishq and Lê Khắc, Phúc and Melas, Luke and Ghosh, Ritobrata},
+      doi = {10.5281/zenodo.5146400},
+      month = {7},
+      title = {DALL·E Mini},
+      url = {https://github.com/borisdayma/dalle-mini},
+      year = {2021}
+}
+```
+
+## References
+
+Original DALL·E from "[Zero-Shot Text-to-Image Generation](https://arxiv.org/abs/2102.12092)" with image quantization from "[Learning Transferable Visual Models From Natural Language Supervision](https://arxiv.org/abs/2103.00020)".
+
+Image encoder from "[Taming Transformers for High-Resolution Image Synthesis](https://arxiv.org/abs/2012.09841v2)".
+
+Sequence to sequence model based on "[BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://arxiv.org/abs/1910.13461v1)" with implementation of a few variants:
+
+* "[GLU Variants Improve Transformer](https://arxiv.org/abs/2002.05202)"
+* "[Deepnet: Scaling Transformers to 1,000 Layers](https://arxiv.org/abs/2203.00555)"
+* "[NormFormer: Improved Transformer Pretraining with Extra Normalization](https://arxiv.org/abs/2110.09456)"
+* "[Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://arxiv.org/abs/2103.14030)"
+* "[CogView: Mastering Text-to-Image Generation via Transformers](https://arxiv.org/abs/2105.13290v2)"
+* "[Root Mean Square Layer Normalization](https://arxiv.org/abs/1910.07467)"
+* "[Sinkformers: Transformers with Doubly Stochastic Attention](https://arxiv.org/abs/2110.11773)"
+* "[Foundation Transformers](https://arxiv.org/abs/2210.06423)
+
+Main optimizer (Distributed Shampoo) from "[Scalable Second Order Optimization for Deep Learning](https://arxiv.org/abs/2002.09018)".
+
+### Citations
+
+```text
+@misc{
+  title={Zero-Shot Text-to-Image Generation}, 
+  author={Aditya Ramesh and Mikhail Pavlov and Gabriel Goh and Scott Gray and Chelsea Voss and Alec Radford and Mark Chen and Ilya Sutskever},
+  year={2021},
+  eprint={2102.12092},
+  archivePrefix={arXiv},
+  primaryClass={cs.CV}
+}
+```
+
+```text
+@misc{
+  title={Learning Transferable Visual Models From Natural Language Supervision}, 
+  author={Alec Radford and Jong Wook Kim and Chris Hallacy and Aditya Ramesh and Gabriel Goh and Sandhini Agarwal and Girish Sastry and Amanda Askell and Pamela Mishkin and Jack Clark and Gretchen Krueger and Ilya Sutskever},
+  year={2021},
+  eprint={2103.00020},
+  archivePrefix={arXiv},
+  primaryClass={cs.CV}
+}
+```
+
+```text
+@misc{
+  title={Taming Transformers for High-Resolution Image Synthesis}, 
+  author={Patrick Esser and Robin Rombach and Björn Ommer},
+  year={2021},
+  eprint={2012.09841},
+  archivePrefix={arXiv},
+  primaryClass={cs.CV}
+}
+```
+
+```text
+@misc{
+  title={BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension}, 
+  author={Mike Lewis and Yinhan Liu and Naman Goyal and Marjan Ghazvininejad and Abdelrahman Mohamed and Omer Levy and Ves Stoyanov and Luke Zettlemoyer},
+  year={2019},
+  eprint={1910.13461},
+  archivePrefix={arXiv},
+  primaryClass={cs.CL}
+}
+```
+
+```text
+@misc{
+  title={Scalable Second Order Optimization for Deep Learning},
+  author={Rohan Anil and Vineet Gupta and Tomer Koren and Kevin Regan and Yoram Singer},
+  year={2021},
+  eprint={2002.09018},
+  archivePrefix={arXiv},
+  primaryClass={cs.LG}
+}
+```
+
+```text
+@misc{
+  title={GLU Variants Improve Transformer},
+  author={Noam Shazeer},
+  year={2020},
+  url={https://arxiv.org/abs/2002.05202}    
+}
+```
+
+```text
+ @misc{
+  title={DeepNet: Scaling transformers to 1,000 layers},
+  author={Wang, Hongyu and Ma, Shuming and Dong, Li and Huang, Shaohan and Zhang, Dongdong and Wei, Furu},
+  year={2022},
+  eprint={2203.00555}
+  archivePrefix={arXiv},
+  primaryClass={cs.LG}
+} 
+```
+
+```text
+@misc{
+  title={NormFormer: Improved Transformer Pretraining with Extra Normalization},
+  author={Sam Shleifer and Jason Weston and Myle Ott},
+  year={2021},
+  eprint={2110.09456},
+  archivePrefix={arXiv},
+  primaryClass={cs.CL}
+}
+```
+
+```text
+@inproceedings{
+  title={Swin Transformer V2: Scaling Up Capacity and Resolution}, 
+  author={Ze Liu and Han Hu and Yutong Lin and Zhuliang Yao and Zhenda Xie and Yixuan Wei and Jia Ning and Yue Cao and Zheng Zhang and Li Dong and Furu Wei and Baining Guo},
+  booktitle={International Conference on Computer Vision and Pattern Recognition (CVPR)},
+  year={2022}
+}
+```
+
+```text
+@misc{
+  title = {CogView: Mastering Text-to-Image Generation via Transformers},
+  author = {Ming Ding and Zhuoyi Yang and Wenyi Hong and Wendi Zheng and Chang Zhou and Da Yin and Junyang Lin and Xu Zou and Zhou Shao and Hongxia Yang and Jie Tang},
+  year = {2021},
+  eprint = {2105.13290},
+  archivePrefix = {arXiv},
+  primaryClass = {cs.CV}
+}
+```
+
+```text
+@misc{
+  title = {Root Mean Square Layer Normalization},
+  author = {Biao Zhang and Rico Sennrich},
+  year = {2019},
+  eprint = {1910.07467},
+  archivePrefix = {arXiv},
+  primaryClass = {cs.LG}
+}
+```
+
+```text
+@misc{
+  title = {Sinkformers: Transformers with Doubly Stochastic Attention},
+  url = {https://arxiv.org/abs/2110.11773},
+  author = {Sander, Michael E. and Ablin, Pierre and Blondel, Mathieu and Peyré, Gabriel},
+  publisher = {arXiv},
+  year = {2021},
+}
+```
+
+```text
+@misc{
+  title = {Smooth activations and reproducibility in deep networks},
+  url = {https://arxiv.org/abs/2010.09931},
+  author = {Shamir, Gil I. and Lin, Dong and Coviello, Lorenzo},
+  publisher = {arXiv},
+  year = {2020},
+}
+```
+
+```text
+@misc{
+  title = {Foundation Transformers},
+  url = {https://arxiv.org/abs/2210.06423},
+  author = {Wang, Hongyu and Ma, Shuming and Huang, Shaohan and Dong, Li and Wang, Wenhui and Peng, Zhiliang and Wu, Yu and Bajaj, Payal and Singhal, Saksham and Benhaim, Alon and Patra, Barun and Liu, Zhun and Chaudhary, Vishrav and Song, Xia and Wei, Furu},
+  publisher = {arXiv},
+  year = {2022},
+}
+```

app/gradio/app.py

@@ -0,0 +1,53 @@
+#!/usr/bin/env python
+# coding: utf-8
+import os
+
+import gradio as gr
+from backend import get_images_from_backend
+
+block = gr.Blocks(css=".container { max-width: 800px; margin: auto; }")
+backend_url = os.environ["BACKEND_SERVER"] + "/generate"
+
+
+def infer(prompt):
+    response = get_images_from_backend(prompt, backend_url)
+    return response["images"]
+
+
+with block:
+    gr.Markdown("<h1><center>DALL·E mini</center></h1>")
+    gr.Markdown(
+        "DALL·E mini is an AI model that generates images from any prompt you give!"
+    )
+    with gr.Group():
+        with gr.Box():
+            with gr.Row().style(mobile_collapse=False, equal_height=True):
+                text = gr.Textbox(
+                    label="Enter your prompt", show_label=False, max_lines=1
+                ).style(
+                    border=(True, False, True, True),
+                    margin=False,
+                    rounded=(True, False, False, True),
+                    container=False,
+                )
+                btn = gr.Button("Run").style(
+                    margin=False,
+                    rounded=(False, True, True, False),
+                )
+        gallery = gr.Gallery(label="Generated images", show_label=False).style(
+            grid=[3], height="auto"
+        )
+        text.submit(infer, inputs=text, outputs=gallery)
+        btn.click(infer, inputs=text, outputs=gallery)
+
+    gr.Markdown(
+        """___
+   <p style='text-align: center'>
+   Created by <a href="https://twitter.com/borisdayma" target="_blank">Boris Dayma</a> et al. 2021-2022
+   <br/>
+   <a href="https://github.com/borisdayma/dalle-mini" target="_blank">GitHub</a> | <a href="https://wandb.ai/dalle-mini/dalle-mini/reports/DALL-E-mini-Generate-images-from-any-text-prompt--VmlldzoyMDE4NDAy" target="_blank">Project Report</a>
+   </p>"""
+    )
+
+
+block.launch(enable_queue=False)

app/gradio/backend.py

@@ -0,0 +1,33 @@
+# Client requests to Dalle-Mini Backend server
+
+import base64
+from io import BytesIO
+
+import requests
+from PIL import Image
+
+
+class ServiceError(Exception):
+    def __init__(self, status_code):
+        self.status_code = status_code
+
+
+def get_images_from_backend(prompt, backend_url):
+    r = requests.post(backend_url, json={"prompt": prompt})
+    if r.status_code == 200:
+        json = r.json()
+        images = json["images"]
+        images = [Image.open(BytesIO(base64.b64decode(img))) for img in images]
+        version = json.get("version", "unknown")
+        return {"images": images, "version": version}
+    else:
+        raise ServiceError(r.status_code)
+
+
+def get_model_version(url):
+    r = requests.get(url)
+    if r.status_code == 200:
+        version = r.json()["version"]
+        return version
+    else:
+        raise ServiceError(r.status_code)

app/streamlit/app.py

@@ -0,0 +1,108 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+import streamlit as st
+from backend import ServiceError, get_images_from_backend
+
+st.sidebar.markdown(
+    """
+<style>
+.aligncenter {
+    text-align: center;
+}
+</style>
+<p class="aligncenter">
+    <img src="https://raw.githubusercontent.com/borisdayma/dalle-mini/main/img/logo.png"/>
+</p>
+""",
+    unsafe_allow_html=True,
+)
+st.sidebar.markdown(
+    """
+___
+<p style='text-align: center'>
+DALL·E mini is an AI model that generates images from any prompt you give!
+</p>
+
+<p style='text-align: center'>
+Created by Boris Dayma et al. 2021-2022
+<br/>
+<a href="https://github.com/borisdayma/dalle-mini" target="_blank">GitHub</a> | <a href="https://wandb.ai/dalle-mini/dalle-mini/reports/DALL-E-mini--Vmlldzo4NjIxODA" target="_blank">Project Report</a>
+</p>
+        """,
+    unsafe_allow_html=True,
+)
+
+st.header("DALL·E mini")
+st.subheader("Generate images from text")
+
+prompt = st.text_input("What do you want to see?")
+
+DEBUG = False
+if prompt != "":
+    container = st.empty()
+    container.markdown(
+        f"""
+        <style> p {{ margin:0 }} div {{ margin:0 }} </style>
+        <div data-stale="false" class="element-container css-1e5imcs e1tzin5v1">
+        <div class="stAlert">
+        <div role="alert" data-baseweb="notification" class="st-ae st-af st-ag st-ah st-ai st-aj st-ak st-g3 st-am st-b8 st-ao st-ap st-aq st-ar st-as st-at st-au st-av st-aw st-ax st-ay st-az st-b9 st-b1 st-b2 st-b3 st-b4 st-b5 st-b6">
+        <div class="st-b7">
+        <div class="css-whx05o e13vu3m50">
+        <div data-testid="stMarkdownContainer" class="css-1ekf893 e16nr0p30">
+                <img src="https://raw.githubusercontent.com/borisdayma/dalle-mini/main/app/streamlit/img/loading.gif" width="30"/>
+                Generating predictions for: <b>{prompt}</b>
+        </div>
+        </div>
+        </div>
+        </div>
+        </div>
+        </div>
+        <small><i>Predictions may take up to 5mn under high load. Please stand by.</i></small>
+    """,
+        unsafe_allow_html=True,
+    )
+
+    try:
+        backend_url = st.secrets["BACKEND_SERVER"] + "/generate"
+        response = get_images_from_backend(prompt, backend_url)
+        selected = response["images"]
+        version = response["version"]
+
+        margin = 0.1  # for better position of zoom in arrow
+        n_columns = 3
+        cols = st.columns([1] + [margin, 1] * (n_columns - 1))
+        for i, img in enumerate(selected):
+            cols[(i % n_columns) * 2].image(img)
+        container.markdown(f"**{prompt}**")
+
+        # st.sidebar.markdown(
+        #    f"<small><center>{version}</center></small>", unsafe_allow_html=True
+        # )
+
+        # st.markdown(
+        #    f"""
+        # These results have been obtained using model `{version}` from [an ongoing training run](https://wandb.ai/dalle-mini/dalle-mini/runs/mheh9e55).
+        # """
+        # )
+
+        st.button("Again!", key="again_button")
+
+    except ServiceError as error:
+        container.text(f"Service unavailable, status: {error.status_code}")
+    except KeyError:
+        if DEBUG:
+            container.markdown(
+                """
+            **Error: BACKEND_SERVER unset**
+
+            Please, create a file called `.streamlit/secrets.toml` inside the app's folder and include a line to configure the server URL:
+            ```
+            BACKEND_SERVER="<server url>"
+            ```
+            """
+            )
+        else:
+            container.markdown(
+                "Error -5, please try again or [report it](mailto:pcuenca-dalle@guenever.net)."
+            )

app/streamlit/backend.py

@@ -0,0 +1,33 @@
+# Client requests to Dalle-Mini Backend server
+
+import base64
+from io import BytesIO
+
+import requests
+from PIL import Image
+
+
+class ServiceError(Exception):
+    def __init__(self, status_code):
+        self.status_code = status_code
+
+
+def get_images_from_backend(prompt, backend_url):
+    r = requests.post(backend_url, json={"prompt": prompt})
+    if r.status_code == 200:
+        json = r.json()
+        images = json["images"]
+        images = [Image.open(BytesIO(base64.b64decode(img))) for img in images]
+        version = json.get("version", "unknown")
+        return {"images": images, "version": version}
+    else:
+        raise ServiceError(r.status_code)
+
+
+def get_model_version(url):
+    r = requests.get(url)
+    if r.status_code == 200:
+        version = r.json()["version"]
+        return version
+    else:
+        raise ServiceError(r.status_code)

pyproject.toml

@@ -0,0 +1,2 @@
+[tool.isort]
+profile = "black"

run_docker_image.sh

@@ -0,0 +1,4 @@
+#!/bin/bash
+
+# This script is used to run the docker image. Change or remove GPU flag if you dont have nvidia-docker or the needed GPUs
+docker run --rm --name dallemini -it -p 8888:8888  --gpus all  -v "${PWD}":/workspace dalle-mini:latest

setup.cfg

@@ -0,0 +1,47 @@
+[metadata]
+name = dalle-mini
+version = attr: dalle_mini.__version__
+author = Boris Dayma et al.
+author_email = boris.dayma@gmail.com
+description = DALL·E mini - Generate images from a text prompt
+long_description = file: README.md
+long_description_content_type = text/markdown
+url = https://github.com/borisdayma/dalle-mini
+project_urls =
+    Bug Tracker = https://github.com/borisdayma/dalle-mini/issues
+classifiers =
+    Programming Language :: Python :: 3
+    License :: OSI Approved :: Apache Software License
+    Operating System :: OS Independent
+    Topic :: Scientific/Engineering :: Artificial Intelligence
+    Development Status :: 3 - Alpha
+    Intended Audience :: Developers
+
+[options]
+package_dir =
+    =src
+packages = find:
+python_requires = >=3.6
+install_requires =
+    transformers==4.25.1
+    einops
+    unidecode
+    ftfy
+    emoji
+    pillow
+    jax==0.3.25
+    flax==0.6.3
+    orbax==0.0.23
+    wandb
+
+[options.extras_require]
+dev =
+    tqdm
+    optax
+    braceexpand
+    datasets[streaming]
+    black[jupyter]
+    isort
+
+[options.packages.find]
+where = src

setup.py

@@ -0,0 +1,4 @@
+from setuptools import setup
+
+if __name__ == "__main__":
+    setup()

src/dalle_mini/__init__.py

@@ -0,0 +1,3 @@
+__version__ = "0.1.5"
+
+from .model import DalleBart, DalleBartProcessor

src/dalle_mini/data.py

@@ -0,0 +1,461 @@
+import random
+from dataclasses import dataclass, field
+from functools import partial
+from pathlib import Path
+
+import jax
+import jax.numpy as jnp
+import numpy as np
+from braceexpand import braceexpand
+from datasets import Dataset, load_dataset
+
+from .model.text import TextNormalizer
+
+
+@dataclass
+class Dataset:
+    dataset_repo_or_path: str
+    train_file: str = None
+    validation_file: str = None
+    streaming: bool = True
+    use_auth_token: bool = False
+    text_column: str = "caption"
+    encoding_column: str = "encoding"
+    max_train_samples: int = None
+    max_eval_samples: int = None
+    preprocessing_num_workers: int = None
+    overwrite_cache: bool = False
+    do_train: bool = False
+    do_eval: bool = True
+    seed_dataset: int = None
+    shard_by_host: bool = False
+    blank_caption_prob: float = 0.0
+    clip_score_column: str = "clip_score"
+    min_clip_score: float = None
+    max_clip_score: float = None
+    filter_column: str = None
+    filter_value: str = None
+    multi_eval_ds: bool = False
+    train_dataset: Dataset = field(init=False)
+    eval_dataset: Dataset = field(init=False)
+    other_eval_datasets: list = field(init=False)
+    rng_dataset: jnp.ndarray = field(init=False)
+    multi_hosts: bool = field(init=False)
+
+    def __post_init__(self):
+        if self.seed_dataset is None:
+            # create a random seed
+            self.seed_dataset = random.randint(0, 2**32 - 1)
+        # set numpy rng
+        self.np_rng = np.random.default_rng(self.seed_dataset)
+        self.multi_hosts = jax.process_count() > 1
+        # feed blank captions only in streaming mode for now
+        # otherwise dataset could be cached with same blanked captions
+        if self.blank_caption_prob:
+            assert (
+                self.streaming is True
+            ), "blank_caption_prob can only be used in streaming mode"
+        # define data_files
+        if self.train_file is not None or self.validation_file is not None:
+            # accept braceexpand notation
+            for k in ["train_file", "validation_file"]:
+                f = getattr(self, k)
+                if isinstance(f, str):
+                    setattr(self, k, list(braceexpand(f)))
+            # for list of files, split training data shards by host
+            if (
+                isinstance(self.train_file, list)
+                and self.multi_hosts
+                and self.shard_by_host
+            ):
+                self.train_file = self.train_file[
+                    jax.process_index() :: jax.process_count()
+                ]
+            data_files = {
+                "train": self.train_file,
+                "validation": self.validation_file,
+            }
+        else:
+            data_files = None
+
+        # multiple validation datasets
+        if self.multi_eval_ds:
+            assert Path(
+                self.dataset_repo_or_path
+            ).is_dir(), f"{self.dataset_repo_or_path} is not a directory, required for multi_eval_ds"
+            data_files = {
+                split.name: [str(f) for f in split.glob("*.parquet")]
+                for split in Path(self.dataset_repo_or_path).glob("*")
+            }
+            # rename "valid" to "validation" if present for consistency
+            if "valid" in data_files:
+                data_files["validation"] = data_files["valid"]
+                del data_files["valid"]
+            self.dataset_repo_or_path = "parquet"
+
+        # load dataset
+        dataset = load_dataset(
+            self.dataset_repo_or_path,
+            data_files=data_files,
+            streaming=self.streaming,
+            use_auth_token=self.use_auth_token,
+        )
+        if self.do_train:
+            if "train" not in dataset:
+                raise ValueError("Training requires a training dataset")
+            self.train_dataset = dataset["train"]
+            if self.max_train_samples is not None:
+                self.train_dataset = (
+                    self.train_dataset.take(self.max_train_samples)
+                    if self.streaming
+                    else self.train_dataset.select(range(self.max_train_samples))
+                )
+        if self.do_eval:
+            if "validation" not in dataset:
+                raise ValueError("Evaluating requires a validation dataset")
+            self.eval_dataset = dataset["validation"]
+            if self.max_eval_samples is not None:
+                self.eval_dataset = (
+                    self.eval_dataset.take(self.max_eval_samples)
+                    if self.streaming
+                    else self.eval_dataset.select(range(self.max_eval_samples))
+                )
+            # other eval datasets
+            other_eval_splits = dataset.keys() - {"train", "validation"}
+            self.other_eval_datasets = {
+                split: dataset[split] for split in other_eval_splits
+            }
+
+    def preprocess(self, tokenizer, config):
+        # get required config variables
+        decoder_start_token_id = config.decoder_start_token_id
+        normalize_text = config.normalize_text
+        max_length = config.max_text_length
+
+        if self.streaming:
+            # we need to shuffle early in streaming mode
+            if hasattr(self, "train_dataset"):
+                self.train_dataset = self.train_dataset.shuffle(
+                    buffer_size=5000, seed=self.seed_dataset
+                )
+        else:
+            self.rng_dataset = jax.random.PRNGKey(self.seed_dataset)
+
+        # filter data
+        partial_filter_function = partial(
+            filter_function,
+            filter_column=self.filter_column,
+            filter_value=self.filter_value,
+            clip_score_column=self.clip_score_column,
+            min_clip_score=self.min_clip_score,
+            max_clip_score=self.max_clip_score,
+        )
+        for ds in ["train_dataset", "eval_dataset"]:
+            if hasattr(self, ds):
+                setattr(
+                    self,
+                    ds,
+                    (
+                        getattr(self, ds).filter(partial_filter_function)
+                        if self.streaming
+                        else getattr(self, ds).filter(
+                            partial_filter_function,
+                            num_proc=self.preprocessing_num_workers,
+                            load_from_cache_file=not self.overwrite_cache,
+                            desc="Filtering datasets",
+                        )
+                    ),
+                )
+        if hasattr(self, "other_eval_datasets"):
+            self.other_eval_datasets = {
+                split: (
+                    ds.filter(partial_filter_function)
+                    if self.streaming
+                    else ds.filter(
+                        partial_filter_function,
+                        num_proc=self.preprocessing_num_workers,
+                        load_from_cache_file=not self.overwrite_cache,
+                        desc="Filtering datasets",
+                    )
+                )
+                for split, ds in self.other_eval_datasets.items()
+            }
+
+        # normalize text
+        if normalize_text:
+            text_normalizer = TextNormalizer()
+            partial_normalize_function = partial(
+                normalize_function,
+                text_column=self.text_column,
+                text_normalizer=text_normalizer,
+            )
+            for ds in ["train_dataset", "eval_dataset"]:
+                if hasattr(self, ds):
+                    setattr(
+                        self,
+                        ds,
+                        (
+                            getattr(self, ds).map(partial_normalize_function)
+                            if self.streaming
+                            else getattr(self, ds).map(
+                                partial_normalize_function,
+                                num_proc=self.preprocessing_num_workers,
+                                load_from_cache_file=not self.overwrite_cache,
+                                desc="Normalizing datasets",
+                            )
+                        ),
+                    )
+            if hasattr(self, "other_eval_datasets"):
+                self.other_eval_datasets = {
+                    split: (
+                        ds.map(partial_normalize_function)
+                        if self.streaming
+                        else ds.map(
+                            partial_normalize_function,
+                            num_proc=self.preprocessing_num_workers,
+                            load_from_cache_file=not self.overwrite_cache,
+                            desc="Normalizing datasets",
+                        )
+                    )
+                    for split, ds in self.other_eval_datasets.items()
+                }
+
+        # blank captions
+        if self.blank_caption_prob:
+            partial_blank_caption_function = partial(
+                blank_caption_function,
+                text_column=self.text_column,
+                blank_caption_prob=self.blank_caption_prob,
+                rng=self.np_rng,
+            )
+            if hasattr(self, "train_dataset"):
+                self.train_dataset = (
+                    self.train_dataset.map(partial_blank_caption_function)
+                    if self.streaming
+                    else self.train_dataset.map(
+                        partial_blank_caption_function,
+                        num_proc=None
+                        if self.seed_dataset
+                        else self.preprocessing_num_workers,
+                        load_from_cache_file=False,
+                        desc="Blanking some captions",
+                    )
+                )
+
+        # preprocess
+        partial_preprocess_function = partial(
+            preprocess_function,
+            tokenizer=tokenizer,
+            text_column=self.text_column,
+            encoding_column=self.encoding_column,
+            max_length=max_length,
+            decoder_start_token_id=decoder_start_token_id,
+        )
+        for ds in ["train_dataset", "eval_dataset"]:
+            if hasattr(self, ds):
+                setattr(
+                    self,
+                    ds,
+                    (
+                        getattr(self, ds).map(
+                            partial_preprocess_function,
+                            batched=True,
+                            remove_columns=[
+                                self.text_column,
+                                self.encoding_column,
+                            ],
+                        )
+                        if self.streaming
+                        else getattr(self, ds).map(
+                            partial_preprocess_function,
+                            batched=True,
+                            remove_columns=getattr(ds, "column_names"),
+                            num_proc=self.preprocessing_num_workers,
+                            load_from_cache_file=not self.overwrite_cache,
+                            desc="Preprocessing datasets",
+                        )
+                    ),
+                )
+        if hasattr(self, "other_eval_datasets"):
+            self.other_eval_datasets = {
+                split: (
+                    ds.map(
+                        partial_preprocess_function,
+                        batched=True,
+                        remove_columns=[
+                            self.text_column,
+                            self.encoding_column,
+                        ],
+                    )
+                    if self.streaming
+                    else ds.map(
+                        partial_preprocess_function,
+                        batched=True,
+                        remove_columns=getattr(ds, "column_names"),
+                        num_proc=self.preprocessing_num_workers,
+                        load_from_cache_file=not self.overwrite_cache,
+                        desc="Preprocessing datasets",
+                    )
+                )
+                for split, ds in self.other_eval_datasets.items()
+            }
+
+    def dataloader(self, split, batch_size, epoch=None):
+        def _dataloader_datasets_non_streaming(
+            dataset: Dataset,
+            rng: jax.random.PRNGKey = None,
+        ):
+            """
+            Returns batches of size `batch_size` from truncated `dataset`, sharded over all local devices.
+            Shuffle batches if rng is set.
+            """
+            steps_per_epoch = len(dataset) // batch_size
+
+            if rng is not None:
+                batch_idx = jax.random.permutation(rng, len(dataset))
+            else:
+                batch_idx = jnp.arange(len(dataset))
+
+            batch_idx = batch_idx[
+                : steps_per_epoch * batch_size
+            ]  # Skip incomplete batch.
+            batch_idx = batch_idx.reshape((steps_per_epoch, batch_size))
+
+            for idx in batch_idx:
+                batch = dataset[idx]
+                batch = {k: jnp.array(v) for k, v in batch.items()}
+                yield batch
+
+        def _dataloader_datasets_streaming(
+            dataset: Dataset,
+            epoch: int,
+        ):
+            keys = ["input_ids", "attention_mask", "labels", "decoder_input_ids"]
+            batch = {k: [] for k in keys}
+            first_loop = True  # stop after one loop in some cases
+            while (self.multi_hosts and split == "train") or first_loop:
+                # in multi-host, we run forever (no epoch) as hosts need to stop
+                # at the same time and training data may not be split equally
+                # For validation data we put the entire batch on each host and then
+                # keep only the one specific to each host (could be improved but not necessary)
+                if epoch is not None:
+                    assert split == "train"
+                    # reshuffle training data at each epoch
+                    dataset.set_epoch(epoch)
+                    epoch += 1
+                for item in dataset:
+                    for k in keys:
+                        batch[k].append(item[k])
+                    if len(batch[keys[0]]) == batch_size:
+                        batch = {k: jnp.array(v) for k, v in batch.items()}
+                        yield batch
+                        batch = {k: [] for k in keys}
+                first_loop = False
+
+        if split == "train":
+            ds = self.train_dataset
+        elif split == "eval":
+            ds = self.eval_dataset
+        else:
+            ds = self.other_eval_datasets[split]
+
+        if self.streaming:
+            return _dataloader_datasets_streaming(ds, epoch)
+        else:
+            if split == "train":
+                self.rng_dataset, input_rng = jax.random.split(self.rng_dataset)
+            return _dataloader_datasets_non_streaming(ds, input_rng)
+
+    @property
+    def length(self):
+        len_train_dataset, len_eval_dataset = None, None
+        if self.streaming:
+            # we don't know the length, let's just assume max_samples if defined
+            if self.max_train_samples is not None:
+                len_train_dataset = self.max_train_samples
+            if self.max_eval_samples is not None:
+                len_eval_dataset = self.max_eval_samples
+        else:
+            len_train_dataset = (
+                len(self.train_dataset) if hasattr(self, "train_dataset") else None
+            )
+            len_eval_dataset = (
+                len(self.eval_dataset) if hasattr(self, "eval_dataset") else None
+            )
+        return len_train_dataset, len_eval_dataset
+
+
+def shift_tokens_right(input_ids: np.array, decoder_start_token_id: int):
+    """
+    Shift input ids one token to the right.
+    """
+    shifted_input_ids = np.zeros(input_ids.shape)
+    shifted_input_ids[:, 1:] = input_ids[:, :-1]
+    shifted_input_ids[:, 0] = decoder_start_token_id
+    return shifted_input_ids
+
+
+def blank_caption_function(example, text_column, blank_caption_prob, rng=None):
+    if (
+        blank_caption_prob
+        and (rng.random() if rng is not None else np.random.random())
+        < blank_caption_prob
+    ):
+        example[text_column] = ""
+    return example
+
+
+def normalize_function(example, text_column, text_normalizer):
+    example[text_column] = text_normalizer(example[text_column])
+    return example
+
+
+def filter_function(
+    example,
+    min_clip_score,
+    max_clip_score,
+    clip_score_column,
+    filter_column,
+    filter_value,
+):
+    if min_clip_score is not None and example[clip_score_column] < min_clip_score:
+        return False
+    if max_clip_score is not None and example[clip_score_column] > max_clip_score:
+        return False
+    if filter_column is not None and example[filter_column] != filter_value:
+        return False
+    return True
+
+
+def preprocess_function(
+    examples,
+    tokenizer,
+    text_column,
+    encoding_column,
+    max_length,
+    decoder_start_token_id,
+):
+    inputs = examples[text_column]
+    # Setting padding="max_length" as we need fixed length inputs for jitted functions
+    model_inputs = tokenizer(
+        inputs,
+        max_length=max_length,
+        padding="max_length",
+        truncation=True,
+        return_tensors="np",
+    )
+
+    # set up targets
+    # Note: labels correspond to our target indices
+    # decoder input ids are the same but shifted to the right with bos at the beginning (and without last token)
+    labels = examples[encoding_column]
+    labels = np.asarray(labels)
+
+    # We need the labels, in addition to the decoder_input_ids, for the compute_loss function
+    model_inputs["labels"] = labels
+
+    # In our case, this prepends the bos token and removes the last one
+    decoder_input_ids = shift_tokens_right(labels, decoder_start_token_id)
+    model_inputs["decoder_input_ids"] = decoder_input_ids
+
+    return model_inputs

src/dalle_mini/model/__init__.py

@@ -0,0 +1,5 @@
+from .configuration import DalleBartConfig
+from .modeling import DalleBart
+from .partitions import set_partitions
+from .processor import DalleBartProcessor
+from .tokenizer import DalleBartTokenizer

src/dalle_mini/model/configuration.py

@@ -0,0 +1,185 @@
+# coding=utf-8
+# Copyright 2021 The Fairseq Authors and The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+""" DalleBart model configuration """
+import warnings
+
+from transformers.configuration_utils import PretrainedConfig
+from transformers.utils import logging
+
+from .utils import PretrainedFromWandbMixin
+
+logger = logging.get_logger(__name__)
+
+
+class DalleBartConfig(PretrainedFromWandbMixin, PretrainedConfig):
+    model_type = "dallebart"
+    keys_to_ignore_at_inference = ["past_key_values"]
+    attribute_map = {
+        "num_attention_heads": "encoder_attention_heads",
+        "hidden_size": "d_model",
+    }
+
+    def __init__(
+        self,
+        normalize_text=False,
+        encoder_vocab_size=50264,
+        image_vocab_size=16384,  # encoded image token space
+        image_length=256,  # number of encoded tokens
+        max_text_length=64,  # max number of text tokens
+        encoder_layers=12,
+        encoder_ffn_dim=4096,
+        encoder_attention_heads=16,
+        decoder_layers=12,
+        decoder_ffn_dim=4096,
+        decoder_attention_heads=16,
+        activation_function="gelu",
+        d_model=1024,
+        dropout=0.1,
+        attention_dropout=0.0,
+        activation_dropout=0.0,
+        init_std=0.02,
+        scale_embedding=False,
+        gradient_checkpointing=True,
+        use_scan=None,
+        use_cache=True,
+        is_encoder_decoder=True,
+        forced_eos_token_id=None,
+        tie_word_embeddings=False,  # different modalities and sizes
+        do_sample=True,
+        # transformer variants
+        use_bias=False,  # use bias in attention and dense layers (except for lm_head)
+        ln_type="layernorm",  # layer normalization type, "rmsnorm", "layernorm"
+        ln_positions="normformer",  # layer normalization positions, "normformer", "swinv2", "cogview", "postln", "preln", "deepnet" (same as postln), "subln"
+        use_head_scale=False,  # used in NormFormer
+        use_cosine_attention=False,  # used in Swin v2
+        tau_init=0.05,  # used only in cosine attention (Swin v2)
+        use_absolute_position_embeddings=True,  # default
+        use_swin_position_embeddings=False,  # used in Swin v1/v2
+        use_deepnet_scaling=False,  # used in Deepnet
+        use_subln_init=False,
+        use_glu=True,  # "GLU Variants Improve Transformer"
+        use_alibi=False,  # Not implemented yet - from "Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation"
+        sinkhorn_iters=1,  # used in SinkFormers
+        use_final_ln_encoder=True,  # final layer normalization in encoder
+        use_final_ln_decoder=True,  # final layer normalization in decoder
+        # parameters that should not be necessary but could affect results
+        force_ln_scale=False,  # force scale in layernorm even when followed by dense layers
+        **kwargs,
+    ):
+        # text normalizer
+        self.normalize_text = normalize_text
+
+        # transformer variants
+        self.use_bias = use_bias
+        assert ln_type in [
+            "rmsnorm",
+            "layernorm",
+        ], "ln_type must be 'rmsnorm' or 'layernorm'"
+        self.ln_type = ln_type
+        if ln_positions == "deepnet":
+            ln_positions = "postln"
+        assert ln_positions in [
+            "normformer",
+            "swinv2",
+            "cogview",
+            "postln",
+            "preln",
+            "subln",
+        ], "ln_positions must be 'normformer', 'swinv2', 'cogview', 'postln', 'preln', 'subln'"
+        self.use_head_scale = use_head_scale
+        assert use_alibi is False, "use_alibi is not supported yet"
+        self.ln_positions = ln_positions
+        self.use_cosine_attention = use_cosine_attention
+        self.tau_init = tau_init
+        self.use_absolute_position_embeddings = use_absolute_position_embeddings
+        self.use_swin_position_embeddings = use_swin_position_embeddings
+        self.use_deepnet_scaling = use_deepnet_scaling
+        self.use_subln_init = use_subln_init
+        self.use_glu = use_glu
+        self.use_alibi = use_alibi
+        self.sinkhorn_iters = sinkhorn_iters
+        if ln_positions == "postln":
+            assert (
+                use_final_ln_encoder
+            ), "use_final_ln_encoder must be True when ln_positions is 'postln'"
+            assert (
+                use_final_ln_decoder
+            ), "use_final_ln_decoder must be True when ln_positions is 'postln'"
+        self.use_final_ln_encoder = use_final_ln_encoder
+        self.use_final_ln_decoder = use_final_ln_decoder
+        self.force_ln_scale = force_ln_scale
+
+        # common parameters
+        self.encoder_vocab_size = encoder_vocab_size
+        self.image_vocab_size = image_vocab_size
+        self.image_length = image_length
+        self.max_text_length = max_text_length
+        self.d_model = d_model
+        self.encoder_ffn_dim = encoder_ffn_dim
+        self.encoder_layers = encoder_layers
+        self.encoder_attention_heads = encoder_attention_heads
+        self.decoder_ffn_dim = decoder_ffn_dim
+        self.decoder_layers = decoder_layers
+        self.decoder_attention_heads = decoder_attention_heads
+        self.dropout = dropout
+        self.attention_dropout = attention_dropout
+        self.activation_dropout = activation_dropout
+        self.activation_function = activation_function
+        self.init_std = init_std
+        self.use_cache = use_cache
+        self.gradient_checkpointing = gradient_checkpointing
+        # all layers are the same in most configurations
+        self.use_scan = use_scan if use_scan is not None else ln_positions != "swinv2"
+        assert not (
+            self.use_scan and ln_positions == "swinv2"
+        ), "scan cannot be used with 'swinv2'"
+        self.scale_embedding = (
+            scale_embedding  # scale factor will be sqrt(d_model) if True
+        )
+
+        # special token id's are appended to vocab if not provided
+        decoder_start_token_id = kwargs.pop("decoder_start_token_id", image_vocab_size)
+        bos_token_id = kwargs.pop("bos_token_id", image_vocab_size)
+        pad_token_id = kwargs.pop("pad_token_id", image_vocab_size)
+        eos_token_id = kwargs.pop("eos_token_id", image_vocab_size)
+
+        # we generate to image_length + 1 (for bos) by default
+        min_length = kwargs.pop("min_length", image_length + 1)
+        max_length = kwargs.pop("max_length", image_length + 1)
+
+        super().__init__(
+            # args required in parent class
+            is_encoder_decoder=is_encoder_decoder,
+            tie_word_embeddings=tie_word_embeddings,
+            forced_eos_token_id=forced_eos_token_id,
+            decoder_start_token_id=decoder_start_token_id,
+            bos_token_id=bos_token_id,
+            pad_token_id=pad_token_id,
+            eos_token_id=eos_token_id,
+            min_length=min_length,
+            max_length=max_length,
+            do_sample=do_sample,
+            **kwargs,
+        )
+
+        # ensure backward compatibility for BART CNN models
+        if self.forced_bos_token_id is None and kwargs.get(
+            "force_bos_token_to_be_generated", False
+        ):
+            self.forced_bos_token_id = self.bos_token_id
+            warnings.warn(
+                f"Please make sure the config includes `forced_bos_token_id={self.bos_token_id}` in future versions."
+                "The config can simply be saved and uploaded again to be fixed."
+            )

src/dalle_mini/model/modeling.py

@@ -0,0 +1,1953 @@
+# coding=utf-8
+# Copyright 2021-2022 The Fairseq Authors and The Google Flax Team Authors And The HuggingFace Inc. team and & DALL·E Mini team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+""" DalleBart model. """
+
+import math
+from functools import partial
+from typing import Any, Dict, Optional, Tuple
+
+import flax
+import flax.linen as nn
+import jax
+import jax.numpy as jnp
+from einops import rearrange
+from flax.core.frozen_dict import unfreeze
+from flax.linen import combine_masks, make_causal_mask
+from flax.linen import partitioning as nn_partitioning
+from flax.linen.linear import PrecisionLike
+from flax.traverse_util import flatten_dict, unflatten_dict
+from jax import custom_jvp, lax
+from jax.random import PRNGKey
+from transformers.modeling_flax_outputs import (
+    FlaxBaseModelOutput,
+    FlaxBaseModelOutputWithPastAndCrossAttentions,
+    FlaxCausalLMOutputWithCrossAttentions,
+    FlaxSeq2SeqLMOutput,
+)
+from transformers.modeling_flax_utils import ACT2FN
+from transformers.models.bart.modeling_flax_bart import (
+    FlaxBartAttention,
+    FlaxBartForConditionalGeneration,
+    FlaxBartForConditionalGenerationModule,
+    FlaxBartModule,
+)
+from transformers.utils import ModelOutput, logging
+
+from .configuration import DalleBartConfig
+from .utils import PretrainedFromWandbMixin
+
+logger = logging.get_logger(__name__)
+
+remat = nn_partitioning.remat
+
+
+def smelu(beta: Any = 1.0):
+    """
+    Implementation of "Real World Large Scale Recommendation Systems Reproducibility and Smooth Activations"
+    https://arxiv.org/abs/2202.06499
+    """
+
+    @custom_jvp
+    @jax.jit
+    def _smelu(x: Any) -> Any:
+        x = jnp.where(x <= -beta, 0.0, x)
+        return jnp.where(x >= beta, x, jnp.square(x + beta) / (4 * beta))
+
+    _smelu.defjvps(
+        lambda g, ans, x: lax.select(
+            x == -beta,
+            lax.full_like(g, 0),
+            lax.select(x == beta, lax.full_like(g, 1), g),
+        )
+    )
+    return _smelu
+
+
+ACT2FN.update({"smelu": smelu()})
+
+
+# deepnet initialization
+def deepnet_init(init_std, gain=1):
+    init = jax.nn.initializers.normal(init_std)
+
+    def _init(*args, **kwargs):
+        return gain * init(*args, **kwargs)
+
+    return _init
+
+
+# deepnet gain
+deepnet_gain = {
+    "encoder": {
+        "alpha": lambda config: 0.81
+        * (config.encoder_layers**4 * config.decoder_layers) ** 0.0625,
+        "beta": lambda config: 0.87
+        * (config.encoder_layers**4 * config.decoder_layers) ** -0.0625,
+    },
+    "decoder": {
+        "alpha": lambda config: (3 * config.decoder_layers) ** 0.25,
+        "beta": lambda config: (12 * config.decoder_layers) ** -0.25,
+    },
+}
+
+# subln gain
+subln_gain = {
+    "encoder": lambda config: math.sqrt(
+        1.0
+        / 3.0
+        * math.log(3 * config.decoder_layers)
+        * math.log(2 * config.encoder_layers)
+    ),
+    "decoder": lambda config: math.sqrt(math.log(3 * config.decoder_layers)),
+}
+
+
+class RMSNorm(nn.Module):
+    """
+    From "Root Mean Square Layer Normalization" by https://arxiv.org/abs/1910.07467
+
+    Adapted from flax.linen.LayerNorm
+    """
+
+    epsilon: float = 1e-6
+    dtype: Any = jnp.float32
+    param_dtype: Any = jnp.float32
+    use_scale: bool = True
+    scale_init: Any = jax.nn.initializers.ones
+
+    @nn.compact
+    def __call__(self, x):
+        reduction_axes = (-1,)
+        feature_axes = (-1,)
+
+        rms_sq = self._compute_rms_sq(x, reduction_axes)
+
+        return self._normalize(
+            self,
+            x,
+            rms_sq,
+            reduction_axes,
+            feature_axes,
+            self.dtype,
+            self.param_dtype,
+            self.epsilon,
+            self.use_scale,
+            self.scale_init,
+        )
+
+    def _compute_rms_sq(self, x, axes):
+        x = jnp.asarray(x, jnp.promote_types(jnp.float32, jnp.result_type(x)))
+        rms_sq = jnp.mean(jax.lax.square(x), axes)
+        return rms_sq
+
+    def _normalize(
+        self,
+        mdl,
+        x,
+        rms_sq,
+        reduction_axes,
+        feature_axes,
+        dtype,
+        param_dtype,
+        epsilon,
+        use_scale,
+        scale_init,
+    ):
+        reduction_axes = nn.normalization._canonicalize_axes(x.ndim, reduction_axes)
+        feature_axes = nn.normalization._canonicalize_axes(x.ndim, feature_axes)
+        stats_shape = list(x.shape)
+        for axis in reduction_axes:
+            stats_shape[axis] = 1
+        rms_sq = rms_sq.reshape(stats_shape)
+        feature_shape = [1] * x.ndim
+        reduced_feature_shape = []
+        for ax in feature_axes:
+            feature_shape[ax] = x.shape[ax]
+            reduced_feature_shape.append(x.shape[ax])
+        mul = lax.rsqrt(rms_sq + epsilon)
+        if use_scale:
+            scale = mdl.param(
+                "scale", scale_init, reduced_feature_shape, param_dtype
+            ).reshape(feature_shape)
+            mul *= scale
+        y = mul * x
+        return jnp.asarray(y, dtype)
+
+
+def norm(type, *args, **kwargs):
+    if type == "rmsnorm":
+        return RMSNorm(*args, **kwargs)
+    elif type == "layernorm":
+        return nn.LayerNorm(*args, **kwargs)
+    else:
+        raise ValueError(f"Unknown norm type {type}")
+
+
+def dot_product_attention_weights(
+    query: Any,
+    key: Any,
+    bias: Optional[Any] = None,
+    mask: Optional[Any] = None,
+    embed_pos: Optional[Any] = None,
+    broadcast_dropout: bool = True,
+    dropout_rng: Optional[PRNGKey] = None,
+    dropout_rate: float = 0.0,
+    deterministic: bool = False,
+    dtype: Any = jnp.float32,
+    precision: PrecisionLike = None,
+    sinkhorn_iters: int = 1,
+    is_encoder: bool = False,
+    tau=None,
+):
+    """
+    Computes dot-product attention weights given query and key.
+    mask is included into the bias.
+
+    Adapted from flax.linen.attention.dot_product_attention_weights"
+    """
+    assert query.ndim == key.ndim, "q, k must have same rank."
+    assert query.shape[:-3] == key.shape[:-3], "q, k batch dims must match."
+    assert query.shape[-2] == key.shape[-2], "q, k num_heads must match."
+    assert query.shape[-1] == key.shape[-1], "q, k depths must match."
+
+    # attn weight shape is (batch..., num_heads, q_length, kv_length)
+    attn_weights = jnp.einsum("...qhd,...khd->...hqk", query, key, precision=precision)
+
+    # divide by tau (used in Swin v2)
+    if tau is not None:
+        attn_weights = attn_weights / tau
+    else:
+        depth = query.shape[-1]
+        attn_weights = attn_weights / jnp.sqrt(depth).astype(dtype)
+
+    # apply attention bias: masking, dropout, proximity bias, etc.
+    if bias is not None:
+        attn_weights = attn_weights + bias
+
+    # add relative position
+    if embed_pos is not None:
+        attn_weights = attn_weights + embed_pos
+
+    # normalize the attention weights
+    if not is_encoder or sinkhorn_iters == 1:
+        # sinkhorn does not work for causal (leaks info of future tokens into past)
+        attn_weights = jax.nn.softmax(attn_weights).astype(dtype)
+    else:
+        # adapted from https://github.com/lucidrains/sinkhorn-transformer
+        for i in range(sinkhorn_iters):
+            # when causal, some attn_weights have been set to -inf through bias
+            if i % 2 == 0:
+                attn_weights -= jax.nn.logsumexp(attn_weights, axis=-1, keepdims=True)
+            else:
+                attn_weights -= jax.nn.logsumexp(attn_weights, axis=-2, keepdims=True)
+            if mask is not None:
+                attn_weights = jnp.where(mask, attn_weights, -jnp.inf)
+        attn_weights = jnp.exp(attn_weights).astype(dtype)
+
+    # apply attention dropout
+    if not deterministic and dropout_rate > 0.0:
+        keep_prob = 1.0 - dropout_rate
+        if broadcast_dropout:
+            # dropout is broadcast across the batch + head dimensions
+            dropout_shape = tuple([1] * (key.ndim - 2)) + attn_weights.shape[-2:]
+            keep = jax.random.bernoulli(dropout_rng, keep_prob, dropout_shape)
+        else:
+            keep = jax.random.bernoulli(dropout_rng, keep_prob, attn_weights.shape)
+        multiplier = keep.astype(attn_weights.dtype) / jnp.asarray(
+            keep_prob, dtype=dtype
+        )
+        attn_weights = attn_weights * multiplier
+
+    return attn_weights
+
+
+class FlaxBartAttention(FlaxBartAttention):
+    """
+    Edits:
+    - causal mask is used only in decoder and considers image_length
+    - scale attention heads per NormFormer paper
+    """
+
+    is_encoder: bool = False
+    is_cross_attention: bool = False
+    q_length: int = None
+    k_length: int = None
+
+    def setup(self) -> None:
+        self.head_dim = self.embed_dim // self.num_heads
+        if self.head_dim * self.num_heads != self.embed_dim:
+            raise ValueError(
+                f"embed_dim must be divisible by num_heads (got `embed_dim`: {self.embed_dim}"
+                f" and `num_heads`: {self.num_heads})."
+            )
+
+        dense = partial(
+            nn.Dense,
+            self.embed_dim,
+            use_bias=self.bias,
+            dtype=self.dtype,
+        )
+
+        if self.config.use_deepnet_scaling:
+            gain = deepnet_gain["encoder" if self.is_encoder else "decoder"]["beta"](
+                self.config
+            )
+        elif self.config.use_subln_init and not self.is_cross_attention:
+            gain = subln_gain["encoder" if self.is_encoder else "decoder"](self.config)
+
+        self.q_proj = dense(
+            kernel_init=jax.nn.initializers.normal(self.config.init_std)
+        )
+        self.k_proj = dense(
+            kernel_init=jax.nn.initializers.normal(self.config.init_std)
+        )
+        self.v_proj = dense(
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (
+                self.config.use_deepnet_scaling
+                or (self.config.use_subln_init and not self.is_cross_attention)
+            )
+            else jax.nn.initializers.normal(self.config.init_std)
+        )
+        self.out_proj = dense(
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (
+                self.config.use_deepnet_scaling
+                or (self.config.use_subln_init and not self.is_cross_attention)
+            )
+            else jax.nn.initializers.normal(self.config.init_std)
+        )
+        self.dropout_layer = nn.Dropout(rate=self.dropout)
+
+        if self.config.use_head_scale:
+            self.head_scale = self.param(
+                "head_scale", jax.nn.initializers.ones, (1, 1, self.num_heads, 1)
+            )
+
+        if self.config.use_cosine_attention:
+            # TODO: try using a learnt scale, somehow it immediately diverges in my experiments
+            self.tau = self.config.tau_init
+
+        if self.config.use_swin_position_embeddings:
+            self.rel_bias = nn.Embed(
+                self.q_length,
+                self.k_length * self.num_heads,
+                embedding_init=jax.nn.initializers.normal(self.config.init_std),
+            )
+
+        if self.causal:
+            # used only in decoder
+            self.causal_mask = make_causal_mask(
+                jnp.ones((1, self.config.image_length), dtype="bool"), dtype="bool"
+            )
+
+        if self.config.ln_positions in ["subln"] and not self.is_cross_attention:
+            self.mid_layernorm = norm(
+                self.config.ln_type, dtype=self.dtype, epsilon=1e-05
+            )
+
+    def __call__(
+        self,
+        hidden_states: jnp.ndarray,
+        key_value_states: Optional[jnp.ndarray] = None,
+        attention_mask: Optional[jnp.ndarray] = None,
+        init_cache: bool = False,
+        deterministic: bool = True,
+    ) -> Tuple[jnp.ndarray]:
+        """Input shape: Batch x Time x Channel"""
+
+        # if key_value_states are provided this layer is used as a cross-attention layer
+        # for the decoder
+        is_cross_attention = key_value_states is not None
+        batch_size = hidden_states.shape[0]
+
+        # get query proj
+        query_states = self.q_proj(hidden_states)
+        # get key, value proj
+        if is_cross_attention:
+            # cross_attentions
+            key_states = self.k_proj(key_value_states)
+            value_states = self.v_proj(key_value_states)
+        else:
+            # self_attention
+            key_states = self.k_proj(hidden_states)
+            value_states = self.v_proj(hidden_states)
+
+        query_states = self._split_heads(query_states)
+        key_states = self._split_heads(key_states)
+        value_states = self._split_heads(value_states)
+
+        # handle cache prepare causal attention mask
+        if self.causal:
+            query_length, key_length = query_states.shape[1], key_states.shape[1]
+            if self.has_variable("cache", "cached_key"):
+                mask_shift = self.variables["cache"]["cache_index"]
+                max_decoder_length = self.variables["cache"]["cached_key"].shape[1]
+                causal_mask = lax.dynamic_slice(
+                    self.causal_mask,
+                    (0, 0, mask_shift, 0),
+                    (1, 1, query_length, max_decoder_length),
+                )
+            else:
+                causal_mask = self.causal_mask[:, :, :query_length, :key_length]
+            causal_mask = jnp.broadcast_to(
+                causal_mask, (batch_size,) + causal_mask.shape[1:]
+            )
+
+        # combine masks if needed
+        if attention_mask is not None and self.causal:
+            attention_mask = jnp.broadcast_to(
+                jnp.expand_dims(attention_mask, axis=(-3, -2)), causal_mask.shape
+            )
+            attention_mask = combine_masks(attention_mask, causal_mask)
+        elif self.causal:
+            attention_mask = causal_mask
+        elif attention_mask is not None:
+            attention_mask = jnp.expand_dims(attention_mask, axis=(-3, -2))
+
+        # During fast autoregressive decoding, we feed one position at a time,
+        # and cache the keys and values step by step.
+        if self.causal and (self.has_variable("cache", "cached_key") or init_cache):
+            key_states, value_states, attention_mask = self._concatenate_to_cache(
+                key_states, value_states, query_states, attention_mask
+            )
+
+        # Convert the boolean attention mask to an attention bias.
+        if attention_mask is not None:
+            # attention mask in the form of attention bias
+            attention_bias = lax.select(
+                attention_mask > 0,
+                jnp.full(attention_mask.shape, 0.0).astype(self.dtype),
+                jnp.full(attention_mask.shape, -jnp.inf).astype(self.dtype),
+            )
+        else:
+            attention_bias = None
+
+        dropout_rng = None
+        if not deterministic and self.dropout > 0.0:
+            dropout_rng = self.make_rng("dropout")
+
+        if self.config.use_cosine_attention:
+            # normalize q and k
+            query_states = query_states / (
+                jnp.linalg.norm(query_states, axis=-1, keepdims=True) + 1e-8
+            )
+            key_states = key_states / (
+                jnp.linalg.norm(key_states, axis=-1, keepdims=True) + 1e-8
+            )
+
+        # relative position embeddings
+        if self.config.use_swin_position_embeddings:
+            position_ids = jnp.arange(self.q_length)
+            embed_pos = self.rel_bias(position_ids)
+            embed_pos = rearrange(embed_pos, "q (k h) -> 1 h q k", h=self.num_heads)
+        else:
+            embed_pos = None
+
+        tau = self.tau if self.config.use_cosine_attention else None
+        attn_weights = dot_product_attention_weights(
+            query_states,
+            key_states,
+            bias=attention_bias,
+            mask=attention_mask,
+            embed_pos=embed_pos,
+            dropout_rng=dropout_rng,
+            dropout_rate=self.dropout,
+            broadcast_dropout=True,
+            deterministic=deterministic,
+            dtype=self.dtype,
+            precision=None,
+            sinkhorn_iters=self.config.sinkhorn_iters,
+            is_encoder=self.is_encoder,
+            tau=tau,
+        )
+
+        attn_output = jnp.einsum("...hqk,...khd->...qhd", attn_weights, value_states)
+        if self.config.use_head_scale:
+            # per Normformer
+            attn_output = attn_output * self.head_scale
+        attn_output = self._merge_heads(attn_output)
+
+        if self.config.ln_positions in ["subln"] and not self.is_cross_attention:
+            attn_output = self.mid_layernorm(attn_output)
+
+        attn_output = self.out_proj(attn_output)
+
+        return attn_output, attn_weights
+
+
+class GLU(nn.Module):
+    """From "GLU Variants Improve Transformer" by https://arxiv.org/abs/2002.05202"""
+
+    config: DalleBartConfig
+    ffn_dim: int
+    embed_dim: int
+    dtype: jnp.dtype = jnp.float32
+    is_encoder: bool = False
+
+    @nn.compact
+    def __call__(self, x: jnp.ndarray, deterministic: bool = True) -> jnp.ndarray:
+        if self.config.use_deepnet_scaling:
+            gain = deepnet_gain["encoder" if self.is_encoder else "decoder"]["beta"](
+                self.config
+            )
+        elif self.config.use_subln_init:
+            gain = subln_gain["encoder" if self.is_encoder else "decoder"](self.config)
+
+        if self.config.ln_positions in ["normformer", "cogview", "preln", "subln"]:
+            x = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )(x)
+        w = nn.Dense(
+            self.ffn_dim,
+            dtype=self.dtype,
+            use_bias=self.config.use_bias,
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (self.config.use_deepnet_scaling or self.config.use_subln_init)
+            else jax.nn.initializers.normal(self.config.init_std),
+        )(x)
+        w = ACT2FN[self.config.activation_function](w)
+        v = nn.Dense(
+            self.ffn_dim,
+            dtype=self.dtype,
+            use_bias=self.config.use_bias,
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (self.config.use_deepnet_scaling or self.config.use_subln_init)
+            else jax.nn.initializers.normal(self.config.init_std),
+        )(x)
+        x = w * v
+        if self.config.ln_positions in ["normformer", "subln"]:
+            x = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )(x)
+        x = nn.Dropout(rate=self.config.activation_dropout)(
+            x, deterministic=deterministic
+        )
+
+        x = nn.Dense(
+            self.embed_dim,
+            dtype=self.dtype,
+            use_bias=self.config.use_bias,
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (self.config.use_deepnet_scaling or self.config.use_subln_init)
+            else jax.nn.initializers.normal(self.config.init_std),
+        )(x)
+        if self.config.ln_positions in ["swinv2", "cogview"]:
+            x = norm(self.config.ln_type, dtype=self.dtype, epsilon=1e-05)(x)
+        x = nn.Dropout(rate=self.config.dropout)(x, deterministic=deterministic)
+        return x
+
+
+class FFN(nn.Module):
+    """Simple FFN layer"""
+
+    config: DalleBartConfig
+    ffn_dim: int
+    embed_dim: int
+    dtype: jnp.dtype = jnp.float32
+    is_encoder: bool = False
+
+    @nn.compact
+    def __call__(self, x: jnp.ndarray, deterministic: bool = True) -> jnp.ndarray:
+        if self.config.use_deepnet_scaling:
+            gain = deepnet_gain["encoder" if self.is_encoder else "decoder"]["beta"](
+                self.config
+            )
+        elif self.config.use_subln_init:
+            gain = subln_gain["encoder" if self.is_encoder else "decoder"](self.config)
+        if self.config.ln_positions in ["normformer", "cogview", "preln", "subln"]:
+            x = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )(x)
+        x = nn.Dense(
+            self.ffn_dim,
+            dtype=self.dtype,
+            use_bias=self.config.use_bias,
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (self.config.use_deepnet_scaling or self.config.use_subln_init)
+            else jax.nn.initializers.normal(self.config.init_std),
+        )(x)
+        x = ACT2FN[self.config.activation_function](x)
+        if self.config.ln_positions in ["normformer", "subln"]:
+            x = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )(x)
+        x = nn.Dropout(rate=self.config.activation_dropout)(
+            x, deterministic=deterministic
+        )
+        x = nn.Dense(
+            self.embed_dim,
+            dtype=self.dtype,
+            use_bias=self.config.use_bias,
+            kernel_init=deepnet_init(self.config.init_std, gain)
+            if (self.config.use_deepnet_scaling or self.config.use_subln_init)
+            else jax.nn.initializers.normal(self.config.init_std),
+        )(x)
+        if self.config.ln_positions in ["swinv2", "cogview"]:
+            x = norm(self.config.ln_type, dtype=self.dtype, epsilon=1e-05)(x)
+        x = nn.Dropout(rate=self.config.dropout)(x, deterministic=deterministic)
+        return x
+
+
+class FlaxBartEncoderLayer(nn.Module):
+    """
+    Edits:
+    - no bias
+    - use custom FlaxBartAttention
+    """
+
+    config: DalleBartConfig
+    dtype: jnp.dtype = jnp.float32
+    add_norm: bool = False
+    use_scale: bool = True
+
+    @nn.compact
+    def __call__(
+        self,
+        hidden_states: jnp.ndarray,
+        attention_mask: jnp.ndarray,
+        output_attentions: bool = True,
+        deterministic: bool = True,
+    ) -> Tuple[jnp.ndarray]:
+        if self.config.use_scan:
+            hidden_states = hidden_states[0]
+
+        res_gain = (
+            deepnet_gain["encoder"]["alpha"](self.config)
+            if self.config.use_deepnet_scaling
+            else 1
+        )
+
+        embed_dim = self.config.d_model
+        residual = hidden_states
+        if self.config.ln_positions in ["normformer", "cogview", "preln", "subln"]:
+            hidden_states = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )(hidden_states)
+        hidden_states, attn_weights = FlaxBartAttention(
+            config=self.config,
+            embed_dim=embed_dim,
+            num_heads=self.config.encoder_attention_heads,
+            dropout=self.config.attention_dropout,
+            bias=self.config.use_bias,
+            dtype=self.dtype,
+            is_encoder=True,
+            is_cross_attention=False,
+            q_length=self.config.max_text_length,
+            k_length=self.config.max_text_length,
+        )(hidden_states=hidden_states, attention_mask=attention_mask)
+
+        if self.config.ln_positions in ["normformer", "swinv2", "cogview"]:
+            hidden_states = norm(self.config.ln_type, dtype=self.dtype, epsilon=1e-05)(
+                hidden_states
+            )
+        hidden_states = nn.Dropout(rate=self.config.dropout)(
+            hidden_states, deterministic=deterministic
+        )
+        hidden_states = residual * res_gain + hidden_states
+        if self.config.ln_positions in ["postln"]:
+            hidden_states = norm(self.config.ln_type, dtype=self.dtype, epsilon=1e-05)(
+                hidden_states
+            )
+
+        residual = hidden_states
+        ff_block = (
+            GLU(
+                config=self.config,
+                ffn_dim=self.config.encoder_ffn_dim,
+                embed_dim=embed_dim,
+                dtype=self.dtype,
+                is_encoder=True,
+            )
+            if self.config.use_glu
+            else FFN(
+                config=self.config,
+                ffn_dim=self.config.encoder_ffn_dim,
+                embed_dim=embed_dim,
+                dtype=self.dtype,
+                is_encoder=True,
+            )
+        )
+        hidden_states = ff_block(hidden_states, deterministic=deterministic)
+        hidden_states = residual * res_gain + hidden_states
+        if self.add_norm:
+            use_scale = self.use_scale or self.config.force_ln_scale
+            hidden_states = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=use_scale,
+            )(hidden_states)
+
+        outputs = (hidden_states,)
+
+        if output_attentions:
+            outputs += (attn_weights,)
+
+        if self.config.use_scan:
+            outputs = (outputs, None)
+
+        return outputs
+
+
+class FlaxBartDecoderLayer(nn.Module):
+    """
+    Edits:
+    - no bias
+    - use custom FlaxBartAttention
+    """
+
+    config: DalleBartConfig
+    dtype: jnp.dtype = jnp.float32
+    add_norm: bool = False
+    use_scale: bool = True
+
+    @nn.compact
+    def __call__(
+        self,
+        hidden_states: jnp.ndarray,
+        attention_mask: jnp.ndarray,
+        encoder_hidden_states: Optional[jnp.ndarray] = None,
+        encoder_attention_mask: Optional[jnp.ndarray] = None,
+        init_cache: bool = False,
+        output_attentions: bool = True,
+        deterministic: bool = True,
+    ) -> Tuple[jnp.ndarray]:
+        if self.config.use_scan:
+            hidden_states = hidden_states[0]
+
+        res_gain = (
+            deepnet_gain["decoder"]["alpha"](self.config)
+            if self.config.use_deepnet_scaling
+            else 1
+        )
+
+        embed_dim = self.config.d_model
+        residual = hidden_states
+
+        # Self Attention
+        if self.config.ln_positions in ["normformer", "cogview", "preln"]:
+            hidden_states = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )(hidden_states)
+        hidden_states, attn_weights = FlaxBartAttention(
+            config=self.config,
+            embed_dim=embed_dim,
+            num_heads=self.config.decoder_attention_heads,
+            dropout=self.config.attention_dropout,
+            causal=True,
+            bias=self.config.use_bias,
+            dtype=self.dtype,
+            is_encoder=False,
+            is_cross_attention=False,
+            q_length=self.config.image_length,
+            k_length=self.config.image_length,
+        )(
+            hidden_states=hidden_states,
+            attention_mask=attention_mask,
+            init_cache=init_cache,
+        )
+
+        if self.config.ln_positions in ["normformer", "swinv2", "cogview"]:
+            hidden_states = norm(self.config.ln_type, dtype=self.dtype, epsilon=1e-05)(
+                hidden_states
+            )
+        hidden_states = nn.Dropout(rate=self.config.dropout)(
+            hidden_states, deterministic=deterministic
+        )
+        hidden_states = residual * res_gain + hidden_states
+        if self.config.ln_positions in ["postln"]:
+            hidden_states = norm(self.config.ln_type, dtype=self.dtype, epsilon=1e-05)(
+                hidden_states
+            )
+
+        # Cross Attention
+        cross_attn_weights = None
+        if encoder_hidden_states is not None:
+            residual = hidden_states
+            if self.config.ln_positions in ["normformer", "cogview", "preln"]:
+                hidden_states = norm(
+                    self.config.ln_type,
+                    dtype=self.dtype,
+                    epsilon=1e-05,
+                    use_scale=self.config.force_ln_scale,
+                )(hidden_states)
+            hidden_states, cross_attn_weights = FlaxBartAttention(
+                config=self.config,
+                embed_dim=embed_dim,
+                num_heads=self.config.decoder_attention_heads,
+                dropout=self.config.attention_dropout,
+                bias=self.config.use_bias,
+                dtype=self.dtype,
+                is_encoder=False,
+                is_cross_attention=True,
+                q_length=self.config.image_length,
+                k_length=self.config.max_text_length,
+            )(
+                hidden_states=hidden_states,
+                key_value_states=encoder_hidden_states,
+                attention_mask=encoder_attention_mask,
+            )
+            if self.config.ln_positions in ["normformer", "swinv2", "cogview"]:
+                hidden_states = norm(
+                    self.config.ln_type, dtype=self.dtype, epsilon=1e-05
+                )(hidden_states)
+            hidden_states = nn.Dropout(rate=self.config.dropout)(
+                hidden_states, deterministic=deterministic
+            )
+            hidden_states = residual * res_gain + hidden_states
+            if self.config.ln_positions in ["postln"]:
+                hidden_states = norm(
+                    self.config.ln_type, dtype=self.dtype, epsilon=1e-05
+                )(hidden_states)
+
+        # Feed forward
+        residual = hidden_states
+        ff_block = (
+            GLU(
+                config=self.config,
+                ffn_dim=self.config.decoder_ffn_dim,
+                embed_dim=embed_dim,
+                dtype=self.dtype,
+                is_encoder=False,
+            )
+            if self.config.use_glu
+            else FFN(
+                config=self.config,
+                ffn_dim=self.config.decoder_ffn_dim,
+                embed_dim=embed_dim,
+                dtype=self.dtype,
+                is_encoder=False,
+            )
+        )
+        hidden_states = ff_block(hidden_states, deterministic=deterministic)
+        hidden_states = residual * res_gain + hidden_states
+        if self.add_norm:
+            use_scale = self.use_scale or self.config.force_ln_scale
+            hidden_states = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=use_scale,
+            )(hidden_states)
+
+        outputs = (hidden_states,)
+
+        if output_attentions:
+            outputs += (attn_weights, cross_attn_weights)
+
+        if self.config.use_scan:
+            outputs = (outputs, None)
+
+        return outputs
+
+
+class FlaxBartEncoderLayerCollection(nn.Module):
+    config: DalleBartConfig
+    dtype: jnp.dtype = jnp.float32  # the dtype of the computation
+    """
+    Edits:
+    - use custom FlaxBartEncoderLayer
+    - allow Gradient Checkpointing (nn.remat)
+    """
+
+    @nn.compact
+    def __call__(
+        self,
+        hidden_states,
+        attention_mask,
+        deterministic: bool = True,
+        output_attentions: bool = False,
+        output_hidden_states: bool = False,
+        return_dict: bool = True,
+    ):
+        all_hidden_states = () if output_hidden_states else None
+        all_self_attns = () if output_attentions else None
+
+        n_layers = self.config.encoder_layers
+        layer = (
+            remat(
+                FlaxBartEncoderLayer,
+                static_argnums=(2, 3),
+                prevent_cse=not self.config.use_scan,
+            )
+            if self.config.gradient_checkpointing
+            else FlaxBartEncoderLayer
+        )
+
+        if self.config.use_scan:
+            # all blocks are the same so we use nn.scan
+            assert not output_attentions, "cannot scan with output_attentions"
+            assert not output_hidden_states, "cannot scan with output_hidden_states"
+            hidden_states = (hidden_states,)
+            # we use a scale on all norms (even last layer) to allow scanning
+            hidden_states, _ = nn.scan(
+                layer,
+                variable_axes={"params": 0, "cache": 0},
+                split_rngs={"params": True, "dropout": True},
+                in_axes=(nn.broadcast, nn.broadcast, nn.broadcast),
+                length=n_layers,
+            )(
+                self.config,
+                dtype=self.dtype,
+                add_norm=self.config.ln_positions == "postln",
+                name="FlaxBartEncoderLayers",
+            )(
+                hidden_states,
+                attention_mask,
+                output_attentions,
+                deterministic,
+            )
+            hidden_states = hidden_states[0]
+        else:
+            for i in range(n_layers):
+                if output_hidden_states:
+                    all_hidden_states += (hidden_states,)
+                # final layernorm on the output of the last layer
+                # or every 6 layers for Swin v2
+                add_norm = self.config.ln_positions == "postln" or (
+                    self.config.ln_positions == "swinv2"
+                    and ((i + 1) % 6 == 0)
+                    and (i != n_layers - 1)
+                )
+                # we don't need to scale the norm for the last layer
+                use_scale = i != n_layers - 1
+                layer_outputs = layer(
+                    self.config,
+                    dtype=self.dtype,
+                    add_norm=add_norm,
+                    use_scale=use_scale,
+                    name=f"FlaxBartEncoderLayer_{i}",
+                )(
+                    hidden_states,
+                    attention_mask,
+                    output_attentions,
+                    deterministic,
+                )
+                hidden_states = layer_outputs[0]
+                if output_attentions:
+                    all_self_attns += (layer_outputs[1],)
+
+            # add hidden states from the last layer
+            if output_hidden_states:
+                all_hidden_states += (hidden_states,)
+
+        outputs = [
+            hidden_states,
+            all_hidden_states,
+            all_self_attns,
+        ]
+
+        if not return_dict:
+            return tuple(v for v in outputs if v is not None)
+
+        return FlaxBaseModelOutput(
+            last_hidden_state=hidden_states,
+            hidden_states=all_hidden_states,
+            attentions=all_self_attns,
+        )
+
+
+class FlaxBartDecoderLayerCollection(nn.Module):
+    config: DalleBartConfig
+    dtype: jnp.dtype = jnp.float32  # the dtype of the computation
+    """
+    Edits:
+    - use custom FlaxBartDecoderLayer
+    - allow Gradient Checkpointing (nn.remat)
+    """
+
+    @nn.compact
+    def __call__(
+        self,
+        hidden_states,
+        attention_mask,
+        encoder_hidden_states: Optional[jnp.ndarray] = None,
+        encoder_attention_mask: Optional[jnp.ndarray] = None,
+        deterministic: bool = True,
+        init_cache: bool = False,
+        output_attentions: bool = False,
+        output_hidden_states: bool = False,
+        return_dict: bool = True,
+    ):
+        # decoder layers
+        all_hidden_states = () if output_hidden_states else None
+        all_self_attns = () if output_attentions else None
+        all_cross_attentions = (
+            () if (output_attentions and encoder_hidden_states is not None) else None
+        )
+
+        n_layers = self.config.decoder_layers
+        layer = (
+            remat(
+                FlaxBartDecoderLayer,
+                static_argnums=(4, 5, 6),
+                prevent_cse=not self.config.use_scan,
+            )
+            if self.config.gradient_checkpointing
+            else FlaxBartDecoderLayer
+        )
+
+        if self.config.use_scan:
+            # all blocks are the same so we use nn.scan
+            assert not output_attentions, "cannot scan with output_attentions"
+            assert not output_hidden_states, "cannot scan with output_hidden_states"
+            hidden_states = (hidden_states,)
+            # we use a scale on all norms (even last layer) to allow scanning
+            hidden_states, _ = nn.scan(
+                layer,
+                variable_axes={"params": 0, "cache": 0},
+                split_rngs={"params": True, "dropout": True},
+                in_axes=(
+                    nn.broadcast,
+                    nn.broadcast,
+                    nn.broadcast,
+                    nn.broadcast,
+                    nn.broadcast,
+                    nn.broadcast,
+                ),
+                length=n_layers,
+            )(
+                self.config,
+                dtype=self.dtype,
+                add_norm=self.config.ln_positions == "postln",
+                name="FlaxBartDecoderLayers",
+            )(
+                hidden_states,
+                attention_mask,
+                encoder_hidden_states,
+                encoder_attention_mask,
+                init_cache,
+                output_attentions,
+                deterministic,
+            )
+            hidden_states = hidden_states[0]
+
+        else:
+            for i in range(n_layers):
+                if output_hidden_states:
+                    all_hidden_states += (hidden_states,)
+                # final layernorm on the output of the last layer
+                # or every 6 layers for Swin v2
+                add_norm = self.config.ln_positions == "postln" or (
+                    self.config.ln_positions == "swinv2"
+                    and ((i + 1) % 6 == 0)
+                    and (i != n_layers - 1)
+                )
+                # we don't need to scale the norm for the last layer
+                use_scale = i != n_layers - 1
+                layer_outputs = layer(
+                    self.config,
+                    dtype=self.dtype,
+                    add_norm=add_norm,
+                    use_scale=use_scale,
+                    name=f"FlaxBartDecoderLayer_{i}",
+                )(
+                    hidden_states,
+                    attention_mask,
+                    encoder_hidden_states,
+                    encoder_attention_mask,
+                    init_cache,
+                    output_attentions,
+                    deterministic,
+                )
+
+                hidden_states = layer_outputs[0]
+                if output_attentions:
+                    all_self_attns += (layer_outputs[1],)
+
+                    if encoder_hidden_states is not None:
+                        all_cross_attentions += (layer_outputs[2],)
+
+            # add hidden states from the last decoder layer
+            if output_hidden_states:
+                all_hidden_states += (hidden_states,)
+
+        outputs = [
+            hidden_states,
+            all_hidden_states,
+            all_self_attns,
+            all_cross_attentions,
+        ]
+
+        if not return_dict:
+            return tuple(v for v in outputs if v is not None)
+
+        return FlaxBaseModelOutputWithPastAndCrossAttentions(
+            last_hidden_state=hidden_states,
+            hidden_states=all_hidden_states,
+            attentions=all_self_attns,
+            cross_attentions=all_cross_attentions,
+        )
+
+
+class FlaxBartEncoder(nn.Module):
+    config: DalleBartConfig
+    embed_tokens: nn.Embed
+    dtype: jnp.dtype = jnp.float32  # the dtype of the computation
+    """
+    Edits:
+    - offset set to 0 (no padding token)
+    - use max_text_length instead of max_position_embeddings
+    - use custom FlaxBartEncoderLayerCollection
+    - embed_tokens cannot be None (issue at compile time)
+    """
+
+    def setup(self):
+        self.dropout_layer = nn.Dropout(rate=self.config.dropout)
+
+        embed_dim = self.config.d_model
+        self.padding_idx = self.config.pad_token_id
+        self.embed_scale = math.sqrt(embed_dim) if self.config.scale_embedding else 1.0
+
+        # Bart is set up so that if padding_idx is specified then offset the embedding ids by 2
+        # and adjust num_embeddings appropriately. Other models don't have this hack
+        self.offset = 0
+        if self.config.use_absolute_position_embeddings:
+            self.embed_positions = nn.Embed(
+                self.config.max_text_length + self.offset,  # image length for BOS
+                embed_dim,
+                embedding_init=jax.nn.initializers.normal(self.config.init_std),
+            )
+        self.layers = FlaxBartEncoderLayerCollection(self.config, self.dtype)
+        self.layernorm_embedding = norm(
+            self.config.ln_type, dtype=self.dtype, epsilon=1e-05
+        )
+
+        # postln is already applied in every layer
+        if self.config.use_final_ln_encoder and self.config.ln_positions != "postln":
+            self.final_ln = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )
+        else:
+            self.final_ln = None
+
+    def __call__(
+        self,
+        input_ids,
+        attention_mask,
+        position_ids,
+        output_attentions: bool = False,
+        output_hidden_states: bool = False,
+        return_dict: bool = True,
+        deterministic: bool = True,
+    ):
+        input_shape = input_ids.shape
+        input_ids = input_ids.reshape(-1, input_shape[-1])
+
+        hidden_states = self.embed_tokens(input_ids) * self.embed_scale
+
+        if self.config.use_absolute_position_embeddings:
+            embed_pos = self.embed_positions(position_ids + self.offset)
+            hidden_states = hidden_states + embed_pos
+
+        hidden_states = self.layernorm_embedding(hidden_states)
+        hidden_states = self.dropout_layer(hidden_states, deterministic=deterministic)
+
+        outputs = self.layers(
+            hidden_states,
+            attention_mask,
+            deterministic=deterministic,
+            output_attentions=output_attentions,
+            output_hidden_states=output_hidden_states,
+            return_dict=return_dict,
+        )
+
+        if self.final_ln is None:
+            final_output = outputs[0]
+        else:
+            final_output = self.final_ln(outputs[0])
+
+        if not return_dict:
+            return (final_output,) + outputs[1:]
+
+        return FlaxBaseModelOutput(
+            last_hidden_state=final_output,
+            hidden_states=outputs.hidden_states,
+            attentions=outputs.attentions,
+        )
+
+
+class FlaxBartDecoder(nn.Module):
+    config: DalleBartConfig
+    embed_tokens: nn.Embed
+    dtype: jnp.dtype = jnp.float32  # the dtype of the computation
+    """
+    Edits:
+    - offset set to 0 (no padding token)
+    - use image_length instead of max_position_embeddings
+    - use custom FlaxBartDecoderLayerCollection
+    - embed_tokens cannot be None (issue at compile time)
+    """
+
+    def setup(self):
+        self.dropout_layer = nn.Dropout(rate=self.config.dropout)
+
+        embed_dim = self.config.d_model
+        self.padding_idx = self.config.pad_token_id
+        self.embed_scale = (
+            math.sqrt(self.config.d_model) if self.config.scale_embedding else 1.0
+        )
+
+        # Bart is set up so that if padding_idx is specified then offset the embedding ids by 2
+        # and adjust num_embeddings appropriately. Other models don't have this hack
+        self.offset = 0
+        if self.config.use_absolute_position_embeddings:
+            self.embed_positions = nn.Embed(
+                self.config.image_length + self.offset,  # image length for BOS
+                embed_dim,
+                embedding_init=jax.nn.initializers.normal(self.config.init_std),
+            )
+
+        self.layers = FlaxBartDecoderLayerCollection(self.config, self.dtype)
+        self.layernorm_embedding = norm(
+            self.config.ln_type, dtype=self.dtype, epsilon=1e-05
+        )
+
+        # postln is already applied in every layer
+        if self.config.use_final_ln_decoder and self.config.ln_positions != "postln":
+            self.final_ln = norm(
+                self.config.ln_type,
+                dtype=self.dtype,
+                epsilon=1e-05,
+                use_scale=self.config.force_ln_scale,
+            )
+
+    def __call__(
+        self,
+        input_ids,
+        attention_mask,
+        position_ids,
+        encoder_hidden_states: Optional[jnp.ndarray] = None,
+        encoder_attention_mask: Optional[jnp.ndarray] = None,
+        init_cache: bool = False,
+        output_attentions: bool = False,
+        output_hidden_states: bool = False,
+        return_dict: bool = True,
+        deterministic: bool = True,
+    ):
+        input_shape = input_ids.shape
+        input_ids = input_ids.reshape(-1, input_shape[-1])
+
+        hidden_states = self.embed_tokens(input_ids) * self.embed_scale
+
+        if self.config.use_absolute_position_embeddings:
+            embed_pos = self.embed_positions(position_ids + self.offset)
+            hidden_states = hidden_states + embed_pos
+
+        hidden_states = self.layernorm_embedding(hidden_states)
+        hidden_states = self.dropout_layer(hidden_states, deterministic=deterministic)
+
+        outputs = self.layers(
+            hidden_states,
+            attention_mask,
+            encoder_hidden_states,
+            encoder_attention_mask,
+            deterministic=deterministic,
+            init_cache=init_cache,
+            output_attentions=output_attentions,
+            output_hidden_states=output_hidden_states,
+            return_dict=return_dict,
+        )
+
+        if self.final_ln is None:
+            final_output = outputs[0]
+        else:
+            final_output = self.final_ln(outputs[0])
+
+        if not return_dict:
+            return (final_output,) + outputs[1:]
+
+        return FlaxBaseModelOutputWithPastAndCrossAttentions(
+            last_hidden_state=final_output,
+            hidden_states=outputs.hidden_states,
+            attentions=outputs.attentions,
+            cross_attentions=outputs.cross_attentions,
+        )
+
+
+class FlaxBartModule(FlaxBartModule):
+    """
+    Edits
+    - use custom FlaxBartEncoder & FlaxBartDecoder
+    - use separate embeddings for Encoder & Decoder
+    """
+
+    def setup(self):
+        encoder_embed_tokens = nn.Embed(
+            self.config.encoder_vocab_size,
+            self.config.d_model,
+            embedding_init=jax.nn.initializers.normal(self.config.init_std),
+        )
+        decoder_embed_tokens = nn.Embed(
+            self.config.image_vocab_size + 1,  # image vocab size + 1 for BOS
+            self.config.d_model,
+            embedding_init=jax.nn.initializers.normal(self.config.init_std),
+        )
+
+        self.encoder = FlaxBartEncoder(
+            self.config, dtype=self.dtype, embed_tokens=encoder_embed_tokens
+        )
+        self.decoder = FlaxBartDecoder(
+            self.config, dtype=self.dtype, embed_tokens=decoder_embed_tokens
+        )
+
+
+class FlaxBartForConditionalGenerationModule(FlaxBartForConditionalGenerationModule):
+    """
+    Edits:
+    - no bias
+    - lm_head set to image_vocab_size + 1 (for BOS)
+    - uses custom FlaxBartModule
+    """
+
+    def setup(self):
+        self.model = FlaxBartModule(config=self.config, dtype=self.dtype)
+        self.lm_head = nn.Dense(
+            self.config.image_vocab_size
+            + 1,  # image vocab size + 1 for BOS to have same size as decoder inputs (for sharding)
+            use_bias=False,
+            dtype=self.dtype,
+            kernel_init=jax.nn.initializers.normal(self.config.init_std),
+        )
+
+    def __call__(
+        self,
+        input_ids,
+        attention_mask,
+        decoder_input_ids,
+        decoder_attention_mask,
+        position_ids,
+        decoder_position_ids,
+        output_attentions: bool = False,
+        output_hidden_states: bool = False,
+        return_dict: bool = True,
+        deterministic: bool = True,
+    ):
+        outputs = self.model(
+            input_ids=input_ids,
+            attention_mask=attention_mask,
+            decoder_input_ids=decoder_input_ids,
+            decoder_attention_mask=decoder_attention_mask,
+            position_ids=position_ids,
+            decoder_position_ids=decoder_position_ids,
+            output_attentions=output_attentions,
+            output_hidden_states=output_hidden_states,
+            return_dict=return_dict,
+            deterministic=deterministic,
+        )
+
+        hidden_states = outputs[0]
+
+        if self.config.tie_word_embeddings:
+            shared_embedding = self.model.variables["params"]["shared"]["embedding"]
+            lm_logits = self.lm_head.apply(
+                {"params": {"kernel": shared_embedding.T}}, hidden_states
+            )
+        else:
+            lm_logits = self.lm_head(hidden_states)
+
+        if not return_dict:
+            output = (lm_logits,) + outputs[1:]
+            return output
+
+        return FlaxSeq2SeqLMOutput(
+            logits=lm_logits,
+            decoder_hidden_states=outputs.decoder_hidden_states,
+            decoder_attentions=outputs.decoder_attentions,
+            cross_attentions=outputs.cross_attentions,
+            encoder_last_hidden_state=outputs.encoder_last_hidden_state,
+            encoder_hidden_states=outputs.encoder_hidden_states,
+            encoder_attentions=outputs.encoder_attentions,
+        )
+
+
+@flax.struct.dataclass
+class SampleState:
+    cur_len: jnp.ndarray
+    sequences: jnp.ndarray
+    running_token: jnp.ndarray
+    is_sent_finished: jnp.ndarray
+    prng_key: jnp.ndarray
+    model_kwargs: Dict[str, jnp.ndarray]
+    model_kwargs_uncond: Dict[str, jnp.ndarray]
+
+
+@flax.struct.dataclass
+class FlaxSampleOutput(ModelOutput):
+    """
+    Flax Base class for outputs of decoder-only generation models using sampling.
+
+
+    Args:
+        sequences (`jnp.ndarray` of shape `(batch_size, max_length)`):
+            The generated sequences.
+    """
+
+    sequences: jnp.ndarray = None
+
+
+class DalleBart(PretrainedFromWandbMixin, FlaxBartForConditionalGeneration):
+    """
+    Edits:
+    - renamed from FlaxBartForConditionalGeneration
+    - uses custom FlaxBartForConditionalGenerationModule
+    - no bias in decode method
+    - custom prepare_inputs_for_generation using "max_length - 1" to avoid issues
+      related to position embedding during model.generate()
+    - custom generate method to allow super conditions
+    - num_params property
+    - unscan function
+    """
+
+    module_class = FlaxBartForConditionalGenerationModule
+    config_class = DalleBartConfig
+
+    def num_params(self, params=None):
+        if params is None:
+            params = self.params
+        num_params = jax.tree_util.tree_map(
+            lambda param: param.size, flatten_dict(unfreeze(params))
+        ).values()
+        return sum(list(num_params))
+
+    def unscan(self, params):
+        if self.config.use_scan:
+            self.config.use_scan = False
+            params = flatten_dict(params)
+            scanned_keys = [k for k in params.keys() if "layers" in k]
+            for k in scanned_keys:
+                v = params[k]
+                name_idx = k.index("layers") + 1
+                for i in range(len(v)):
+                    new_k = (
+                        *k[:name_idx],
+                        f"{k[name_idx][:-1]}_{i}",
+                        *k[name_idx + 1 :],
+                    )
+                    params[new_k] = v[i]
+                del params[k]
+            params = unflatten_dict(params)
+        return params
+
+    def decode(
+        self,
+        decoder_input_ids,
+        encoder_outputs,
+        encoder_attention_mask: Optional[jnp.ndarray] = None,
+        decoder_attention_mask: Optional[jnp.ndarray] = None,
+        decoder_position_ids: Optional[jnp.ndarray] = None,
+        past_key_values: dict = None,
+        output_attentions: Optional[bool] = None,
+        output_hidden_states: Optional[bool] = None,
+        return_dict: Optional[bool] = None,
+        train: bool = False,
+        params: dict = None,
+        dropout_rng: PRNGKey = None,
+    ):
+        output_attentions = (
+            output_attentions
+            if output_attentions is not None
+            else self.config.output_attentions
+        )
+        output_hidden_states = (
+            output_hidden_states
+            if output_hidden_states is not None
+            else self.config.output_hidden_states
+        )
+        return_dict = (
+            return_dict if return_dict is not None else self.config.return_dict
+        )
+
+        encoder_hidden_states = encoder_outputs[0]
+        if encoder_attention_mask is None:
+            batch_size, sequence_length = encoder_hidden_states.shape[:2]
+            encoder_attention_mask = jnp.ones((batch_size, sequence_length))
+
+        batch_size, sequence_length = decoder_input_ids.shape
+        if decoder_attention_mask is None:
+            decoder_attention_mask = jnp.ones((batch_size, sequence_length))
+
+        if decoder_position_ids is None:
+            if past_key_values is not None:
+                raise ValueError(
+                    "Make sure to provide `decoder_position_ids` when passing `past_key_values`."
+                )
+
+            decoder_position_ids = jnp.broadcast_to(
+                jnp.arange(sequence_length)[None, :], (batch_size, sequence_length)
+            )
+
+        # Handle any PRNG if needed
+        rngs = {}
+        if dropout_rng is not None:
+            rngs["dropout"] = dropout_rng
+
+        inputs = {"params": params or self.params}
+
+        # if past_key_values are passed then cache is already initialized a private flag init_cache has to be
+        # passed down to ensure cache is used. It has to be made sure that cache is marked as mutable so that
+        # it can be changed by FlaxBartAttention module
+        if past_key_values:
+            inputs["cache"] = past_key_values
+            mutable = ["cache"]
+        else:
+            mutable = False
+
+        def _decoder_forward(
+            module,
+            decoder_input_ids,
+            decoder_attention_mask,
+            decoder_position_ids,
+            **kwargs,
+        ):
+            decoder_module = module._get_decoder_module()
+            outputs = decoder_module(
+                decoder_input_ids,
+                decoder_attention_mask,
+                decoder_position_ids,
+                **kwargs,
+            )
+            hidden_states = outputs[0]
+
+            if self.config.tie_word_embeddings:
+                shared_embedding = module.model.variables["params"]["shared"][
+                    "embedding"
+                ]
+                lm_logits = module.lm_head.apply(
+                    {"params": {"kernel": shared_embedding.T}}, hidden_states
+                )
+            else:
+                lm_logits = module.lm_head(hidden_states)
+
+            return lm_logits, outputs
+
+        outputs = self.module.apply(
+            inputs,
+            decoder_input_ids=jnp.array(decoder_input_ids, dtype="i4"),
+            decoder_attention_mask=jnp.array(decoder_attention_mask, dtype="i4"),
+            decoder_position_ids=jnp.array(decoder_position_ids, dtype="i4"),
+            encoder_hidden_states=encoder_hidden_states,
+            encoder_attention_mask=jnp.array(encoder_attention_mask, dtype="i4"),
+            output_attentions=output_attentions,
+            output_hidden_states=output_hidden_states,
+            return_dict=return_dict,
+            deterministic=not train,
+            rngs=rngs,
+            mutable=mutable,
+            method=_decoder_forward,
+        )
+
+        if past_key_values is None:
+            lm_logits, decoder_outputs = outputs
+        else:
+            (lm_logits, decoder_outputs), past = outputs
+
+        if return_dict:
+            outputs = FlaxCausalLMOutputWithCrossAttentions(
+                logits=lm_logits,
+                hidden_states=decoder_outputs.hidden_states,
+                attentions=decoder_outputs.attentions,
+                cross_attentions=decoder_outputs.cross_attentions,
+            )
+        else:
+            outputs = (lm_logits,) + decoder_outputs[1:]
+
+        # add updated cache to model output
+        if past_key_values is not None and return_dict:
+            outputs["past_key_values"] = unfreeze(past["cache"])
+            return outputs
+        elif past_key_values is not None and not return_dict:
+            outputs = outputs[:1] + (unfreeze(past["cache"]),) + outputs[1:]
+
+        return outputs
+
+    def prepare_inputs_for_generation(
+        self,
+        decoder_input_ids,
+        max_length,
+        attention_mask: Optional[jnp.DeviceArray] = None,
+        decoder_attention_mask: Optional[jnp.DeviceArray] = None,
+        encoder_outputs=None,
+        **kwargs,
+    ):
+        # initializing the cache
+        batch_size, seq_length = decoder_input_ids.shape
+
+        past_key_values = self.init_cache(batch_size, max_length - 1, encoder_outputs)
+        # Note that usually one would have to put 0's in the attention_mask for x > input_ids.shape[-1] and x < cache_length.
+        # But since the decoder uses a causal mask, those positions are masked anyways.
+        # Thus we can create a single static attention_mask here, which is more efficient for compilation
+        extended_attention_mask = jnp.ones((batch_size, max_length - 1), dtype="i4")
+        if decoder_attention_mask is not None:
+            position_ids = decoder_attention_mask.cumsum(axis=-1) - 1
+            extended_attention_mask = lax.dynamic_update_slice(
+                extended_attention_mask, decoder_attention_mask, (0, 0)
+            )
+        else:
+            position_ids = jnp.broadcast_to(
+                jnp.arange(seq_length, dtype="i4")[None, :], (batch_size, seq_length)
+            )
+
+        return {
+            "past_key_values": past_key_values,
+            "encoder_outputs": encoder_outputs,
+            "encoder_attention_mask": attention_mask,
+            "decoder_attention_mask": extended_attention_mask,
+            "decoder_position_ids": position_ids,
+        }
+
+    def generate(
+        self,
+        input_ids: jnp.ndarray,
+        attention_mask: Optional[jnp.ndarray] = None,
+        max_length: Optional[int] = None,
+        pad_token_id: Optional[int] = None,
+        bos_token_id: Optional[int] = None,
+        eos_token_id: Optional[int] = None,
+        decoder_start_token_id: Optional[int] = None,
+        do_sample: Optional[bool] = None,
+        prng_key: Optional[jnp.ndarray] = None,
+        top_k: Optional[int] = None,
+        top_p: Optional[float] = None,
+        temperature: Optional[float] = None,
+        num_beams: Optional[int] = None,
+        no_repeat_ngram_size: Optional[int] = None,
+        min_length: Optional[int] = None,
+        forced_bos_token_id: Optional[int] = None,
+        forced_eos_token_id: Optional[int] = None,
+        length_penalty: Optional[float] = None,
+        early_stopping: Optional[bool] = None,
+        trace: bool = True,
+        params: Optional[Dict[str, jnp.ndarray]] = None,
+        condition_scale: Optional[float] = 1.0,
+        input_ids_uncond: Optional[jnp.ndarray] = None,
+        attention_mask_uncond: Optional[jnp.ndarray] = None,
+        **model_kwargs,
+    ):
+        """Edit: Allow super conditioning."""
+
+        # set init values
+        max_length = max_length if max_length is not None else self.config.max_length
+        bos_token_id = (
+            bos_token_id if bos_token_id is not None else self.config.bos_token_id
+        )
+        pad_token_id = (
+            pad_token_id if pad_token_id is not None else self.config.pad_token_id
+        )
+        eos_token_id = (
+            eos_token_id if eos_token_id is not None else self.config.eos_token_id
+        )
+        decoder_start_token_id = (
+            decoder_start_token_id
+            if decoder_start_token_id
+            else self.config.decoder_start_token_id
+        )
+        prng_key = prng_key if prng_key is not None else jax.random.PRNGKey(0)
+
+        if decoder_start_token_id is None and self.config.is_encoder_decoder:
+            raise ValueError(
+                "`decoder_start_token_id` has to be defined for encoder-decoder generation."
+            )
+
+        do_sample = do_sample if do_sample is not None else self.config.do_sample
+        num_beams = num_beams if num_beams is not None else self.config.num_beams
+
+        if self.config.is_encoder_decoder:
+            # add encoder_outputs to model_kwargs
+            if model_kwargs.get("encoder_outputs") is None:
+                model_kwargs_input = dict(model_kwargs)
+                model_kwargs = self._prepare_encoder_decoder_kwargs_for_generation(
+                    input_ids,
+                    params,
+                    {"attention_mask": attention_mask, **model_kwargs_input},
+                )
+                if condition_scale != 1.0:
+                    assert (
+                        input_ids_uncond is not None
+                    ), "`input_ids_uncond` has to be defined for super conditioning."
+                    assert (
+                        do_sample is True
+                    ), "`do_sample` has to be True for super conditioning."
+                    assert (
+                        num_beams == 1
+                    ), "`num_beams` has to be 1 for super conditioning."
+                    model_kwargs_uncond = (
+                        self._prepare_encoder_decoder_kwargs_for_generation(
+                            input_ids_uncond,
+                            params,
+                            {
+                                "attention_mask": attention_mask_uncond,
+                                **model_kwargs_input,
+                            },
+                        )
+                    )
+                else:
+                    model_kwargs_uncond = None
+            # prepare decoder_input_ids for generation
+            input_ids = (
+                jnp.ones((input_ids.shape[0], 1), dtype="i4") * decoder_start_token_id
+            )
+
+        if not do_sample and num_beams == 1:
+            logits_processor = self._get_logits_processor(
+                no_repeat_ngram_size,
+                min_length,
+                max_length,
+                eos_token_id,
+                forced_bos_token_id,
+                forced_eos_token_id,
+            )
+            return self._greedy_search(
+                input_ids,
+                max_length,
+                pad_token_id,
+                eos_token_id,
+                logits_processor=logits_processor,
+                trace=trace,
+                params=params,
+                model_kwargs=model_kwargs,
+            )
+        elif do_sample and num_beams == 1:
+            logits_warper = self._get_logits_warper(
+                top_k=top_k, top_p=top_p, temperature=temperature
+            )
+            logits_processor = self._get_logits_processor(
+                no_repeat_ngram_size,
+                min_length,
+                max_length,
+                eos_token_id,
+                forced_bos_token_id,
+                forced_eos_token_id,
+            )
+            return self._sample(
+                input_ids,
+                max_length,
+                pad_token_id,
+                eos_token_id,
+                prng_key,
+                logits_warper=logits_warper,
+                logits_processor=logits_processor,
+                trace=trace,
+                params=params,
+                model_kwargs=model_kwargs,
+                condition_scale=condition_scale,
+                model_kwargs_uncond=model_kwargs_uncond,
+            )
+        elif not do_sample and num_beams > 1:
+            # broadcast input_ids & encoder_outputs
+            input_ids = self._expand_to_num_beams(input_ids, num_beams=num_beams)
+
+            if "encoder_outputs" in model_kwargs:
+                model_kwargs["encoder_outputs"][
+                    "last_hidden_state"
+                ] = self._expand_to_num_beams(
+                    model_kwargs["encoder_outputs"]["last_hidden_state"],
+                    num_beams=num_beams,
+                )
+
+            if "attention_mask" in model_kwargs:
+                model_kwargs["attention_mask"] = self._expand_to_num_beams(
+                    model_kwargs["attention_mask"], num_beams=num_beams
+                )
+
+            logits_processor = self._get_logits_processor(
+                no_repeat_ngram_size,
+                min_length,
+                max_length,
+                eos_token_id,
+                forced_bos_token_id,
+                forced_eos_token_id,
+            )
+
+            return self._beam_search(
+                input_ids,
+                max_length,
+                pad_token_id,
+                eos_token_id,
+                length_penalty=length_penalty,
+                early_stopping=early_stopping,
+                logits_processor=logits_processor,
+                trace=trace,
+                params=params,
+                model_kwargs=model_kwargs,
+            )
+        else:
+            raise NotImplementedError("`Beam sampling is currently not implemented.")
+
+    def _sample(
+        self,
+        input_ids: None,
+        max_length: Optional[int] = None,
+        pad_token_id: Optional[int] = None,
+        eos_token_id: Optional[int] = None,
+        prng_key: Optional[jnp.ndarray] = None,
+        logits_processor=None,
+        logits_warper=None,
+        trace: bool = True,
+        params: Optional[Dict[str, jnp.ndarray]] = None,
+        model_kwargs: Optional[Dict[str, jnp.ndarray]] = None,
+        condition_scale: float = 1.0,
+        model_kwargs_uncond: Optional[Dict[str, jnp.ndarray]] = None,
+    ):
+        # init values
+        max_length = max_length if max_length is not None else self.config.max_length
+        pad_token_id = (
+            pad_token_id if pad_token_id is not None else self.config.pad_token_id
+        )
+        eos_token_id = (
+            eos_token_id if eos_token_id is not None else self.config.eos_token_id
+        )
+        prng_key = prng_key if prng_key is not None else jax.random.PRNGKey(0)
+
+        batch_size, cur_len = input_ids.shape
+
+        eos_token_id = jnp.array(eos_token_id)
+        pad_token_id = jnp.array(pad_token_id)
+        cur_len = jnp.array(cur_len)
+
+        # per batch-item holding current token in loop.
+        sequences = jnp.full((batch_size, max_length), pad_token_id, dtype=jnp.int32)
+        sequences = lax.dynamic_update_slice(sequences, input_ids, (0, 0))
+
+        # per batch-item state bit indicating if sentence has finished.
+        is_sent_finished = jnp.zeros((batch_size,), dtype=jnp.bool_)
+
+        # For Seq2Seq generation, we only need to use the decoder instead of the whole model in generation loop
+        # and pass it the `encoder_outputs`, which are part of the `model_kwargs`.
+        model = self.decode if self.config.is_encoder_decoder else self
+
+        # initialize model specific kwargs
+        model_kwargs = self.prepare_inputs_for_generation(
+            input_ids, max_length, **model_kwargs
+        )
+        if condition_scale != 1.0:
+            model_kwargs_uncond = self.prepare_inputs_for_generation(
+                input_ids, max_length, **model_kwargs_uncond
+            )
+
+        # initialize state
+        state = SampleState(
+            cur_len=cur_len,
+            sequences=sequences,
+            running_token=input_ids,
+            is_sent_finished=is_sent_finished,
+            prng_key=prng_key,
+            model_kwargs=model_kwargs,
+            model_kwargs_uncond=model_kwargs_uncond,
+        )
+
+        def sample_search_cond_fn(state):
+            """state termination condition fn."""
+            has_reached_max_length = state.cur_len == max_length
+            all_sequence_finished = jnp.all(state.is_sent_finished)
+            finish_generation = jnp.logical_or(
+                has_reached_max_length, all_sequence_finished
+            )
+            return ~finish_generation
+
+        def sample_search_body_fn(state):
+            """state update fn."""
+            prng_key, prng_key_next = jax.random.split(state.prng_key)
+            model_outputs = model(
+                state.running_token, params=params, **state.model_kwargs
+            )
+
+            logits = model_outputs.logits[:, -1]
+
+            # perform super conditioning
+            # Source: @RiversHaveWings - https://twitter.com/RiversHaveWings/status/1478093658716966912?s=20&t=xdm-wZ61Wf7OLnE_NJHZ1w
+            if condition_scale != 1.0:
+                model_outputs_uncond = model(
+                    state.running_token, params=params, **state.model_kwargs_uncond
+                )
+                logits_uncond = model_outputs_uncond.logits[:, -1]
+                logits = logits_uncond + condition_scale * (logits - logits_uncond)
+            else:
+                model_outputs_uncond = None
+
+            # apply min_length, ...
+            logits = logits_processor(state.sequences, logits, state.cur_len)
+            # apply top_k, top_k, temperature
+            logits = logits_warper(logits, logits, state.cur_len)
+
+            next_token = jax.random.categorical(prng_key, logits, axis=-1)
+
+            next_is_sent_finished = state.is_sent_finished | (
+                next_token == eos_token_id
+            )
+            next_token = (
+                next_token * ~next_is_sent_finished
+                + pad_token_id * next_is_sent_finished
+            )
+            next_token = next_token[:, None]
+
+            next_sequences = lax.dynamic_update_slice(
+                state.sequences, next_token, (0, state.cur_len)
+            )
+            next_model_kwargs = self.update_inputs_for_generation(
+                model_outputs, state.model_kwargs
+            )
+            next_model_kwargs_uncond = (
+                self.update_inputs_for_generation(
+                    model_outputs_uncond, state.model_kwargs_uncond
+                )
+                if condition_scale != 1.0
+                else None
+            )
+
+            return SampleState(
+                cur_len=state.cur_len + 1,
+                sequences=next_sequences,
+                running_token=next_token,
+                is_sent_finished=next_is_sent_finished,
+                model_kwargs=next_model_kwargs,
+                model_kwargs_uncond=next_model_kwargs_uncond,
+                prng_key=prng_key_next,
+            )
+
+        # The very first prompt often has sequence length > 1, so run outside of `lax.while_loop` to comply with TPU
+        if input_ids.shape[1] > 1:
+            state = sample_search_body_fn(state)
+
+        if not trace:
+            state = self._run_loop_in_debug(
+                sample_search_cond_fn, sample_search_body_fn, state
+            )
+        else:
+            state = lax.while_loop(sample_search_cond_fn, sample_search_body_fn, state)
+
+        return FlaxSampleOutput(sequences=state.sequences)

src/dalle_mini/model/partitions.py

@@ -0,0 +1,76 @@
+import re
+
+from flax.core.frozen_dict import freeze
+from flax.traverse_util import flatten_dict, unflatten_dict
+from jax.experimental import PartitionSpec as P
+
+# utils adapted from https://github.com/google-research/google-research/blob/master/flax_models/t5x/partitions.py
+# Sentinels
+_unmatched = object()
+
+# For specifying empty leaf dict `{}`
+empty_dict = object()
+
+
+def _match(qs, ks):
+    """Return True if regexes in qs match any window of strings in tuple ks."""
+    # compile regexes and force complete match
+    qts = tuple(map(lambda x: re.compile(x + "$"), qs))
+    for i in range(len(ks) - len(qs) + 1):
+        matches = [x.match(y) for x, y in zip(qts, ks[i:])]
+        if matches and all(matches):
+            return True
+    return False
+
+
+def _replacement_rules(rules):
+    def replace(key, val):
+        for rule, replacement in rules:
+            if _match(rule, key):
+                return replacement
+        return val
+
+    return replace
+
+
+def _get_partition_rules():
+    return [
+        # embeddings
+        (("embed_positions", "embedding"), P("mp", None)),
+        (("embed_tokens", "embedding"), P("mp", None)),
+        (("rel_bias", "embedding"), P(None, "mp")),
+        # attention
+        (("(q_proj|k_proj|v_proj)", "kernel"), P(None, "mp")),
+        (("out_proj", "kernel"), P("mp", None)),
+        # FFN
+        (("Dense_0", "kernel"), P(None, "mp")),
+        (("GLU.*", "Dense_1", "kernel"), P(None, "mp")),
+        (("GLU.*", "Dense_2", "kernel"), P("mp", None)),
+        (("FFN.*", "Dense_1", "kernel"), P("mp", None)),
+        # layer norms
+        (("(bias|scale)",), None),
+        (("lm_head", "kernel"), P(None, "mp")),
+        # head scale and tau
+        (("(head_scale|tau)",), None),
+    ]
+
+
+def set_partitions(in_dict, use_scan):
+    rules = _get_partition_rules()
+    replace = _replacement_rules(rules)
+    initd = {k: _unmatched for k in flatten_dict(in_dict)}
+    result = {k: replace(k, v) for k, v in initd.items()}
+    for k, v in result.items():
+        if v == _unmatched:
+            print(f"Unmatched -> {k}")
+    l = list(result.keys())
+    if use_scan:
+        # add None dimension to layers
+        result = {
+            k: (P(*(None,) + v) if v is not None else None)
+            if any(x in k for x in ["FlaxBartEncoderLayers", "FlaxBartDecoderLayers"])
+            else v
+            for k, v in result.items()
+        }
+    assert _unmatched not in result.values(), "Incomplete partition spec."
+    return freeze(unflatten_dict(result))

src/dalle_mini/model/processor.py

@@ -0,0 +1,60 @@
+""" DalleBart processor """
+
+from typing import List
+
+import jax.numpy as jnp
+
+from .configuration import DalleBartConfig
+from .text import TextNormalizer
+from .tokenizer import DalleBartTokenizer
+from .utils import PretrainedFromWandbMixin
+
+
+class DalleBartProcessorBase:
+    def __init__(
+        self, tokenizer: DalleBartTokenizer, normalize_text: bool, max_text_length: int
+    ):
+        self.tokenizer = tokenizer
+        self.normalize_text = normalize_text
+        self.max_text_length = max_text_length
+        if normalize_text:
+            self.text_processor = TextNormalizer()
+        # create unconditional tokens
+        uncond = self.tokenizer(
+            "",
+            return_tensors="jax",
+            padding="max_length",
+            truncation=True,
+            max_length=self.max_text_length,
+        ).data
+        self.input_ids_uncond = uncond["input_ids"]
+        self.attention_mask_uncond = uncond["attention_mask"]
+
+    def __call__(self, text: List[str] = None):
+        # check that text is not a string
+        assert not isinstance(text, str), "text must be a list of strings"
+
+        if self.normalize_text:
+            text = [self.text_processor(t) for t in text]
+        res = self.tokenizer(
+            text,
+            return_tensors="jax",
+            padding="max_length",
+            truncation=True,
+            max_length=self.max_text_length,
+        ).data
+        # tokens used only with super conditioning
+        n = len(text)
+        res["input_ids_uncond"] = jnp.repeat(self.input_ids_uncond, n, axis=0)
+        res["attention_mask_uncond"] = jnp.repeat(self.attention_mask_uncond, n, axis=0)
+        return res
+
+    @classmethod
+    def from_pretrained(cls, *args, **kwargs):
+        tokenizer = DalleBartTokenizer.from_pretrained(*args, **kwargs)
+        config = DalleBartConfig.from_pretrained(*args, **kwargs)
+        return cls(tokenizer, config.normalize_text, config.max_text_length)
+
+
+class DalleBartProcessor(PretrainedFromWandbMixin, DalleBartProcessorBase):
+    pass

src/dalle_mini/model/text.py

@@ -0,0 +1,262 @@
+"""
+Utilities for processing text.
+"""
+
+import html
+import math
+import random
+import re
+from pathlib import Path
+
+import emoji
+import ftfy
+from huggingface_hub import hf_hub_download
+from unidecode import unidecode
+
+# based on wiki word occurrence
+person_token = [("a person", 282265), ("someone", 121194), ("somebody", 12219)]
+temp_token = "xtokx"  # avoid repeating chars
+
+
+class HashtagProcessor:
+    # Adapted from wordninja library
+    # We use our wikipedia word count + a good heuristic to make it work
+    def __init__(self):
+        wiki_word_frequency = hf_hub_download(
+            "dalle-mini/dalle-mini", filename="enwiki-words-frequency.txt"
+        )
+        self._word_cost = (
+            l.split()[0]
+            for l in Path(wiki_word_frequency).read_text(encoding="utf8").splitlines()
+        )
+        self._word_cost = {
+            str(k): math.log(float(i + 1)) for i, k in enumerate(self._word_cost)
+        }
+        self._max_word = max(len(x) for x in self._word_cost.keys())
+        self._SPLIT_RE = re.compile("[^a-zA-Z0-9']+")
+
+    def __call__(self, s):
+        """Uses dynamic programming to infer the location of spaces in a string without spaces."""
+        l = [self._split(x) for x in self._SPLIT_RE.split(s)]
+        return " ".join([item for sublist in l for item in sublist])
+
+    def _split(self, s):
+        # Find the best match for the i first characters, assuming cost has
+        # been built for the i-1 first characters.
+        # Returns a pair (match_cost, match_length).
+        def best_match(i):
+            candidates = enumerate(reversed(cost[max(0, i - self._max_word) : i]))
+            return min(
+                (c + self._word_cost.get(s[i - k - 1 : i].lower(), 9e999), k + 1)
+                for k, c in candidates
+            )
+
+        # Build the cost array
+        cost = [0]
+        for i in range(1, len(s) + 1):
+            c, k = best_match(i)
+            cost.append(c)
+
+        # Backtrack to recover the minimal-cost string.
+        out = []
+        i = len(s)
+        while i > 0:
+            c, k = best_match(i)
+            assert c == cost[i]
+            newToken = True
+            if not s[i - k : i] == "'":  # ignore a lone apostrophe
+                if len(out) > 0:
+                    # re-attach split 's and split digits
+                    if out[-1] == "'s" or (
+                        s[i - 1].isdigit() and out[-1][0].isdigit()
+                    ):  # digit followed by digit
+                        out[-1] = (
+                            s[i - k : i] + out[-1]
+                        )  # combine current token with previous token
+                        newToken = False
+
+            if newToken:
+                out.append(s[i - k : i])
+
+            i -= k
+
+        return reversed(out)
+
+
+def replace_person_token(t):
+    "Used for CC12M"
+    t = re.sub("<person>([,\s]*(and)*[,\s]*<person>)+", " people ", t)
+    while "<person>" in t:
+        t = t.replace(
+            "<person>", f" {random.choices(*tuple(zip(*person_token)))[0]} ", 1
+        )
+    return t
+
+
+def fix_html(t):
+    # from OpenAI CLIP
+    return html.unescape(html.unescape(t))
+
+
+def replace_punctuation_with_commas(t):
+    return re.sub("[()[\].,|:;?!=+~\-\/{}]", ",", t)
+
+
+def simplify_quotes(t):
+    return re.sub("""['"`]""", ' " ', t)
+
+
+def merge_quotes(t):
+    return re.sub('(\s*"+\s*)+', ' " ', t)
+
+
+def remove_comma_numbers(t):
+    def _f(t):
+        return re.sub("(\d),(\d{3})", r"\1\2", t)
+
+    return _f(_f(t))
+
+
+def pre_process_dot_numbers(t):
+    return re.sub("(\w)\.(\w)", rf"\1{temp_token}dot{temp_token}\2", t)
+
+
+def post_process_dot_numbers(t):
+    return re.sub(f"{temp_token}dot{temp_token}", ".", t)
+
+
+def pre_process_quotes(t):
+    # allows quotes only for 's, 't, 'd, 'm, 'll, 're, 've
+    return re.sub(
+        r"'(?=([stdm]|(ll)|(re)|(ve)|(ll))\b)", rf"{temp_token}quote{temp_token}", t
+    )
+
+
+def post_process_quotes(t):
+    return re.sub(f"{temp_token}quote{temp_token}", "'", t)
+
+
+def pre_process_dates(t):
+    return re.sub("(\d)/(\d)", rf"\1{temp_token}slash{temp_token}\2", t)
+
+
+def post_process_dates(t):
+    return re.sub(f"{temp_token}slash{temp_token}", "/", t)
+
+
+def merge_commas(t):
+    return re.sub("(\s*,+\s*)+", ", ", t)
+
+
+def add_space_after_commas(t):
+    return re.sub(",", ", ", t)
+
+
+def handle_special_chars(t):
+    "Handle special characters"
+    # replace "-" with a space when between words without space
+    t = re.sub("(\w)-(\w)", r"\1 \2", t)
+    # always add space around some characters
+    return re.sub("([%&\/$*])", r" \1 ", t)
+
+
+def expand_hashtags(t, hashtag_processor):
+    "Remove # and try to split words"
+    return re.sub("#(\w+)", lambda m: hashtag_processor(m.group(1)), t)
+
+
+_re_ignore_chars = r"[_#\\]"
+
+
+def ignore_chars(t):
+    "Ignore useless characters"
+    return re.sub(_re_ignore_chars, " ", t)
+
+
+def remove_extra_spaces(t):
+    "Remove extra spaces (including \t and \n)"
+    return re.sub("\s+", " ", t)
+
+
+def remove_repeating_chars(t):
+    "If the same character is present 4+ times (not 3 because of roman 'VIII'), replace with single instance"
+    return re.sub(r"(\D)(\1{3,})", r"\1", t)
+
+
+def remove_urls(t):
+    return re.sub(r"http\S+", "", t)
+
+
+def remove_html_tags(t):
+    return re.sub("<[^<]+?>", " ", t)
+
+
+def remove_first_last_commas(t):
+    t = t.strip()
+    t = t[:-1] if t and t[-1] == "," else t
+    t = t[1:] if t and t[0] == "," else t
+    return t.strip()
+
+
+def remove_wiki_ref(t):
+    t = re.sub(r"\A\s*\[\d+\]", "", t)
+    return re.sub(r"\[\d+\]\s*\Z", "", t)
+
+
+class TextNormalizer:
+    "Normalize text"
+
+    def __init__(self):
+        self._hashtag_processor = HashtagProcessor()
+
+    def __call__(self, t):
+        # fix some characters
+        t = ftfy.fix_text(t)
+        # fix html
+        t = fix_html(t)
+        # decode emojis (would be removed by unidecode)
+        t = emoji.demojize(t)
+        # decode and simplify text: see unidecode library
+        t = unidecode(t)
+        # lower case
+        t = t.lower()
+        # replace <PERSON> (for CC12M)
+        t = replace_person_token(t)
+        # remove wiki reference (for WIT)
+        t = remove_wiki_ref(t)
+        # remove html tags
+        t = remove_html_tags(t)
+        # remove urls
+        t = remove_urls(t)
+        # remove commas in numbers
+        t = remove_comma_numbers(t)
+        # handle dots in numbers and quotes - Part 1
+        t = pre_process_dot_numbers(t)
+        t = pre_process_quotes(t)
+        t = pre_process_dates(t)
+        # handle special characters
+        t = handle_special_chars(t)
+        # handle hashtags
+        t = expand_hashtags(t, self._hashtag_processor)
+        # ignore useless characters
+        t = ignore_chars(t)
+        # simplify quotes
+        t = simplify_quotes(t)
+        # all punctuation becomes commas
+        t = replace_punctuation_with_commas(t)
+        # handle dots in numbers and quotes - Part 2
+        t = post_process_dot_numbers(t)
+        t = post_process_quotes(t)
+        t = post_process_dates(t)
+        # handle repeating characters
+        t = remove_repeating_chars(t)
+        # merge quotes
+        t = merge_quotes(t)
+        # merge commas
+        t = merge_commas(t)
+        # remove multiple spaces
+        t = remove_extra_spaces(t)
+        # remove first and last comma
+        t = remove_first_last_commas(t)
+        # always start with a space
+        return f" {t}"

src/dalle_mini/model/tokenizer.py

@@ -0,0 +1,8 @@
+""" DalleBart tokenizer """
+from transformers import BartTokenizerFast
+
+from .utils import PretrainedFromWandbMixin
+
+
+class DalleBartTokenizer(PretrainedFromWandbMixin, BartTokenizerFast):
+    pass

src/dalle_mini/model/utils.py

@@ -0,0 +1,27 @@
+import os
+import tempfile
+from pathlib import Path
+
+import wandb
+
+
+class PretrainedFromWandbMixin:
+    @classmethod
+    def from_pretrained(cls, pretrained_model_name_or_path, *model_args, **kwargs):
+        """
+        Initializes from a wandb artifact or delegates loading to the superclass.
+        """
+        with tempfile.TemporaryDirectory() as tmp_dir:  # avoid multiple artifact copies
+            if ":" in pretrained_model_name_or_path and not os.path.isdir(
+                pretrained_model_name_or_path
+            ):
+                # wandb artifact
+                if wandb.run is not None:
+                    artifact = wandb.run.use_artifact(pretrained_model_name_or_path)
+                else:
+                    artifact = wandb.Api().artifact(pretrained_model_name_or_path)
+                pretrained_model_name_or_path = artifact.download(tmp_dir)
+
+            return super(PretrainedFromWandbMixin, cls).from_pretrained(
+                pretrained_model_name_or_path, *model_args, **kwargs
+            )

tools/dataset/encode_dataset.ipynb

@@ -0,0 +1,371 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d0b72877",
+   "metadata": {},
+   "source": [
+    "# Pre-encoding a dataset for DALLE·mini"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ba7b31e6",
+   "metadata": {},
+   "source": [
+    "This notebook shows how to pre-encode images to token sequences using JAX, VQGAN and a dataset in the [`webdataset` format](https://webdataset.github.io/webdataset/).\n",
+    "\n",
+    "Adapt it to your own dataset and image encoder.\n",
+    "\n",
+    "At the end you should have a dataset of pairs:\n",
+    "* a caption defined as a string\n",
+    "* an encoded image defined as a list of int."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3b59489e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from tqdm.notebook import tqdm\n",
+    "\n",
+    "import torchvision.transforms as T\n",
+    "\n",
+    "import webdataset as wds\n",
+    "\n",
+    "import jax\n",
+    "import braceexpand\n",
+    "from pathlib import Path"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c7c4c1e6",
+   "metadata": {},
+   "source": [
+    "## Configuration Parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "1265dbfe",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "shards = \"my_images/shard-{0000..0008}.tar\"  # defined using braceexpand format as used by webdataset\n",
+    "encoded_output = Path(\"encoded_data\")  # where we will save our encoded data\n",
+    "\n",
+    "VQGAN_REPO, VQGAN_COMMIT_ID = (\n",
+    "    \"dalle-mini/vqgan_imagenet_f16_16384\",\n",
+    "    \"85eb5d3b51a1c62a0cc8f4ccdee9882c0d0bd384\",\n",
+    ")\n",
+    "\n",
+    "# good defaults for a TPU v3-8\n",
+    "batch_size = 128  # Per device\n",
+    "num_workers = 8  # For parallel processing\n",
+    "total_bs = batch_size * jax.device_count()  # You can use a smaller size while testing\n",
+    "save_frequency = 128  # Number of batches to create a new file (180MB for f16 and 720MB for f8 per file)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "cd956ec6-7d98-4d4d-a454-f80fe857eadd",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['XXX/shard-0000.tar',\n",
+       " 'XXX/shard-0001.tar',\n",
+       " 'XXX/shard-0002.tar',\n",
+       " 'XXX/shard-0003.tar',\n",
+       " 'XXX/shard-0004.tar',\n",
+       " 'XXX/shard-0005.tar',\n",
+       " 'XXX/shard-0006.tar',\n",
+       " 'XXX/shard-0007.tar',\n",
+       " 'XXX/shard-0008.tar']"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "shards = list(\n",
+    "    braceexpand.braceexpand(shards)\n",
+    ")  # better display for tqdm with known length"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "75dba8e2",
+   "metadata": {},
+   "source": [
+    "## Load data"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a1e8fb95",
+   "metadata": {},
+   "source": [
+    "We load data using `webdataset`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9ef5de9e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ds = (\n",
+    "    wds.WebDataset(shards, handler=wds.warn_and_continue)\n",
+    "    .decode(\"rgb\", handler=wds.warn_and_continue)\n",
+    "    .to_tuple(\"jpg\", \"txt\")  # assumes image is in `jpg` and caption in `txt`\n",
+    "    .batched(total_bs)  # load in batch per worker (faster)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "90981824",
+   "metadata": {},
+   "source": [
+    "Note:\n",
+    "* you can also shuffle shards and items using `shardshuffle` and `shuffle` if necessary.\n",
+    "* you may need to resize images in your pipeline (with `map_dict` for example), we assume they are already set to 256x256.\n",
+    "* you can also filter out some items using `select`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "129c377d",
+   "metadata": {},
+   "source": [
+    "We can now inspect our data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8cac98cb",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "%%time\n",
+    "images, captions = next(iter(ds))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "cd268fbf",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "images.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5acfc4d8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "captions[:10]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c24693c0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "T.ToPILImage()(images[0].permute(2, 0, 1))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3059ffb1",
+   "metadata": {},
+   "source": [
+    "Finally we create our dataloader."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c227c551",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dl = (\n",
+    "    wds.WebLoader(ds, batch_size=None, num_workers=8).unbatched().batched(total_bs)\n",
+    ")  # avoid partial batch at the end of each worker"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a354472b",
+   "metadata": {},
+   "source": [
+    "## Image encoder\n",
+    "\n",
+    "We'll use a VQGAN trained with Taming Transformers and converted to a JAX model."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "47a8b818",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "from vqgan_jax.modeling_flax_vqgan import VQModel\n",
+    "from flax.jax_utils import replicate\n",
+    "\n",
+    "vqgan = VQModel.from_pretrained(\"flax-community/vqgan_f16_16384\")\n",
+    "vqgan_params = replicate(vqgan.params)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "62ad01c3",
+   "metadata": {},
+   "source": [
+    "## Encoding"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "20357f74",
+   "metadata": {},
+   "source": [
+    "Encoding is really simple using `shard` to automatically distribute batches across devices and `pmap`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "322a4619",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from flax.training.common_utils import shard\n",
+    "from functools import partial\n",
+    "\n",
+    "\n",
+    "@partial(jax.pmap, axis_name=\"batch\")\n",
+    "def p_encode(batch, params):\n",
+    "    # Not sure if we should `replicate` params, does not seem to have any effect\n",
+    "    _, indices = vqgan.encode(batch, params=params)\n",
+    "    return indices"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ff6c10d4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "\n",
+    "\n",
+    "def encode_dataset(dataloader, output_dir, save_frequency):\n",
+    "    output_dir.mkdir(parents=True, exist_ok=True)\n",
+    "    all_captions = []\n",
+    "    all_encoding = []\n",
+    "    n_file = 1\n",
+    "    for idx, (images, captions) in enumerate(tqdm(dataloader)):\n",
+    "        images = images.numpy()\n",
+    "        n = len(images) // 8 * 8\n",
+    "        if n != len(images):\n",
+    "            # get the max number of images we can (multiple of 8)\n",
+    "            print(f\"Different sizes {n} vs {len(images)}\")\n",
+    "            images = images[:n]\n",
+    "            captions = captions[:n]\n",
+    "        if not len(captions):\n",
+    "            print(f\"No images/captions in batch...\")\n",
+    "            continue\n",
+    "        images = shard(images)\n",
+    "        encoded = p_encode(images, vqgan_params)\n",
+    "        encoded = encoded.reshape(-1, encoded.shape[-1])\n",
+    "        all_captions.extend(captions)\n",
+    "        all_encoding.extend(encoded.tolist())\n",
+    "\n",
+    "        # save files\n",
+    "        if (idx + 1) % save_frequency == 0:\n",
+    "            print(f\"Saving file {n_file}\")\n",
+    "            batch_df = pd.DataFrame.from_dict(\n",
+    "                {\"caption\": all_captions, \"encoding\": all_encoding}\n",
+    "            )\n",
+    "            batch_df.to_parquet(f\"{output_dir}/{n_file:03d}.parquet\")\n",
+    "            all_captions = []\n",
+    "            all_encoding = []\n",
+    "            n_file += 1\n",
+    "\n",
+    "    if len(all_captions):\n",
+    "        print(f\"Saving final file {n_file}\")\n",
+    "        batch_df = pd.DataFrame.from_dict(\n",
+    "            {\"caption\": all_captions, \"encoding\": all_encoding}\n",
+    "        )\n",
+    "        batch_df.to_parquet(f\"{output_dir}/{n_file:03d}.parquet\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7704863d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "encode_dataset(dl, output_dir=encoded_output, save_frequency=save_frequency)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8953dd84",
+   "metadata": {},
+   "source": [
+    "----"
+   ]
+  }
+ ],
+ "metadata": {
+  "interpreter": {
+   "hash": "db471c52d602b4f5f40ecaf278e88ccfef85c29d0a1a07185b0d51fc7acf4e26"
+  },
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

tools/inference/inference_pipeline.ipynb

@@ -0,0 +1,561 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/borisdayma/dalle-mini/blob/main/tools/inference/inference_pipeline.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "118UKH5bWCGa"
+      },
+      "source": [
+        "# DALL·E mini - Inference pipeline\n",
+        "\n",
+        "*Generate images from a text prompt*\n",
+        "\n",
+        "<img src=\"https://github.com/borisdayma/dalle-mini/blob/main/img/logo.png?raw=true\" width=\"200\">\n",
+        "\n",
+        "This notebook illustrates [DALL·E mini](https://github.com/borisdayma/dalle-mini) inference pipeline.\n",
+        "\n",
+        "Just want to play? Use directly [the app](https://www.craiyon.com/).\n",
+        "\n",
+        "For more understanding of the model, refer to [the report](https://wandb.ai/dalle-mini/dalle-mini/reports/DALL-E-mini--Vmlldzo4NjIxODA)."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "dS8LbaonYm3a"
+      },
+      "source": [
+        "## 🛠️ Installation and set-up"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "uzjAM2GBYpZX"
+      },
+      "outputs": [],
+      "source": [
+        "# Required only for colab environments + GPU\n",
+        "!pip install jax==0.3.25 jaxlib==0.3.25 -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html\n",
+        "\n",
+        "# Install required libraries\n",
+        "!pip install -q dalle-mini\n",
+        "!pip install -q git+https://github.com/patil-suraj/vqgan-jax.git"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "ozHzTkyv8cqU"
+      },
+      "source": [
+        "We load required models:\n",
+        "* DALL·E mini for text to encoded images\n",
+        "* VQGAN for decoding images\n",
+        "* CLIP for scoring predictions"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "K6CxW2o42f-w"
+      },
+      "outputs": [],
+      "source": [
+        "# Model references\n",
+        "\n",
+        "# dalle-mega\n",
+        "DALLE_MODEL = \"dalle-mini/dalle-mini/mega-1-fp16:latest\"  # can be wandb artifact or 🤗 Hub or local folder or google bucket\n",
+        "DALLE_COMMIT_ID = None\n",
+        "\n",
+        "# if the notebook crashes too often you can use dalle-mini instead by uncommenting below line\n",
+        "# DALLE_MODEL = \"dalle-mini/dalle-mini/mini-1:v0\"\n",
+        "\n",
+        "# VQGAN model\n",
+        "VQGAN_REPO = \"dalle-mini/vqgan_imagenet_f16_16384\"\n",
+        "VQGAN_COMMIT_ID = \"e93a26e7707683d349bf5d5c41c5b0ef69b677a9\""
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "Yv-aR3t4Oe5v"
+      },
+      "outputs": [],
+      "source": [
+        "import jax\n",
+        "import jax.numpy as jnp\n",
+        "\n",
+        "# check how many devices are available\n",
+        "jax.local_device_count()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "92zYmvsQ38vL"
+      },
+      "outputs": [],
+      "source": [
+        "# Load models & tokenizer\n",
+        "from dalle_mini import DalleBart, DalleBartProcessor\n",
+        "from vqgan_jax.modeling_flax_vqgan import VQModel\n",
+        "from transformers import CLIPProcessor, FlaxCLIPModel\n",
+        "\n",
+        "# Load dalle-mini\n",
+        "model, params = DalleBart.from_pretrained(\n",
+        "    DALLE_MODEL, revision=DALLE_COMMIT_ID, dtype=jnp.float16, _do_init=False\n",
+        ")\n",
+        "\n",
+        "# Load VQGAN\n",
+        "vqgan, vqgan_params = VQModel.from_pretrained(\n",
+        "    VQGAN_REPO, revision=VQGAN_COMMIT_ID, _do_init=False\n",
+        ")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "o_vH2X1tDtzA"
+      },
+      "source": [
+        "Model parameters are replicated on each device for faster inference."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "wtvLoM48EeVw"
+      },
+      "outputs": [],
+      "source": [
+        "from flax.jax_utils import replicate\n",
+        "\n",
+        "params = replicate(params)\n",
+        "vqgan_params = replicate(vqgan_params)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "0A9AHQIgZ_qw"
+      },
+      "source": [
+        "Model functions are compiled and parallelized to take advantage of multiple devices."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "sOtoOmYsSYPz"
+      },
+      "outputs": [],
+      "source": [
+        "from functools import partial\n",
+        "\n",
+        "\n",
+        "# model inference\n",
+        "@partial(jax.pmap, axis_name=\"batch\", static_broadcasted_argnums=(3, 4, 5, 6))\n",
+        "def p_generate(\n",
+        "    tokenized_prompt, key, params, top_k, top_p, temperature, condition_scale\n",
+        "):\n",
+        "    return model.generate(\n",
+        "        **tokenized_prompt,\n",
+        "        prng_key=key,\n",
+        "        params=params,\n",
+        "        top_k=top_k,\n",
+        "        top_p=top_p,\n",
+        "        temperature=temperature,\n",
+        "        condition_scale=condition_scale,\n",
+        "    )\n",
+        "\n",
+        "\n",
+        "# decode image\n",
+        "@partial(jax.pmap, axis_name=\"batch\")\n",
+        "def p_decode(indices, params):\n",
+        "    return vqgan.decode_code(indices, params=params)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "HmVN6IBwapBA"
+      },
+      "source": [
+        "Keys are passed to the model on each device to generate unique inference per device."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "4CTXmlUkThhX"
+      },
+      "outputs": [],
+      "source": [
+        "import random\n",
+        "\n",
+        "# create a random key\n",
+        "seed = random.randint(0, 2**32 - 1)\n",
+        "key = jax.random.PRNGKey(seed)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "BrnVyCo81pij"
+      },
+      "source": [
+        "## 🖍 Text Prompt"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "rsmj0Aj5OQox"
+      },
+      "source": [
+        "Our model requires processing prompts."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "YjjhUychOVxm"
+      },
+      "outputs": [],
+      "source": [
+        "from dalle_mini import DalleBartProcessor\n",
+        "\n",
+        "processor = DalleBartProcessor.from_pretrained(DALLE_MODEL, revision=DALLE_COMMIT_ID)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "BQ7fymSPyvF_"
+      },
+      "source": [
+        "Let's define some text prompts."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "x_0vI9ge1oKr"
+      },
+      "outputs": [],
+      "source": [
+        "prompts = [\n",
+        "    \"sunset over a lake in the mountains\",\n",
+        "    \"the Eiffel tower landing on the moon\",\n",
+        "]"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "XlZUG3SCLnGE"
+      },
+      "source": [
+        "Note: we could use the same prompt multiple times for faster inference."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "VKjEZGjtO49k"
+      },
+      "outputs": [],
+      "source": [
+        "tokenized_prompts = processor(prompts)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "-CEJBnuJOe5z"
+      },
+      "source": [
+        "Finally we replicate the prompts onto each device."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "lQePgju5Oe5z"
+      },
+      "outputs": [],
+      "source": [
+        "tokenized_prompt = replicate(tokenized_prompts)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "phQ9bhjRkgAZ"
+      },
+      "source": [
+        "## 🎨 Generate images\n",
+        "\n",
+        "We generate images using dalle-mini model and decode them with the VQGAN."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "d0wVkXpKqnHA"
+      },
+      "outputs": [],
+      "source": [
+        "# number of predictions per prompt\n",
+        "n_predictions = 8\n",
+        "\n",
+        "# We can customize generation parameters (see https://huggingface.co/blog/how-to-generate)\n",
+        "gen_top_k = None\n",
+        "gen_top_p = None\n",
+        "temperature = None\n",
+        "cond_scale = 10.0"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "SDjEx9JxR3v8"
+      },
+      "outputs": [],
+      "source": [
+        "from flax.training.common_utils import shard_prng_key\n",
+        "import numpy as np\n",
+        "from PIL import Image\n",
+        "from tqdm.notebook import trange\n",
+        "\n",
+        "print(f\"Prompts: {prompts}\\n\")\n",
+        "# generate images\n",
+        "images = []\n",
+        "for i in trange(max(n_predictions // jax.device_count(), 1)):\n",
+        "    # get a new key\n",
+        "    key, subkey = jax.random.split(key)\n",
+        "    # generate images\n",
+        "    encoded_images = p_generate(\n",
+        "        tokenized_prompt,\n",
+        "        shard_prng_key(subkey),\n",
+        "        params,\n",
+        "        gen_top_k,\n",
+        "        gen_top_p,\n",
+        "        temperature,\n",
+        "        cond_scale,\n",
+        "    )\n",
+        "    # remove BOS\n",
+        "    encoded_images = encoded_images.sequences[..., 1:]\n",
+        "    # decode images\n",
+        "    decoded_images = p_decode(encoded_images, vqgan_params)\n",
+        "    decoded_images = decoded_images.clip(0.0, 1.0).reshape((-1, 256, 256, 3))\n",
+        "    for decoded_img in decoded_images:\n",
+        "        img = Image.fromarray(np.asarray(decoded_img * 255, dtype=np.uint8))\n",
+        "        images.append(img)\n",
+        "        display(img)\n",
+        "        print()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "tw02wG9zGmyB"
+      },
+      "source": [
+        "## 🏅 Optional: Rank images by CLIP score\n",
+        "\n",
+        "We can rank images according to CLIP.\n",
+        "\n",
+        "**Note: your session may crash if you don't have a subscription to Colab Pro.**"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "RGjlIW_f6GA0"
+      },
+      "outputs": [],
+      "source": [
+        "# CLIP model\n",
+        "CLIP_REPO = \"openai/clip-vit-base-patch32\"\n",
+        "CLIP_COMMIT_ID = None\n",
+        "\n",
+        "# Load CLIP\n",
+        "clip, clip_params = FlaxCLIPModel.from_pretrained(\n",
+        "    CLIP_REPO, revision=CLIP_COMMIT_ID, dtype=jnp.float16, _do_init=False\n",
+        ")\n",
+        "clip_processor = CLIPProcessor.from_pretrained(CLIP_REPO, revision=CLIP_COMMIT_ID)\n",
+        "clip_params = replicate(clip_params)\n",
+        "\n",
+        "\n",
+        "# score images\n",
+        "@partial(jax.pmap, axis_name=\"batch\")\n",
+        "def p_clip(inputs, params):\n",
+        "    logits = clip(params=params, **inputs).logits_per_image\n",
+        "    return logits"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "FoLXpjCmGpju"
+      },
+      "outputs": [],
+      "source": [
+        "from flax.training.common_utils import shard\n",
+        "\n",
+        "# get clip scores\n",
+        "clip_inputs = clip_processor(\n",
+        "    text=prompts * jax.device_count(),\n",
+        "    images=images,\n",
+        "    return_tensors=\"np\",\n",
+        "    padding=\"max_length\",\n",
+        "    max_length=77,\n",
+        "    truncation=True,\n",
+        ").data\n",
+        "logits = p_clip(shard(clip_inputs), clip_params)\n",
+        "\n",
+        "# organize scores per prompt\n",
+        "p = len(prompts)\n",
+        "logits = np.asarray([logits[:, i::p, i] for i in range(p)]).squeeze()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "4AAWRm70LgED"
+      },
+      "source": [
+        "Let's now display images ranked by CLIP score."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "zsgxxubLLkIu"
+      },
+      "outputs": [],
+      "source": [
+        "for i, prompt in enumerate(prompts):\n",
+        "    print(f\"Prompt: {prompt}\\n\")\n",
+        "    for idx in logits[i].argsort()[::-1]:\n",
+        "        display(images[idx * p + i])\n",
+        "        print(f\"Score: {jnp.asarray(logits[i][idx], dtype=jnp.float32):.2f}\\n\")\n",
+        "    print()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "oZT9i3jCjir0"
+      },
+      "source": [
+        "## 🪄 Optional: Save your Generated Images as W&B Tables\n",
+        "\n",
+        "W&B Tables is an interactive 2D grid with support to rich media logging. Use this to save the generated images on W&B dashboard and share with the world."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "-pSiv6Vwjkn0"
+      },
+      "outputs": [],
+      "source": [
+        "import wandb\n",
+        "\n",
+        "# Initialize a W&B run.\n",
+        "project = \"dalle-mini-tables-colab\"\n",
+        "run = wandb.init(project=project)\n",
+        "\n",
+        "# Initialize an empty W&B Tables.\n",
+        "columns = [\"captions\"] + [f\"image_{i+1}\" for i in range(n_predictions)]\n",
+        "gen_table = wandb.Table(columns=columns)\n",
+        "\n",
+        "# Add data to the table.\n",
+        "for i, prompt in enumerate(prompts):\n",
+        "    # If CLIP scores exist, sort the Images\n",
+        "    if logits is not None:\n",
+        "        idxs = logits[i].argsort()[::-1]\n",
+        "        tmp_imgs = images[i :: len(prompts)]\n",
+        "        tmp_imgs = [tmp_imgs[idx] for idx in idxs]\n",
+        "    else:\n",
+        "        tmp_imgs = images[i :: len(prompts)]\n",
+        "\n",
+        "    # Add the data to the table.\n",
+        "    gen_table.add_data(prompt, *[wandb.Image(img) for img in tmp_imgs])\n",
+        "\n",
+        "# Log the Table to W&B dashboard.\n",
+        "wandb.log({\"Generated Images\": gen_table})\n",
+        "\n",
+        "# Close the W&B run.\n",
+        "run.finish()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "Ck2ZnHwVjnRd"
+      },
+      "source": [
+        "Click on the link above to check out your generated images."
+      ]
+    }
+  ],
+  "metadata": {
+    "accelerator": "GPU",
+    "colab": {
+      "machine_shape": "hm",
+      "name": "DALL·E mini - Inference pipeline.ipynb",
+      "provenance": [],
+      "gpuType": "A100",
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9.7"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 0
+}

tools/inference/run_infer_notebook.sh

@@ -0,0 +1,2 @@
+#!/bin/bash
+jupyter notebook --ip 0.0.0.0 --no-browser --allow-root

tools/train/config/mega/config.json

@@ -0,0 +1,49 @@
+{
+  "activation_dropout": 0.0,
+  "activation_function": "gelu",
+  "attention_dropout": 0.0,
+  "bos_token_id": 16385,
+  "d_model": 2048,
+  "decoder_attention_heads": 32,
+  "decoder_ffn_dim": 4096,
+  "decoder_layerdrop": 0.0,
+  "decoder_layers": 24,
+  "decoder_start_token_id": 16384,
+  "do_sample": true,
+  "dropout": 0.0,
+  "encoder_attention_heads": 32,
+  "encoder_ffn_dim": 4096,
+  "encoder_layerdrop": 0.0,
+  "encoder_layers": 24,
+  "encoder_vocab_size": 50272,
+  "eos_token_id": 16385,
+  "force_ln_scale": false,
+  "gradient_checkpointing": false,
+  "image_length": 256,
+  "image_vocab_size": 16415,
+  "init_std": 0.01,
+  "is_encoder_decoder": true,
+  "ln_positions": "normformer",
+  "ln_type": "layernorm",
+  "max_length": 257,
+  "max_text_length": 64,
+  "min_length": 257,
+  "model_type": "dallebart",
+  "normalize_text": true,
+  "pad_token_id": 16385,
+  "scale_embedding": false,
+  "sinkhorn_iters": 1,
+  "tau_init": 0.05,
+  "tie_word_embeddings": false,
+  "use_absolute_position_embeddings": true,
+  "use_alibi": false,
+  "use_bias": false,
+  "use_cache": true,
+  "use_cosine_attention": false,
+  "use_deepnet_scaling": false,
+  "use_final_ln_decoder": true,
+  "use_final_ln_encoder": true,
+  "use_glu": true,
+  "use_head_scale": false,
+  "use_swin_position_embeddings": false
+}

tools/train/config/micro/config.json

@@ -0,0 +1,30 @@
+{
+  "activation_dropout": 0.0,
+  "activation_function": "gelu",
+  "attention_dropout": 0.0,
+  "bos_token_id": 16385,
+  "d_model": 256,
+  "decoder_attention_heads": 2,
+  "decoder_ffn_dim": 256,
+  "decoder_layerdrop": 0.0,
+  "decoder_layers": 2,
+  "decoder_start_token_id": 16384,
+  "dropout": 0.0,
+  "encoder_attention_heads": 2,
+  "encoder_ffn_dim": 256,
+  "encoder_layerdrop": 0.0,
+  "encoder_layers": 2,
+  "encoder_vocab_size": 50264,
+  "eos_token_id": 16385,
+  "image_length": 256,
+  "image_vocab_size": 16391,
+  "init_std": 0.02,
+  "is_encoder_decoder": true,
+  "max_text_length": 64,
+  "model_type": "dallebart",
+  "normalize_text": true,
+  "pad_token_id": 16385,
+  "scale_embedding": false,
+  "tie_word_embeddings": false,
+  "use_cache": true
+}

tools/train/config/mini/config.json

@@ -0,0 +1,29 @@
+{
+  "activation_dropout": 0.0,
+  "activation_function": "gelu",
+  "attention_dropout": 0.0,
+  "bos_token_id": 16385,
+  "d_model": 1024,
+  "decoder_attention_heads": 16,
+  "decoder_ffn_dim": 4096,
+  "decoder_layers": 12,
+  "decoder_start_token_id": 16384,
+  "dropout": 0.0,
+  "encoder_attention_heads": 16,
+  "encoder_ffn_dim": 4096,
+  "encoder_layers": 12,
+  "encoder_vocab_size": 50264,
+  "eos_token_id": 16385,
+  "gradient_checkpointing": false,
+  "image_length": 256,
+  "image_vocab_size": 16391,
+  "init_std": 0.02,
+  "is_encoder_decoder": true,
+  "max_text_length": 64,
+  "model_type": "dallebart",
+  "normalize_text": true,
+  "pad_token_id": 16385,
+  "scale_embedding": false,
+  "tie_word_embeddings": false,
+  "use_cache": true
+}

tools/train/config/mini_glu/config.json

@@ -0,0 +1,30 @@
+{
+  "activation_dropout": 0.0,
+  "activation_function": "gelu",
+  "attention_dropout": 0.0,
+  "bos_token_id": 16385,
+  "d_model": 1024,
+  "decoder_attention_heads": 16,
+  "decoder_ffn_dim": 2730,
+  "decoder_layers": 12,
+  "decoder_start_token_id": 16384,
+  "dropout": 0.0,
+  "encoder_attention_heads": 16,
+  "encoder_ffn_dim": 2730,
+  "encoder_layers": 12,
+  "encoder_vocab_size": 50300,
+  "eos_token_id": 16385,
+  "gradient_checkpointing": false,
+  "image_length": 256,
+  "image_vocab_size": 16400,
+  "init_std": 0.02,
+  "is_encoder_decoder": true,
+  "max_text_length": 64,
+  "model_type": "dallebart",
+  "normalize_text": true,
+  "pad_token_id": 16385,
+  "scale_embedding": false,
+  "tie_word_embeddings": false,
+  "use_scan": false,
+  "use_cache": true
+}

tools/train/embeddings_retrain_preparation.ipynb

@@ -0,0 +1,1218 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "118UKH5bWCGa"
+   },
+   "source": [
+    "# DALL·E mini - Embedding Retrain Preparation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We'll start with the dalle-mini model for faster experimentation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "id": "K6CxW2o42f-w"
+   },
+   "outputs": [],
+   "source": [
+    "DALLE_MODEL = \"dalle-mini/dalle-mini/mini-1:v0\"  # can be wandb artifact or 🤗 Hub or local folder or google bucket\n",
+    "DALLE_COMMIT_ID = None\n",
+    "\n",
+    "# # dalle-mega\n",
+    "# DALLE_MODEL = \"dalle-mini/dalle-mini/mega-1-fp16:latest\"  # can be wandb artifact or 🤗 Hub or local folder or google bucket\n",
+    "# DALLE_COMMIT_ID = None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "id": "Yv-aR3t4Oe5v"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "8"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import jax\n",
+    "import jax.numpy as jnp\n",
+    "\n",
+    "# check how many devices are available\n",
+    "jax.local_device_count()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Load model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We load the model twice to keep a copy of the original parameters."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "id": "92zYmvsQ38vL"
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[34m\u001b[1mwandb\u001b[0m: Downloading large artifact mini-1:v0, 1673.43MB. 7 files... Done. 0:0:1.2\n",
+      "tcmalloc: large alloc 1751343104 bytes == 0x56011a2c0000 @  0x7f143aaa9680 0x7f143aaca824 0x5600d248253b 0x5600d24c30ba 0x5600d2599a58 0x5600d24f548d 0x5600d23cf328 0x5600d25af66d 0x5600d24f5825 0x5600d24532da 0x5600d24eafe3 0x5600d24ec709 0x5600d249a1ea 0x5600d252be7a 0x5600d24eafe3 0x5600d24ec709 0x5600d245273d 0x5600d24eafe3 0x5600d2597a7c 0x5600d24ebdbb 0x5600d25ce33e 0x5600d24f5571 0x5600d2452088 0x5600d24e07cb 0x5600d252f0fc 0x5600d24e07cb 0x5600d252f0fc 0x5600d24e07cb 0x5600d24f5f94 0x5600d24532da 0x5600d24ebbe4\n",
+      "\u001b[34m\u001b[1mwandb\u001b[0m: Downloading large artifact mini-1:v0, 1673.43MB. 7 files... Done. 0:0:1.2\n",
+      "tcmalloc: large alloc 1751343104 bytes == 0x56011a2c0000 @  0x7f143aaa9680 0x7f143aaca824 0x5600d248253b 0x5600d24c30ba 0x5600d2599a58 0x5600d24f548d 0x5600d23cf328 0x5600d25af66d 0x5600d24f5825 0x5600d24532da 0x5600d24eafe3 0x5600d24ec709 0x5600d249a1ea 0x5600d252be7a 0x5600d24eafe3 0x5600d24ec709 0x5600d245273d 0x5600d24eafe3 0x5600d2597a7c 0x5600d24ebdbb 0x5600d25ce33e 0x5600d24f5571 0x5600d2452088 0x5600d24e07cb 0x5600d252f0fc 0x5600d24e07cb 0x5600d252f0fc 0x5600d24e07cb 0x5600d24f5f94 0x5600d24532da 0x5600d24ebbe4\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Load model\n",
+    "from dalle_mini import DalleBart, DalleBartProcessor\n",
+    "\n",
+    "model, params = DalleBart.from_pretrained(\n",
+    "    DALLE_MODEL, revision=DALLE_COMMIT_ID, dtype=jnp.float16, _do_init=False\n",
+    ")\n",
+    "\n",
+    "_, params_original = DalleBart.from_pretrained(\n",
+    "    DALLE_MODEL, revision=DALLE_COMMIT_ID, dtype=jnp.float16, _do_init=False\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Model surgery: remove layers to be retrained"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's take a look at the params tree."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "437833712"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(x.size for x in jax.tree_leaves(params))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\n",
+      "  \"lm_head\": {\n",
+      "    \"kernel\": [\n",
+      "      1024,\n",
+      "      16385\n",
+      "    ]\n",
+      "  },\n",
+      "  \"model\": {\n",
+      "    \"decoder\": {\n",
+      "      \"embed_positions\": {\n",
+      "        \"embedding\": [\n",
+      "          256,\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"embed_tokens\": {\n",
+      "        \"embedding\": [\n",
+      "          16385,\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"final_ln\": {\n",
+      "        \"bias\": [\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"layernorm_embedding\": {\n",
+      "        \"bias\": [\n",
+      "          1024\n",
+      "        ],\n",
+      "        \"scale\": [\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"layers\": {\n",
+      "        \"FlaxBartDecoderLayers\": {\n",
+      "          \"FlaxBartAttention_0\": {\n",
+      "            \"k_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"out_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"q_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"v_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            }\n",
+      "          },\n",
+      "          \"FlaxBartAttention_1\": {\n",
+      "            \"k_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"out_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"q_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"v_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            }\n",
+      "          },\n",
+      "          \"GLU_0\": {\n",
+      "            \"Dense_0\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                2730\n",
+      "              ]\n",
+      "            },\n",
+      "            \"Dense_1\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                2730\n",
+      "              ]\n",
+      "            },\n",
+      "            \"Dense_2\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                2730,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"LayerNorm_0\": {\n",
+      "              \"bias\": [\n",
+      "                12,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"LayerNorm_1\": {\n",
+      "              \"bias\": [\n",
+      "                12,\n",
+      "                2730\n",
+      "              ]\n",
+      "            }\n",
+      "          },\n",
+      "          \"LayerNorm_0\": {\n",
+      "            \"bias\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ]\n",
+      "          },\n",
+      "          \"LayerNorm_1\": {\n",
+      "            \"bias\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ],\n",
+      "            \"scale\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ]\n",
+      "          },\n",
+      "          \"LayerNorm_2\": {\n",
+      "            \"bias\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ]\n",
+      "          },\n",
+      "          \"LayerNorm_3\": {\n",
+      "            \"bias\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ],\n",
+      "            \"scale\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ]\n",
+      "          }\n",
+      "        }\n",
+      "      }\n",
+      "    },\n",
+      "    \"encoder\": {\n",
+      "      \"embed_positions\": {\n",
+      "        \"embedding\": [\n",
+      "          64,\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"embed_tokens\": {\n",
+      "        \"embedding\": [\n",
+      "          50264,\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"final_ln\": {\n",
+      "        \"bias\": [\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"layernorm_embedding\": {\n",
+      "        \"bias\": [\n",
+      "          1024\n",
+      "        ],\n",
+      "        \"scale\": [\n",
+      "          1024\n",
+      "        ]\n",
+      "      },\n",
+      "      \"layers\": {\n",
+      "        \"FlaxBartEncoderLayers\": {\n",
+      "          \"FlaxBartAttention_0\": {\n",
+      "            \"k_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"out_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"q_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"v_proj\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                1024\n",
+      "              ]\n",
+      "            }\n",
+      "          },\n",
+      "          \"GLU_0\": {\n",
+      "            \"Dense_0\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                2730\n",
+      "              ]\n",
+      "            },\n",
+      "            \"Dense_1\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                1024,\n",
+      "                2730\n",
+      "              ]\n",
+      "            },\n",
+      "            \"Dense_2\": {\n",
+      "              \"kernel\": [\n",
+      "                12,\n",
+      "                2730,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"LayerNorm_0\": {\n",
+      "              \"bias\": [\n",
+      "                12,\n",
+      "                1024\n",
+      "              ]\n",
+      "            },\n",
+      "            \"LayerNorm_1\": {\n",
+      "              \"bias\": [\n",
+      "                12,\n",
+      "                2730\n",
+      "              ]\n",
+      "            }\n",
+      "          },\n",
+      "          \"LayerNorm_0\": {\n",
+      "            \"bias\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ]\n",
+      "          },\n",
+      "          \"LayerNorm_1\": {\n",
+      "            \"bias\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ],\n",
+      "            \"scale\": [\n",
+      "              12,\n",
+      "              1024\n",
+      "            ]\n",
+      "          }\n",
+      "        }\n",
+      "      }\n",
+      "    }\n",
+      "  }\n",
+      "}\n"
+     ]
+    }
+   ],
+   "source": [
+    "import json\n",
+    "\n",
+    "tree = jax.tree_map(lambda x: x.shape, params)\n",
+    "print(json.dumps(tree, indent=2))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We will remove or reinitialize:\n",
+    "- `lm_head`\n",
+    "- `model.decoder.embed_positions`\n",
+    "- `model.decoder.embed_tokens`\n",
+    "- `model.decoder.final_ln`\n",
+    "- `model.decoder.layernorm_embedding`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "del params[\"lm_head\"]\n",
+    "for layer in [\"embed_positions\", \"embed_tokens\", \"final_ln\", \"layernorm_embedding\"]:\n",
+    "    del params[\"model\"][\"decoder\"][layer]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'model': {'decoder': {'layers': {'FlaxBartDecoderLayers': {'FlaxBartAttention_0': {'k_proj': {'kernel': (12,\n",
+       "        1024,\n",
+       "        1024)},\n",
+       "      'out_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'q_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'v_proj': {'kernel': (12, 1024, 1024)}},\n",
+       "     'FlaxBartAttention_1': {'k_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'out_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'q_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'v_proj': {'kernel': (12, 1024, 1024)}},\n",
+       "     'GLU_0': {'Dense_0': {'kernel': (12, 1024, 2730)},\n",
+       "      'Dense_1': {'kernel': (12, 1024, 2730)},\n",
+       "      'Dense_2': {'kernel': (12, 2730, 1024)},\n",
+       "      'LayerNorm_0': {'bias': (12, 1024)},\n",
+       "      'LayerNorm_1': {'bias': (12, 2730)}},\n",
+       "     'LayerNorm_0': {'bias': (12, 1024)},\n",
+       "     'LayerNorm_1': {'bias': (12, 1024), 'scale': (12, 1024)},\n",
+       "     'LayerNorm_2': {'bias': (12, 1024)},\n",
+       "     'LayerNorm_3': {'bias': (12, 1024), 'scale': (12, 1024)}}}},\n",
+       "  'encoder': {'embed_positions': {'embedding': (64, 1024)},\n",
+       "   'embed_tokens': {'embedding': (50264, 1024)},\n",
+       "   'final_ln': {'bias': (1024,)},\n",
+       "   'layernorm_embedding': {'bias': (1024,), 'scale': (1024,)},\n",
+       "   'layers': {'FlaxBartEncoderLayers': {'FlaxBartAttention_0': {'k_proj': {'kernel': (12,\n",
+       "        1024,\n",
+       "        1024)},\n",
+       "      'out_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'q_proj': {'kernel': (12, 1024, 1024)},\n",
+       "      'v_proj': {'kernel': (12, 1024, 1024)}},\n",
+       "     'GLU_0': {'Dense_0': {'kernel': (12, 1024, 2730)},\n",
+       "      'Dense_1': {'kernel': (12, 1024, 2730)},\n",
+       "      'Dense_2': {'kernel': (12, 2730, 1024)},\n",
+       "      'LayerNorm_0': {'bias': (12, 1024)},\n",
+       "      'LayerNorm_1': {'bias': (12, 2730)}},\n",
+       "     'LayerNorm_0': {'bias': (12, 1024)},\n",
+       "     'LayerNorm_1': {'bias': (12, 1024), 'scale': (12, 1024)}}}}}}"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "jax.tree_map(lambda x: x.shape, params)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "404012016"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(x.size for x in jax.tree_leaves(params))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Reinitialize layers"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We save a checkpoint and reload it again. It does not automatically reinitialize the missing keys, but it sets `_missing_keys` appropriately so we can initialize them later. We could do the same by simply setting that property ourselves, but I'll refrain from doing so because it's a private implementation detail."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "trimmed_checkpoint = \"mini-trimmed\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "tcmalloc: large alloc 1610424320 bytes == 0x5632d11c8000 @  0x7f95ccad0680 0x7f95ccaf0bdd 0x7f95be99e29f 0x7f95be9a7750 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a4fc4 0x7f95be9a571e 0x5630fb630f94 0x5630fb58e2da 0x5630fb625fe3 0x5630fb626d24 0x5630fb58d73d 0x5630fb625fe3 0x5630fb626d24 0x5630fb58d73d 0x5630fb626be4 0x5630fb58d088 0x5630fb625fe3 0x5630fb627709 0x5630fb58d73d 0x5630fb625fe3 0x5630fb6d2a7c 0x5630fb626dbb 0x5630fb70933e 0x5630fb630571\n",
+      "tcmalloc: large alloc 3231449088 bytes == 0x56333119a000 @  0x7f95ccad0680 0x7f95ccaf0bdd 0x7f95be99e29f 0x7f95be9a7750 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a4fc4 0x7f95be9a571e 0x5630fb630f94 0x5630fb58e2da 0x5630fb625fe3 0x5630fb626d24 0x5630fb58d73d 0x5630fb625fe3 0x5630fb626d24 0x5630fb58d73d 0x5630fb626be4 0x5630fb58d088 0x5630fb625fe3 0x5630fb627709 0x5630fb58d73d 0x5630fb625fe3 0x5630fb6d2a7c 0x5630fb626dbb 0x5630fb70933e 0x5630fb630571\n"
+     ]
+    }
+   ],
+   "source": [
+    "model.save_pretrained(trimmed_checkpoint, params=params)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "The checkpoint mini-trimmed is missing required keys: {('model', 'decoder', 'embed_tokens', 'embedding'), ('lm_head', 'kernel'), ('model', 'decoder', 'embed_positions', 'embedding'), ('model', 'decoder', 'final_ln', 'bias'), ('model', 'decoder', 'layernorm_embedding', 'scale'), ('model', 'decoder', 'layernorm_embedding', 'bias')}. Make sure to call model.init_weights to initialize the missing weights.\n",
+      "Some weights of DalleBart were not initialized from the model checkpoint at mini-trimmed and are newly initialized: {('model', 'decoder', 'embed_tokens', 'embedding'), ('lm_head', 'kernel'), ('model', 'decoder', 'embed_positions', 'embedding'), ('model', 'decoder', 'final_ln', 'bias'), ('model', 'decoder', 'layernorm_embedding', 'scale'), ('model', 'decoder', 'layernorm_embedding', 'bias')}\n",
+      "You should probably TRAIN this model on a down-stream task to be able to use it for predictions and inference.\n"
+     ]
+    }
+   ],
+   "source": [
+    "model, params = DalleBart.from_pretrained(\n",
+    "    trimmed_checkpoint, revision=None, dtype=jnp.float16, _do_init=False\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{('lm_head', 'kernel'),\n",
+       " ('model', 'decoder', 'embed_positions', 'embedding'),\n",
+       " ('model', 'decoder', 'embed_tokens', 'embedding'),\n",
+       " ('model', 'decoder', 'final_ln', 'bias'),\n",
+       " ('model', 'decoder', 'layernorm_embedding', 'bias'),\n",
+       " ('model', 'decoder', 'layernorm_embedding', 'scale')}"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "model._missing_keys"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "params_reinit = model.init_weights(model.key, model.input_shape, params=params)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Verification"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The structure should be the same as the original `params` dict. Re-initialized layers should have different parameters, but existing layers should be the same."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "FrozenDict({\n",
+       "    lm_head: {\n",
+       "        kernel: (1024, 16385),\n",
+       "    },\n",
+       "    model: {\n",
+       "        decoder: {\n",
+       "            embed_positions: {\n",
+       "                embedding: (256, 1024),\n",
+       "            },\n",
+       "            embed_tokens: {\n",
+       "                embedding: (16385, 1024),\n",
+       "            },\n",
+       "            final_ln: {\n",
+       "                bias: (1024,),\n",
+       "            },\n",
+       "            layernorm_embedding: {\n",
+       "                bias: (1024,),\n",
+       "                scale: (1024,),\n",
+       "            },\n",
+       "            layers: {\n",
+       "                FlaxBartDecoderLayers: {\n",
+       "                    FlaxBartAttention_0: {\n",
+       "                        k_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        out_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        q_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        v_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                    },\n",
+       "                    FlaxBartAttention_1: {\n",
+       "                        k_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        out_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        q_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        v_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                    },\n",
+       "                    GLU_0: {\n",
+       "                        Dense_0: {\n",
+       "                            kernel: (12, 1024, 2730),\n",
+       "                        },\n",
+       "                        Dense_1: {\n",
+       "                            kernel: (12, 1024, 2730),\n",
+       "                        },\n",
+       "                        Dense_2: {\n",
+       "                            kernel: (12, 2730, 1024),\n",
+       "                        },\n",
+       "                        LayerNorm_0: {\n",
+       "                            bias: (12, 1024),\n",
+       "                        },\n",
+       "                        LayerNorm_1: {\n",
+       "                            bias: (12, 2730),\n",
+       "                        },\n",
+       "                    },\n",
+       "                    LayerNorm_0: {\n",
+       "                        bias: (12, 1024),\n",
+       "                    },\n",
+       "                    LayerNorm_1: {\n",
+       "                        bias: (12, 1024),\n",
+       "                        scale: (12, 1024),\n",
+       "                    },\n",
+       "                    LayerNorm_2: {\n",
+       "                        bias: (12, 1024),\n",
+       "                    },\n",
+       "                    LayerNorm_3: {\n",
+       "                        bias: (12, 1024),\n",
+       "                        scale: (12, 1024),\n",
+       "                    },\n",
+       "                },\n",
+       "            },\n",
+       "        },\n",
+       "        encoder: {\n",
+       "            embed_positions: {\n",
+       "                embedding: (64, 1024),\n",
+       "            },\n",
+       "            embed_tokens: {\n",
+       "                embedding: (50264, 1024),\n",
+       "            },\n",
+       "            final_ln: {\n",
+       "                bias: (1024,),\n",
+       "            },\n",
+       "            layernorm_embedding: {\n",
+       "                bias: (1024,),\n",
+       "                scale: (1024,),\n",
+       "            },\n",
+       "            layers: {\n",
+       "                FlaxBartEncoderLayers: {\n",
+       "                    FlaxBartAttention_0: {\n",
+       "                        k_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        out_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        q_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                        v_proj: {\n",
+       "                            kernel: (12, 1024, 1024),\n",
+       "                        },\n",
+       "                    },\n",
+       "                    GLU_0: {\n",
+       "                        Dense_0: {\n",
+       "                            kernel: (12, 1024, 2730),\n",
+       "                        },\n",
+       "                        Dense_1: {\n",
+       "                            kernel: (12, 1024, 2730),\n",
+       "                        },\n",
+       "                        Dense_2: {\n",
+       "                            kernel: (12, 2730, 1024),\n",
+       "                        },\n",
+       "                        LayerNorm_0: {\n",
+       "                            bias: (12, 1024),\n",
+       "                        },\n",
+       "                        LayerNorm_1: {\n",
+       "                            bias: (12, 2730),\n",
+       "                        },\n",
+       "                    },\n",
+       "                    LayerNorm_0: {\n",
+       "                        bias: (12, 1024),\n",
+       "                    },\n",
+       "                    LayerNorm_1: {\n",
+       "                        bias: (12, 1024),\n",
+       "                        scale: (12, 1024),\n",
+       "                    },\n",
+       "                },\n",
+       "            },\n",
+       "        },\n",
+       "    },\n",
+       "})"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "jax.tree_map(lambda x: x.shape, params_reinit)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "FrozenDict({\n",
+       "    embedding: DeviceArray([[ 0.00582082, -0.04113895,  0.00918633, ..., -0.00530822,\n",
+       "                   0.01297319,  0.02720674],\n",
+       "                 [ 0.03540739,  0.03676804, -0.02924041, ...,  0.00163185,\n",
+       "                  -0.01938273, -0.02105987],\n",
+       "                 [ 0.00478452, -0.03438002, -0.0024974 , ..., -0.03892584,\n",
+       "                   0.01721252,  0.02605445],\n",
+       "                 ...,\n",
+       "                 [ 0.02495495,  0.00559381, -0.01588043, ...,  0.01393714,\n",
+       "                  -0.01824111, -0.02007291],\n",
+       "                 [ 0.00983252, -0.00180564, -0.01686333, ..., -0.01001718,\n",
+       "                   0.01886345, -0.00393983],\n",
+       "                 [-0.03589988, -0.00455565,  0.00076276, ..., -0.02145007,\n",
+       "                  -0.00180798, -0.0133148 ]], dtype=float32),\n",
+       "})"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "params_reinit[\"model\"][\"decoder\"][\"embed_positions\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(DeviceArray(-0.09320386, dtype=float32),\n",
+       " DeviceArray(0.08769083, dtype=float32))"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "embedding_new = params_reinit[\"model\"][\"decoder\"][\"embed_positions\"][\"embedding\"]\n",
+    "embedding_new.min(), embedding_new.max()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'embedding': DeviceArray([[ 0.03459017, -0.0065838 , -0.11748601, ..., -0.01451578,\n",
+       "               -0.03927238, -0.00266367],\n",
+       "              [-0.03116009,  0.00438436,  0.02691377, ..., -0.02886203,\n",
+       "               -0.01095741, -0.02649871],\n",
+       "              [-0.03568491, -0.0086962 ,  0.01851564, ..., -0.04736514,\n",
+       "                0.05310551, -0.01648099],\n",
+       "              ...,\n",
+       "              [-0.02454913,  0.03746822, -0.02269235, ...,  0.03377315,\n",
+       "                0.003004  ,  0.04975331],\n",
+       "              [-0.05145862,  0.04472217,  0.11103845, ...,  0.04581303,\n",
+       "                0.02850476,  0.00554514],\n",
+       "              [-0.01037806,  0.00281054, -0.0485299 , ..., -0.03325456,\n",
+       "               -0.0058979 ,  0.01733843]], dtype=float32)}"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "params_original[\"model\"][\"decoder\"][\"embed_positions\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(DeviceArray(-0.25866088, dtype=float32),\n",
+       " DeviceArray(0.08769083, dtype=float32))"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "embedding_original = params_original[\"model\"][\"decoder\"][\"embed_positions\"][\"embedding\"]\n",
+    "embedding_original.min(), embedding_new.max()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assert jnp.allclose(embedding_new, embedding_original).item() == False"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "lm_head_original = params_original[\"lm_head\"][\"kernel\"]\n",
+    "lm_head_reinit = params_reinit[\"lm_head\"][\"kernel\"]\n",
+    "assert jnp.allclose(lm_head_reinit, lm_head_original).item() == False"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assert jnp.allclose(\n",
+    "    params_reinit[\"model\"][\"encoder\"][\"layers\"][\"FlaxBartEncoderLayers\"][\n",
+    "        \"FlaxBartAttention_0\"\n",
+    "    ][\"k_proj\"][\"kernel\"],\n",
+    "    params_original[\"model\"][\"encoder\"][\"layers\"][\"FlaxBartEncoderLayers\"][\n",
+    "        \"FlaxBartAttention_0\"\n",
+    "    ][\"k_proj\"][\"kernel\"],\n",
+    ").item()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Save checkpoint for retrain"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Finally, we save the resulting model to retrain those layers."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "checkpoint_dir = \"mini-reinit\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "tcmalloc: large alloc 3367796736 bytes == 0x5633f235a000 @  0x7f95ccad0680 0x7f95ccaf0bdd 0x7f95be99e29f 0x7f95be9a7750 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a87b4 0x7f95be9a4fc4 0x7f95be9a571e 0x5630fb630f94 0x5630fb58e2da 0x5630fb625fe3 0x5630fb626d24 0x5630fb58d73d 0x5630fb625fe3 0x5630fb626d24 0x5630fb58d73d 0x5630fb626be4 0x5630fb58d088 0x5630fb625fe3 0x5630fb627709 0x5630fb58d73d 0x5630fb625fe3 0x5630fb6d2a7c 0x5630fb626dbb 0x5630fb70933e 0x5630fb630571\n"
+     ]
+    }
+   ],
+   "source": [
+    "model.save_pretrained(checkpoint_dir, params=params_reinit)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Upload checkpoint to W&B"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import wandb\n",
+    "from pathlib import Path"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\u001b[34m\u001b[1mwandb\u001b[0m: Currently logged in as: \u001b[33mpcuenq\u001b[0m (\u001b[33mdalle-mini\u001b[0m). Use \u001b[1m`wandb login --relogin`\u001b[0m to force relogin\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "Tracking run with wandb version 0.12.21"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "Run data is saved locally in <code>/home/pedro/code/dalle-mini/dalle-mini/tools/train/wandb/run-20220722_105625-2v9szi3q</code>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "Syncing run <strong><a href=\"https://wandb.ai/dalle-mini/dalle-mini/runs/2v9szi3q\" target=\"_blank\">astral-durian-2957</a></strong> to <a href=\"https://wandb.ai/dalle-mini/dalle-mini\" target=\"_blank\">Weights & Biases</a> (<a href=\"https://wandb.me/run\" target=\"_blank\">docs</a>)<br/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<button onClick=\"this.nextSibling.style.display='block';this.style.display='none';\">Display W&B run</button><iframe src=\"https://wandb.ai/dalle-mini/dalle-mini/runs/2v9szi3q?jupyter=true\" style=\"border:none;width:100%;height:420px;display:none;\"></iframe>"
+      ],
+      "text/plain": [
+       "<wandb.sdk.wandb_run.Run at 0x7f959a563b80>"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wandb.init(\n",
+    "    entity=\"dalle-mini\",\n",
+    "    project=\"dalle-mini\",\n",
+    "    job_type=\"Seq2Seq\",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "artifact = wandb.Artifact(\n",
+    "    name=f\"model-{wandb.run.id}\",\n",
+    "    type=\"DalleBart_model\",\n",
+    "    metadata={\"embeddings\": \"reset\"},\n",
+    ")\n",
+    "\n",
+    "for filename in [\"config.json\", \"flax_model.msgpack\"]:\n",
+    "    artifact.add_file(f\"{Path(checkpoint_dir) / filename}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<wandb.sdk.wandb_artifacts.Artifact at 0x7f95984c3fd0>"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "wandb.run.log_artifact(artifact)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "Waiting for W&B process to finish... <strong style=\"color:green\">(success).</strong>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "VBox(children=(Label(value='1670.207 MB of 1670.207 MB uploaded (0.000 MB deduped)\\r'), FloatProgress(value=1.…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "Synced <strong style=\"color:#cdcd00\">astral-durian-2957</strong>: <a href=\"https://wandb.ai/dalle-mini/dalle-mini/runs/2v9szi3q\" target=\"_blank\">https://wandb.ai/dalle-mini/dalle-mini/runs/2v9szi3q</a><br/>Synced 5 W&B file(s), 0 media file(s), 2 artifact file(s) and 0 other file(s)"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "Find logs at: <code>./wandb/run-20220722_105625-2v9szi3q/logs</code>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "wandb.finish()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "----"
+   ]
+  }
+ ],
+ "metadata": {
+  "accelerator": "GPU",
+  "colab": {
+   "collapsed_sections": [],
+   "include_colab_link": true,
+   "machine_shape": "hm",
+   "name": "DALL·E mini - Inference pipeline.ipynb",
+   "provenance": []
+  },
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}

tools/train/scalable_shampoo/README.md

@@ -0,0 +1,7 @@
+# Notes
+
+Files copied from [google-research/scalable_shampoo/optax](https://github.com/google-research/google-research/tree/master/scalable_shampoo/optax).
+
+Imports have been modified to be relative.
+
+This will eventually be replaced with `optax-shampoo` package.

tools/train/scalable_shampoo/distributed_shampoo.py

@@ -0,0 +1,2452 @@
+# coding=utf-8
+# Copyright 2022 The Google Research Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# An implementation of distributed Shampoo optimizer from:
+#
+#  Scalable Second Order Optimization for Deep Learning
+#  Rohan Anil, Vineet Gupta, Tomer Koren, Kevin Regan, Yoram Singer
+#  Preprint Paper: https://arxiv.org/abs/2002.09018
+#
+# This implementation moves computation of inverse pth root back to the
+# accelerator (if higher precision is available).
+#
+# Authors: Rohan Anil (rohananil at google dot com)
+#          Vineet Gupta (vineet at google dot com)
+#          James Lottes (jlottes at google dot com)
+#          Anudhyan Boral (anudhyan at google dot com)
+#
+"""Distributed Shampoo Implementation."""
+
+import enum
+import functools
+import itertools
+from typing import Any, Callable, List, NamedTuple, Optional, Tuple, Union
+
+import chex
+import jax
+import jax.numpy as jnp
+import numpy as np
+import optax
+from absl import logging
+from flax import struct
+from jax import lax
+from jax.experimental import pjit
+from jax.experimental.sparse import linalg
+
+from .quantization_utils import QuantizedValue
+from .symmetric_matrices import symmetric_matrices
+
+# Dtype for inverse-pth root routine
+# Switch to f64 if you have hardware that supports it. Enable the jax flag
+# jax_enable_x64 for this to work, otherwise it will default to float32.
+_MAT_INV_PTH_ROOT_DTYPE = jnp.float64
+
+
+@struct.dataclass
+class TrainingMetrics:
+    inverse_pth_root_errors: chex.Array  # Error for inverse-pth roots.
+    # TODO(rohananil): Add more important metrics to track during training.
+
+
+# Per parameter optimizer state used in data-parallel training.
+class ParameterStats(NamedTuple):
+    """State associated to each parameter of the model being trained."""
+
+    diagonal_statistics: QuantizedValue  # Accumulator for diagonal preconditioner
+    statistics: List[Any]  # Statistics (QuantizedValue, chex.Array)
+    preconditioners: List[Any]  # Preconditioners (QuantizedValue, chex.Array)
+    diagonal_momentum: QuantizedValue  # Momentum for the diagonal preconditioner
+    momentum: QuantizedValue  # Momentum for the shampoo preconditioner
+    training_metrics: TrainingMetrics  # Metrics (optional for training).
+
+
+# For training extremely large model; We keep a global state with a concatenated
+# statistics and preconditioner states for all vars. This is so that we can
+# annotate the leading axis to be sharded to save memory at the cost of
+# communication.
+@struct.dataclass
+class GlobalShardedParameterStats:
+    statistics: chex.Array  # Statistics
+    preconditioners: chex.Array  # Preconditioners
+    exponents: chex.Array  # exponents
+
+
+# These are per-parameter local states; All statistics here mirror the parameter
+# Thus the sharding is copied over from the param specification.
+@struct.dataclass
+class LocalShardedParameterStats:
+    """State associated to each parameter of the model being trained."""
+
+    diagonal_statistics: QuantizedValue  # Accumulator for diagonal preconditioner
+    diagonal_momentum: QuantizedValue  # Momentum for the diagonal preconditioner
+    momentum: QuantizedValue  # Momentum for the shampoo preconditioner
+    training_metrics: TrainingMetrics  # Metrics (optional for training).
+    index_start: np.int32 = struct.field(
+        pytree_node=False
+    )  # Index into global statistics array
+    sizes: Any = struct.field(pytree_node=False)  # Sizes of the statistics.
+
+
+def init_training_metrics(num_statistics):
+    # Since the downstream apis expect a jnp.array - we create a dummy one if
+    # num_statistics=0.
+    if not num_statistics:
+        return TrainingMetrics(jnp.array(0, jnp.float32))
+    else:
+        return TrainingMetrics(jnp.zeros([num_statistics], jnp.float32))
+
+
+def init_training_metrics_shapes(num_statistics):
+    # Since the downstream apis expect a jnp.array - we create a dummy one if
+    # num_statistics=0.
+    if not num_statistics:
+        return TrainingMetrics([[], jnp.float32])
+    else:
+        return TrainingMetrics([[num_statistics], jnp.float32])
+
+
+def init_training_metrics_pspec():
+    return TrainingMetrics(pjit.PartitionSpec())
+
+
+class ShardedShampooStats(NamedTuple):
+    """Shampoo state in sharded mode."""
+
+    global_stats: Any
+    local_stats: Any
+
+
+class ShampooState(NamedTuple):
+    count: chex.Array
+    stats: Any
+
+
+class InitFnState(NamedTuple):
+    init_fn: Any
+    pspec_fn: Any
+    shape_and_dtype_fn: Any
+
+
+class GraftingType(enum.IntEnum):
+    SGD = 1
+    ADAGRAD = 2
+    RMSPROP = 3
+    RMSPROP_NORMALIZED = 4
+    SQRT_N = 5
+    ADAGRAD_NORMALIZED = 6
+
+
+class PreconditionerType(enum.IntEnum):
+    # Default, computes preconditioner for each dim
+    ALL = 1
+    # One sided Shampoo, in this cases only on input dim.
+    # Assumes last dim is always the output dim and everything else input dim.
+    INPUT = 2
+
+
+def power_iteration(
+    matrix,
+    num_iters=100,
+    error_tolerance=1e-6,
+    precision=lax.Precision.HIGHEST,
+):
+    r"""Power iteration algorithm.
+
+    The power iteration algorithm takes a symmetric PSD matrix `A`, and produces
+    a scalar `\lambda` , which is the greatest (in absolute value) eigenvalue
+    of `A`, and a vector v, which is the corresponding eigenvector of `A`.
+
+    References:
+      [Wikipedia, 2021](https://en.wikipedia.org/wiki/Power_iteration)
+
+    Args:
+      matrix: the symmetric PSD matrix.
+      num_iters: Number of iterations.
+      error_tolerance: Iterative exit condition.
+      precision: precision XLA related flag, the available options are: a)
+        lax.Precision.DEFAULT (better step time, but not precise) b)
+        lax.Precision.HIGH (increased precision, slower) c) lax.Precision.HIGHEST
+        (best possible precision, slowest)
+
+    Returns:
+      eigen vector, eigen value
+    """
+    matrix_size = matrix.shape[-1]
+
+    def _iter_condition(state):
+        i, unused_v, unused_s, unused_s_v, run_step = state
+        return jnp.logical_and(i < num_iters, run_step)
+
+    def _iter_body(state):
+        """One step of power iteration."""
+        i, new_v, s, s_v, unused_run_step = state
+        new_v = new_v / jnp.linalg.norm(new_v)
+
+        s_v = jnp.einsum("ij,j->i", matrix, new_v, precision=precision)
+        s_new = jnp.einsum("i,i->", new_v, s_v, precision=precision)
+        return (
+            i + 1,
+            s_v,
+            s_new,
+            s_v,
+            jnp.greater(jnp.abs(s_new - s), error_tolerance),
+        )
+
+    # Figure out how to use step as seed for random.
+    v_0 = (
+        np.random.RandomState(1729).uniform(-1.0, 1.0, matrix_size).astype(matrix.dtype)
+    )
+
+    init_state = tuple([0, v_0, jnp.zeros([], dtype=matrix.dtype), v_0, True])
+    _, v_out, s_out, _, _ = lax.while_loop(_iter_condition, _iter_body, init_state)
+    v_out = v_out / jnp.linalg.norm(v_out)
+    return v_out, s_out
+
+
+def mat_power(
+    mat_m,
+    p,
+    precision=lax.Precision.HIGHEST,
+):
+    """A simple matrix power method. M^p where p can be TracedValue."""
+    power = jnp.eye(mat_m.shape[0], dtype=_MAT_INV_PTH_ROOT_DTYPE)
+
+    def _iter_condition(state):
+        i, _, _ = state
+        return i > 0
+
+    def _iter_body(state):
+        i, power, mat = state
+
+        power = jax.lax.cond(
+            i % 2 == 1,
+            lambda: jnp.matmul(mat, power, precision=precision),
+            lambda: power,
+        )
+        i //= 2
+        mat = jnp.matmul(mat, mat, precision=precision)
+        return i, power, mat
+
+    _, result, _ = lax.while_loop(_iter_condition, _iter_body, (p, power, mat_m))
+    return result
+
+
+def _pth_root_difference(w, alpha, beta, p):
+    """Computes (w+alpha)^(-1/p)-(w+beta)^(-1/p)."""
+
+    a = w + alpha
+    b = w + beta
+    a_minus_b = alpha - beta
+    exp = -1 / p
+
+    def _stable_subtract(b, a_minus_b):
+        # Mathematically identical to the target expression, with (w+beta)^(-1/p)
+        # term factored out and w cancellation in the subtraction.
+        return (b**exp) * jnp.expm1(exp * jnp.log1p(a_minus_b / b))
+
+    return jnp.where(
+        # Choose the branch with the best log1p approximation.
+        jnp.abs(a_minus_b / b) < jnp.abs(a_minus_b / a),
+        -_stable_subtract(a, -a_minus_b),
+        _stable_subtract(b, a_minus_b),
+    )
+
+
+def matrix_inverse_pth_root(
+    matrix,
+    p,
+    num_iters=100,
+    ridge_epsilon=1e-6,
+    error_tolerance=1e-6,
+    precision=lax.Precision.HIGHEST,
+    relative_matrix_epsilon=True,
+    lobpcg_topk_precondition=0,
+    lobpcg_max_iter=0,
+):
+    """Computes `matrix^(-1/p)`, where `p` is a positive integer.
+
+    This function uses the Coupled newton iterations algorithm for
+    the computation of a matrix's inverse pth root.
+
+
+    References:
+      [Functions of Matrices, Theory and Computation,
+       Nicholas J Higham, Pg 184, Eq 7.18](
+       https://epubs.siam.org/doi/book/10.1137/1.9780898717778)
+
+    Args:
+      matrix: the symmetric PSD matrix whose power it to be computed
+      p: exponent, for p a positive integer.
+      num_iters: Maximum number of iterations.
+      ridge_epsilon: Ridge epsilon added to make the matrix positive definite.
+      error_tolerance: Error indicator, useful for early termination.
+      precision: precision XLA related flag, the available options are: a)
+        lax.Precision.DEFAULT (better step time, but not precise) b)
+        lax.Precision.HIGH (increased precision, slower) c) lax.Precision.HIGHEST
+        (best possible precision, slowest)
+      relative_matrix_epsilon: Whether to use relative epsilon to the max eigen
+        value when computing inverse-pth root.
+      lobpcg_topk_precondition: If nonzero, specifies the number of top
+        eigenvectors to subtract out before performing LOBPCG. Note this makes
+        relative_matrix_epsilon essentially free.
+      lobpcg_max_iter: Maximum iteration count for LOBPCG, defaults to
+        `lobpcg_topk_precondition`.
+
+    Returns:
+      matrix^(-1/p) and the error
+    """
+
+    # If the input is not square, materialize it from the concatenated form.
+    if matrix.shape[0] != matrix.shape[1]:
+        matrix = symmetric_matrices.materialize_matrix_from_concat(matrix)
+
+    assert matrix.shape[0] == matrix.shape[1]
+
+    # We use _MAT_INV_PTH_ROOT_DTYPE for the matrix inverse pth root.
+    # Switch to f64 if you have hardware that supports it. Enable the jax flag
+    # jax_enable_x64 for this to work.
+    matrix_size = matrix.shape[0]
+    orig_dtype = matrix.dtype
+    matrix = matrix.astype(_MAT_INV_PTH_ROOT_DTYPE)
+    alpha = jnp.asarray(-1.0 / p, _MAT_INV_PTH_ROOT_DTYPE)
+    identity = jnp.eye(matrix_size, dtype=_MAT_INV_PTH_ROOT_DTYPE)
+    original_matrix = matrix
+
+    if lobpcg_topk_precondition > 0:
+        # TODO(vladf): reuse previous top-k as the initial search directions
+        pad_shape = (matrix_size - lobpcg_topk_precondition, lobpcg_topk_precondition)
+        search_dirs = jnp.concatenate(
+            (jnp.eye(lobpcg_topk_precondition), jnp.zeros(pad_shape)), axis=0
+        )
+        eigvals, eigvecs, actual_iters = linalg.lobpcg_standard(
+            matrix,
+            search_dirs,
+            lobpcg_topk_precondition if lobpcg_max_iter == 0 else lobpcg_max_iter,
+        )
+        del actual_iters  # TODO(vladf): return diagnostics dictionary
+
+        # The minimal eigenvalue among top-k becomes the maximal one in the whole
+        # matrix after deflation.
+        max_ev = jnp.min(eigvals)
+        deflation = eigvals - max_ev
+        scaled_vecs = eigvecs * jnp.sqrt(deflation)
+
+        # Deflate out top eigenvectors to reduce matrix condition number.
+        matrix -= scaled_vecs.dot(scaled_vecs.T, precision=jax.lax.Precision.HIGHEST)
+
+    # Only use power iteration if lobpcg wasn't already used to derive the
+    # top eigenvalue.
+    elif relative_matrix_epsilon:
+        _, max_ev = power_iteration(
+            matrix=matrix, num_iters=100, error_tolerance=1e-6, precision=precision
+        )
+        eigvals, eigvecs = None, None  # Unused but required by pytype.
+
+    # Use absolute matrix epsilon scaling otherwise.
+    else:
+        max_ev = 1.0
+        eigvals, eigvecs = None, None  # Unused but required by pytype.
+
+    ridge_epsilon = ridge_epsilon * jnp.maximum(max_ev, 1e-6)
+
+    def _iter_condition(state):
+        (i, unused_mat_m, unused_mat_h, unused_old_mat_h, error, run_step) = state
+        error_above_threshold = jnp.logical_and(error > error_tolerance, run_step)
+        return jnp.logical_and(i < num_iters, error_above_threshold)
+
+    def _iter_body(state):
+        (i, mat_m, mat_h, unused_old_mat_h, error, unused_run_step) = state
+        mat_m_i = (1 - alpha) * identity + alpha * mat_m
+        new_mat_m = jnp.matmul(mat_power(mat_m_i, p), mat_m, precision=precision)
+        new_mat_h = jnp.matmul(mat_h, mat_m_i, precision=precision)
+        new_error = jnp.max(jnp.abs(new_mat_m - identity))
+        # sometimes error increases after an iteration before decreasing and
+        # converging. 1.2 factor is used to bound the maximal allowed increase.
+        return (i + 1, new_mat_m, new_mat_h, mat_h, new_error, new_error < error * 1.2)
+
+    if matrix_size == 1:
+        resultant_mat_h = (matrix + ridge_epsilon) ** alpha
+        error = jnp.array(0, jnp.float32)
+    else:
+        damped_matrix = matrix + ridge_epsilon * identity
+
+        z = (1 + p) / (2 * jnp.linalg.norm(damped_matrix))
+        new_mat_m_0 = damped_matrix * z
+        new_error = jnp.max(jnp.abs(new_mat_m_0 - identity))
+        new_mat_h_0 = identity * jnp.power(z, 1.0 / p)
+        init_state = tuple([0, new_mat_m_0, new_mat_h_0, new_mat_h_0, new_error, True])
+        _, mat_m, mat_h, old_mat_h, error, convergence = lax.while_loop(
+            _iter_condition, _iter_body, init_state
+        )
+        error = jnp.max(jnp.abs(mat_m - identity)).astype(jnp.float32)
+        is_converged = jnp.asarray(convergence, old_mat_h.dtype)
+        resultant_mat_h = is_converged * mat_h + (1 - is_converged) * old_mat_h
+        resultant_mat_h = jnp.asarray(resultant_mat_h, orig_dtype)
+
+    if lobpcg_topk_precondition > 0:
+        # Since we deflated the top eigenvectors prior to p-th root inverse,
+        # the resultant matrix has larger eigenvalues associated with those
+        # same eigenvectors, which we need to now re-deflate.
+        #
+        # Note that _pth_root_difference returns positive values for this
+        # particular argument ordering as min(eigvals) <= eigvals for the
+        # jnp.sqrt below.
+        pth_diff = _pth_root_difference(ridge_epsilon, jnp.min(eigvals), eigvals, p)
+        scaled_vecs = eigvecs * jnp.sqrt(pth_diff)
+        resultant_mat_h = (
+            resultant_mat_h.astype(scaled_vecs.dtype)
+            - scaled_vecs.dot(scaled_vecs.T, precision=jax.lax.Precision.HIGHEST)
+        ).astype(orig_dtype)
+        mat_m = jnp.matmul(
+            mat_power(resultant_mat_h, p),
+            original_matrix,
+            precision=jax.lax.Precision.HIGHEST,
+        )
+        error = jnp.max(jnp.abs(mat_m - identity)).astype(jnp.float32)
+
+    return resultant_mat_h, error
+
+
+def merge_small_dims(shape_to_merge, max_dim):
+    """Merge small dimensions.
+
+    If there are some small dimensions, we collapse them:
+    e.g. [1, 2, 512, 1, 2048, 1, 3, 4] --> [1024, 2048, 12] if max_dim = 1024
+         [1, 2, 768, 1, 2048] --> [2, 768, 2048]
+
+    Args:
+      shape_to_merge: Shape to merge small dimensions.
+      max_dim: Maximal dimension of output shape used in merging.
+
+    Returns:
+      Merged shape.
+    """
+    if shape_to_merge and np.all(np.array(shape_to_merge) == 1):
+        return [1]
+
+    resulting_shape = []
+    product = 1
+    for d in shape_to_merge:
+        if product * d <= max_dim:
+            product *= d
+        else:
+            if product > 1:
+                resulting_shape.append(product)
+            product = d
+    if product > 1:
+        resulting_shape.append(product)
+    return resulting_shape
+
+
+def pad_square_matrix(mat, max_size):
+    """Pad a square matrix up to max_size.
+
+    Args:
+      mat: a matrix to pad.
+      max_size: matrix size requested.
+
+    Returns:
+      Given M returns [[M, 0], [0, I]]
+    """
+    rows, cols = mat.shape
+    if rows != cols:
+        raise ValueError(
+            f"Must have rows == cols, instead got rows={rows}, cols={cols}"
+        )
+    if cols > max_size:
+        raise ValueError(
+            f"Must have cols <= max_size. Instead got cols={cols}, max_size={max_size}."
+        )
+    if rows == max_size:
+        return mat
+    pad_size = max_size - rows
+
+    zs1 = jnp.zeros([rows, pad_size], dtype=mat.dtype)
+    zs2 = jnp.zeros([pad_size, rows], dtype=mat.dtype)
+    eye = jnp.eye(pad_size, dtype=mat.dtype)
+    mat = jnp.concatenate([mat, zs1], 1)
+    mat = jnp.concatenate([mat, jnp.concatenate([zs2, eye], 1)], 0)
+    return mat
+
+
+def make_sliced_padding(
+    symmetric_block_size,
+    num_blocks,
+    starting_block,
+    dtype,
+):
+    """Returns padding for symmetric block matrix.
+
+    Specifically, the padding is given concatenated rectangular matrices
+    representing the lower-triangular rows below the starting block. For example,
+    if we want to pad the symmetric matrix
+
+    M = [[A, B^T]
+         [B, C]],
+
+    the desired output (in terms of the full matrix) with num_blocks = 4 is
+
+    M_padded = [[A, B^T, 0, 0]
+                [B, C,   0, 0]
+                [0, 0,   I, 0]
+                 0, 0,   0, I].
+
+    We would represent M as the block matrix mat = [A, B, C]. In this form, the
+    additional padding to provide has form [0, 0, I, 0, 0, 0, I] (only the lower
+    triangular parts in the third and fourth rows).
+
+    Args:
+      symmetric_block_size: The size of each block.
+      num_blocks: The total number of blocks.
+      starting_block: The block where to start the padding.
+      dtype: The type to use for the blocks.
+    """
+    if starting_block == num_blocks:
+        return jnp.zeros(shape=(symmetric_block_size, 0), dtype=dtype)
+
+    blocks = []
+    for i in range(starting_block, num_blocks):
+        blocks.append(
+            jnp.zeros(
+                shape=(symmetric_block_size, symmetric_block_size * i), dtype=dtype
+            )
+        )
+        blocks.append(jnp.eye(symmetric_block_size, dtype=dtype))
+    return jnp.concatenate(blocks, axis=-1)
+
+
+def pad_block_symmetric_matrix(
+    mat,
+    symmetric_block_size,
+    max_num_blocks,
+):
+    """Returns the padded blocked symmetric matrix.
+
+    The size of the padded matrix will be:
+      [symmetric_block_size, symmetric_block_size * max_num_blocks]
+
+    The input matrix can either:
+      - Be square with size less or equal to symmetric_block_size. In this case,
+        mat will first be padded to a square matrix of size symmetric_block_size,
+        and then be padded again up to the full size of the blocked matrix.
+      - Be a rectangle with number of rows equal to block size.
+        In this case, number of columns must be a multiple of number of rows, and
+        the ratio must correspond to a block representation of a symmetric matrix.
+        That is, the ratio must have form x * (x + 1) / 2. Here, x represents the
+        number of block rows represented by the matrix.
+
+    Args:
+      mat: The input block matrix.
+      symmetric_block_size: The size of blocks.
+      max_num_blocks: The largest number of blocks to pad to.
+    """
+    rows, cols = mat.shape
+    if rows > symmetric_block_size:
+        raise ValueError(
+            "Must have rows <= symmetric_block_size. Instead got "
+            f"rows={rows}, symmetric_block_size={symmetric_block_size}."
+        )
+    if rows > cols:
+        raise ValueError(
+            f"Must have rows <= cols, instead got rows={rows}, cols={cols}."
+        )
+    if cols > symmetric_block_size * max_num_blocks:
+        raise ValueError(
+            "Must have cols <= symmetric_block_size * max_num_blocks "
+            f"Instead got cols={cols}, "
+            f"symmetric_block_size={symmetric_block_size}, "
+            f"max_num_blocks={max_num_blocks}."
+        )
+    if rows < symmetric_block_size:
+        mat = pad_square_matrix(mat, max_size=symmetric_block_size)
+    # Update rows and cols after possibly padding in pad_square_matrix.
+    rows, cols = mat.shape
+    assert rows == symmetric_block_size
+    assert cols % rows == 0
+    filled_blocks = cols // rows
+    padding_blocks = make_sliced_padding(
+        symmetric_block_size=symmetric_block_size,
+        num_blocks=symmetric_matrices.num_blocks_from_total_blocks(max_num_blocks),
+        starting_block=symmetric_matrices.num_blocks_from_total_blocks(filled_blocks),
+        dtype=mat.dtype,
+    )
+    return jnp.concatenate([mat, padding_blocks], axis=-1)
+
+
+def pad_vector(vec, max_size):
+    """Pad a vector to a max_size.
+
+    Args:
+      vec: a vector to pad.
+      max_size: matrix size requested.
+
+    Returns:
+      Given V returns [V, 0]
+    """
+    size = vec.shape[0]
+    assert size <= max_size
+    if size == max_size:
+        return vec
+    pad_size = max_size - size
+    zs1 = jnp.zeros([pad_size], dtype=vec.dtype)
+    return jnp.concatenate([vec, zs1], 0)
+
+
+def efficient_cond(predicate, compute_fn, init_state, *args, **kwargs):
+    """Avoids wasteful buffer allocation with XLA."""
+
+    def _iter_body(unused_state):
+        results = compute_fn(*args, **kwargs)
+        return tuple([False] + list(results))
+
+    def _iter_condition(state):
+        return state[0]
+
+    results = jax.lax.while_loop(
+        _iter_condition, _iter_body, tuple([predicate] + init_state)
+    )
+    return tuple(results[1:])
+
+
+class BlockPartitioner:
+    """Partitions a tensor into smaller tensors."""
+
+    def __init__(self, param, block_size):
+        self._shape = param.shape
+        self._splits = []
+        split_sizes = []
+        # We split params into smaller blocks. Here we store the metadata to make
+        # that split.
+        for i, d in enumerate(param.shape):
+            if 0 < block_size < d:
+                # d-1, otherwise split appends a 0-size array.
+                nsplit = (d - 1) // block_size
+                indices = (np.arange(nsplit, dtype=np.int32) + 1) * block_size
+                sizes = np.ones(nsplit + 1, dtype=np.int32) * block_size
+                sizes[-1] = d - indices[-1]
+                self._splits.append((i, indices))
+                split_sizes.append(sizes)
+            else:
+                split_sizes.append(np.array([d], dtype=np.int32))
+        self._split_sizes = split_sizes
+
+    def split_sizes(self):
+        return self._split_sizes
+
+    def partition(self, tensor):
+        """Partition tensor into blocks."""
+
+        assert tensor.shape == self._shape
+        tensors = [tensor]
+        for i, indices in self._splits:
+            tensors_local = []
+            for t in tensors:
+                tensors_local.extend(jnp.split(t, indices_or_sections=indices, axis=i))
+            tensors = tensors_local
+        return tensors
+
+    def merge_partitions(self, partitions):
+        """Merge partitions back to original shape."""
+
+        for i, indices in reversed(self._splits):
+            n = len(indices) + 1
+            partial_merged_tensors = []
+            ind = 0
+            while ind < len(partitions):
+                partial_merged_tensors.append(
+                    jnp.concatenate(partitions[ind : ind + n], axis=i)
+                )
+                ind += n
+            partitions = partial_merged_tensors
+        assert len(partitions) == 1
+        return partitions[0]
+
+
+def gram_weighted_update(old_stats, g, axis, w1, w2, precision=None):
+    """Updated statistics via weighted average with new Gram matrix.
+
+      Returns w₁ R + w₂ Gᵀ G where R is `old_stats` and G is the matrix whose
+      columns are the flattened slices of the tensor `g` along the given `axis`.
+      (So, `old_stats` and the returned matrix have dimensions n x n where
+      n = `g.shape[axis]`).
+
+    Args:
+      old_stats:  Old statistics.
+      g:  Gradient tensor.
+      axis:  Axis along which to slice `g`.
+      w1:  Scalar weight for old statistics.
+      w2:  Scalar weight for new Gram matrix.
+      precision: Optional precision XLA related flag, the available options are:
+        a) lax.Precision.DEFAULT (better step time, but not precise)
+        b) lax.Precision.HIGH (increased precision, slower)
+        c) lax.Precision.HIGHEST (best possible precision, slowest)
+
+    Returns:
+      Weighted average of old and new statistics.
+    """
+    axes = [i for i in range(g.ndim) if i != axis]
+    gram_matrix = jnp.tensordot(g, g, axes=(axes, axes), precision=precision)
+    return w1 * old_stats + w2 * gram_matrix
+
+
+class Preconditioner:
+    """Compute statistics/shape from gradients for preconditioning."""
+
+    def __init__(
+        self,
+        param,
+        block_size,
+        merge_small_dims_block_size,
+        best_effort_shape_interpretation,
+        preconditioner_type=PreconditionerType.ALL,
+    ):
+        """Initializes the preconditioner.
+
+        Args:
+          param: parameter to precondition.
+          block_size: Block size used to split param.
+          merge_small_dims_block_size: Block size for merging dims.
+          best_effort_shape_interpretation: Whether to collapse/merge dims together.
+          preconditioner_type: Type of preconditioner to use.
+        """
+        self._original_shape = param.shape
+        self._transformed_shape = param.shape
+        if best_effort_shape_interpretation:
+            self._transformed_shape = merge_small_dims(
+                self._original_shape, merge_small_dims_block_size
+            )
+        reshaped_param = jnp.reshape(param, self._transformed_shape)
+        self._partitioner = BlockPartitioner(reshaped_param, block_size)
+        self._preconditioner_type = preconditioner_type
+
+    def updated_statistics_from_grad(
+        self,
+        stats,
+        grad,
+        w1,
+        w2,
+        to_float=None,
+        from_float=None,
+        precision=None,
+    ):
+        """Update statistics from gradients.
+
+        Args:
+          stats: Old statistics or its Cholesky factor if `cholesky` is True.
+          grad: Gradient to compute statistics from.
+          w1: Weight for old statistics.
+          w2: Weight for new statistics.
+          to_float: Optional function for converting stats to floating point.
+          from_float: Optional function for converting from floating point.
+          precision: Optional precision XLA related flag, the available options are:
+            a) lax.Precision.DEFAULT (better step time, but not precise)
+            b) lax.Precision.HIGH (increased precision, slower)
+            c) lax.Precision.HIGHEST (best possible precision, slowest)
+
+        Returns:
+          A list of updated gradient statistics for each partition.
+        """
+        to_float = to_float if to_float is not None else (lambda x: x)
+        from_float = from_float if from_float is not None else (lambda x: x)
+        update = functools.partial(gram_weighted_update, precision=precision)
+        reshaped_grad = jnp.reshape(grad, self._transformed_shape)
+        partitioned_grads = self._partitioner.partition(reshaped_grad)
+        new_stats = []
+        index = 0
+        for g in partitioned_grads:
+            should_preconditioned_dims = self.should_precondition_dims()
+            num_preconditioners = sum(should_preconditioned_dims)
+            for axis in range(num_preconditioners):
+                new_stat = update(to_float(stats[index]), g, axis, w1, w2)
+                new_stats.append(from_float(new_stat))
+                index += 1
+        return new_stats
+
+    def should_precondition_dims(self):
+        """A vector containing indicator indicating if the dim is preconditioned."""
+        split_sizes = self._partitioner.split_sizes()
+        rank = len(split_sizes)
+        if self._preconditioner_type == PreconditionerType.ALL or rank <= 1:
+            return [True] * rank
+        else:
+            return [True] * (rank - 1) + [False]
+
+    def shapes_for_preconditioners(self):
+        """Returns shape from statistics."""
+        split_sizes = self._partitioner.split_sizes()
+        rank = len(split_sizes)
+        # We ignore preconditioner types if rank == 1
+        preconditioner_shapes = []
+        for t in itertools.product(*split_sizes):
+            if self._preconditioner_type == PreconditionerType.ALL or rank <= 1:
+                preconditioner_shapes.extend([[d, d] for d in t])
+            else:
+                preconditioner_shapes.extend([[d, d] for d in t[:-1]])
+        return preconditioner_shapes
+
+    def exponent_for_preconditioner(self):
+        """Returns exponent to use for inverse-pth root M^{-1/p}."""
+        should_preconditioned_dims = self.should_precondition_dims()
+        num_preconditioners = sum(should_preconditioned_dims)
+        return 2 * num_preconditioners
+
+    def preconditioned_grad(self, grad, preconditioners):
+        """Precondition the gradient.
+
+        Args:
+          grad: A gradient tensor to precondition.
+          preconditioners: A list of preconditioners to apply.
+
+        Returns:
+          A preconditioned gradient.
+        """
+
+        reshaped_grad = jnp.reshape(grad, self._transformed_shape)
+        partitioned_grads = self._partitioner.partition(reshaped_grad)
+        preconditioned_partitioned_grads = []
+        for i, g in enumerate(partitioned_grads):
+            should_preconditioned_dims = self.should_precondition_dims()
+            num_preconditioners = sum(should_preconditioned_dims)
+            preconditioners_for_grad = preconditioners[
+                i * num_preconditioners : (i + 1) * num_preconditioners
+            ]
+            precond_g = g
+            rank = len(g.shape)
+            for j, precondition in enumerate(should_preconditioned_dims):
+                if precondition:
+                    precond_g = jnp.tensordot(
+                        precond_g, preconditioners_for_grad[j], axes=[[0], [0]]
+                    )
+                else:
+                    precond_g = jnp.transpose(precond_g, axes=(*range(1, rank), 0))
+            preconditioned_partitioned_grads.append(precond_g)
+        merged_grad = self._partitioner.merge_partitions(
+            preconditioned_partitioned_grads
+        )
+        return jnp.reshape(merged_grad, self._original_shape)
+
+
+def _convert_to_parameter_stats(global_stats, local_stat, convert_statistics=True):
+    """Creates parameter stats from sharded stats."""
+    index_start = int(local_stat.index_start)
+    index_end = int(len(local_stat.sizes)) + index_start
+    statistics = global_stats.statistics[index_start:index_end, :, :]
+    preconditioners = global_stats.preconditioners[index_start:index_end, :, :]
+    new_statistics = []
+    new_preconditioners = []
+    for i, size in enumerate(local_stat.sizes):
+        new_statistics.append(statistics[i][:size, :size])
+        new_preconditioners.append(preconditioners[i][:size, :size])
+    if not convert_statistics:
+        new_statistics = None
+    return ParameterStats(
+        local_stat.diagonal_statistics,
+        new_statistics,
+        new_preconditioners,
+        local_stat.diagonal_momentum,
+        local_stat.momentum,
+        local_stat.training_metrics,
+    )
+
+
+def _convert_from_parameter_stats(parameter_stats, local_stats):
+    """Creates sharded stats from paramter stats."""
+    return LocalShardedParameterStats(
+        parameter_stats.diagonal_statistics,
+        parameter_stats.diagonal_momentum,
+        parameter_stats.momentum,
+        parameter_stats.training_metrics,
+        local_stats.index_start,
+        local_stats.sizes,
+    )
+
+
+def _add_error_into_local_stats(local_stats, errors, inverse_failure_threshold):
+    """Adds errors back into local statistics."""
+    new_local_stats = []
+    for local_stat in local_stats:
+        if local_stat.sizes:
+            index_start = int(local_stat.index_start)
+            index_end = int(len(local_stat.sizes)) + index_start
+            per_stat_error = errors[index_start:index_end]
+        else:
+            per_stat_error = jnp.array(0, jnp.float32)
+        if local_stat.sizes:
+            per_stat_error = jnp.where(
+                jnp.logical_and(
+                    per_stat_error > 0.0, per_stat_error != inverse_failure_threshold
+                ),
+                per_stat_error,
+                local_stat.training_metrics.inverse_pth_root_errors,
+            )
+        new_local_stats.append(
+            LocalShardedParameterStats(
+                local_stat.diagonal_statistics,
+                local_stat.diagonal_momentum,
+                local_stat.momentum,
+                TrainingMetrics(per_stat_error),
+                local_stat.index_start,
+                local_stat.sizes,
+            )
+        )
+    return new_local_stats
+
+
+def batch(x, num_devices):
+    """Batch `x` so that so that leading axis is num_devices."""
+    n = len(x)
+    b = int(n / num_devices)
+    return jnp.stack([jnp.stack(x[idx : idx + b]) for idx in range(0, n, b)])
+
+
+def unbatch(batched_values):
+    """Unbatch values across leading axis and return a list of elements."""
+    b1, b2 = batched_values.shape[0], batched_values.shape[1]
+    results = []
+    for v_array in jnp.split(batched_values, indices_or_sections=b1, axis=0):
+        v_array = jnp.squeeze(v_array)
+        # b2 = batches (number of preconditioner computation) per core.
+        if b2 > 1:
+            for v in jnp.split(v_array, indices_or_sections=b2, axis=0):
+                results.append(jnp.squeeze(v))
+        else:
+            results.append(v_array)
+    return results
+
+
+def distributed_shampoo(
+    learning_rate,
+    block_size,
+    beta1=0.9,
+    beta2=0.999,
+    diagonal_epsilon=1e-10,
+    matrix_epsilon=1e-6,
+    weight_decay=0.0,
+    start_preconditioning_step=5,
+    preconditioning_compute_steps=1,
+    statistics_compute_steps=1,
+    best_effort_shape_interpretation=True,
+    graft_type=GraftingType.SGD,
+    nesterov=True,
+    exponent_override=0,
+    # Pass pmap 'batch axis name' in pmap mode.
+    batch_axis_name=None,
+    ### Only set following 3 params in pjit/spmd mode.
+    ### WARNING: Experimental
+    statistics_partition_spec=None,
+    preconditioner_partition_spec=None,
+    num_devices_for_pjit=None,
+    shard_optimizer_states=False,
+    ###
+    ### Experimental memory reduction mode
+    best_effort_memory_usage_reduction=False,
+    ###
+    inverse_failure_threshold=0.1,
+    moving_average_for_momentum=False,
+    skip_preconditioning_dim_size_gt=4096,
+    clip_by_scaled_gradient_norm=None,
+    precision=lax.Precision.HIGHEST,
+    tensordot_precision=None,
+    relative_matrix_epsilon=True,
+    merge_small_dims_block_size=4096,
+    lobpcg_topk_precondition=0,
+    lobpcg_max_iter=0,
+    precondtioner_type=PreconditionerType.ALL,
+    skip_preconditioning_rank_lt=1,
+    decoupled_learning_rate=True,
+    decoupled_weight_decay=False,
+):
+    """Distributed Shampoo optimizer.
+
+    Distributed Shampoo is a second-order preconditioned method (concretely, a
+    variant of full-matrix Adagrad), that provides significant convergence and
+    wall-clock time improvements compared to conventional first-order methods,
+    and that has been shown to scale to large state-of-the-art deep learning
+    models.
+
+    References:
+      Scalable Second Order Optimization for Deep Learning,
+      Rohan Anil, Vineet Gupta, Tomer Koren, Kevin Regan, Yoram Singer
+
+      Preprint: https://arxiv.org/abs/2002.09018
+
+    Args:
+      learning_rate: the step size used to update the parameters.
+      block_size: Block size for large layers (if > 0). Preconditioning compute
+        operation is cubic in the dimension of the tensor. Block size allows us to
+        chunk the layers into sub-layers of maximal dimension dictated by this
+        value. Use 128 as default (increase if you have compute budget).
+      beta1: momentum parameter.
+      beta2: second moment averaging parameter.
+      diagonal_epsilon: epsilon for diagonal adagrad (only if layerwise grafting
+        to AdaGrad is enabled).
+      matrix_epsilon: epsilon to add to statistics before computing inverse pth
+        root. If you are running in f32 precision for inverse pth root
+        (recommended today) this can go upto 1e-6. If you have latest hardware
+        with native f64 precision, set this upto 1e-12.
+      weight_decay: Weight decay for regularization.
+      start_preconditioning_step: When to start Shampoo update before which
+        diagonal update is used. This is because we dont have enough information
+        to do stable inverse.
+      preconditioning_compute_steps: How often to compute preconditioner.
+        Performance tuning params for controlling memory and compute requirements.
+        Ideally set this and statistics_compute_steps params to 1.
+      statistics_compute_steps: How often to compute statistics.
+      best_effort_shape_interpretation: If there are some small dimensions,
+        collapse them e.g. [1, 2, 512, 1, 2048, 1, 3, 4] --> [1024, 2048, 12] if
+        block = 1024, [1, 2, 768, 1, 2048] --> [2, 768, 2048]
+      graft_type: Grafting is a technique to fix the layerwise scale of Shampoo
+        optimizer. This allows us to plugin the Shampoo optimizer into settings
+        where SGD/AdaGrad is already well tuned.
+      nesterov: Nesterov momentum.
+      exponent_override: Override the exponent used in matrix inverse.
+      batch_axis_name: labeled axis over pmap for data-parallel training the
+        optimizer used for.
+      statistics_partition_spec: PartitionSpec to be used in sharded mode.
+      preconditioner_partition_spec: PartitionSpec to be used in sharded mode.
+      num_devices_for_pjit: Number of devices to parallelize over when using pjit.
+      shard_optimizer_states: Shard optimizer states to save memory in model
+        parallel training.
+      best_effort_memory_usage_reduction: Best effort memory usage reduction. -
+        diagonal_statistics -> jnp.bfloat16 - momentum buffers (2x) -> jnp.int8 -
+        statistics, preconditioners -> jnp.int16 + diagonals
+      inverse_failure_threshold: numerics are hard and inverses fail sometimes; we
+        determine that using this threshold.
+      moving_average_for_momentum: Whether to use moving average for momentum
+        instead of exponential moving average.
+      skip_preconditioning_dim_size_gt: Skip if preconditioning dim size is
+        greater than this value.
+      clip_by_scaled_gradient_norm: Clip by scaled gradient norm (only useful when
+        using RMSProp Grafting).
+      precision: precision XLA related flag, the available options are: a)
+        lax.Precision.DEFAULT (better step time, but not precise) b)
+        lax.Precision.HIGH (increased precision, slower) c) lax.Precision.HIGHEST
+        (best possible precision, slowest)
+      tensordot_precision: Optional precision to use for the tensordot operation
+        when computing statistics (e.g., G Gᵀ). Same options as `precision` above.
+      relative_matrix_epsilon: Whether to use relative epsilon to the max eigen
+        value when computing inverse-pth root.
+      merge_small_dims_block_size: Used as the maximum block size
+        to merge the shapes.
+      lobpcg_topk_precondition: If nonzero, specifies the number of top
+        eigenvectors to subtract out before performing LOBPCG. Note this makes
+        relative_matrix_epsilon essentially free.
+      lobpcg_max_iter: Number of LOBPCG iterations, if zero defaults to
+        `lobpcg_topk_precondition`.
+      precondtioner_type: Preconditioner type to select all, left only or right
+        only preconditioners.
+      skip_preconditioning_rank_lt: Skips preconditioning for parameters with
+        rank less than this value.
+      decoupled_learning_rate: If True, use decoupled learning rate, otherwise
+        couple it with preconditioned gradient computation. (Default True)
+      decoupled_weight_decay: If True, use decoupled weight decay, otherwise
+        couple with weight decay. (Default False)
+    Returns:
+      a GradientTransformation.
+    """
+
+    def _graft_type_has_diagonal_statistics():
+        """Returns True if using diagonal firt order method for grafting."""
+        return graft_type != GraftingType.SGD and graft_type != GraftingType.SQRT_N
+
+    def quantized_dtype_for_momentum_buffers(var):
+        return (
+            jnp.int8
+            if best_effort_memory_usage_reduction and len(var.shape) > 1
+            else jnp.float32
+        )
+
+    # Preconditioner and statistics are both stores as int16 in this mode.
+    # We take out the diagonal to make quantization easier.
+    def quantized_dtype_for_second_moment_statistics_buffers():
+        return (
+            jnp.int16
+            if best_effort_memory_usage_reduction and batch_axis_name
+            else jnp.float32
+        )
+
+    # Preconditioner and statistics are both stores as int16 in this mode.
+    # We take out the diagonal to make quantization easier.
+    def quantized_dtype_for_second_moment_preconditioner_buffers():
+        return (
+            jnp.int16
+            if best_effort_memory_usage_reduction and batch_axis_name
+            else jnp.float32
+        )
+
+    def _to_float(maybe_quantized):
+        if isinstance(maybe_quantized, QuantizedValue):
+            return maybe_quantized.to_float()
+        else:
+            return maybe_quantized
+
+    def _maybe_quantize_statistics(statistics_list):
+        return _maybe_quantize_matrices_with_dtype(
+            statistics_list, quantized_dtype_for_second_moment_statistics_buffers()
+        )
+
+    def _maybe_quantize_preconditioners(statistics_list):
+        return _maybe_quantize_matrices_with_dtype(
+            statistics_list, quantized_dtype_for_second_moment_preconditioner_buffers()
+        )
+
+    def _maybe_quantize_matrices_with_dtype(statistics_list, quantized_dtype):
+        if quantized_dtype != jnp.float32:
+            return [
+                QuantizedValue.from_float_value(
+                    s, quantized_dtype, extract_diagonal=True
+                )
+                for s in statistics_list
+            ]
+        else:
+            return statistics_list
+
+    def _maybe_dequantize_preconditioners(preconditioner_list):
+        return _maybe_dequantize_matrices_with_dtype(
+            preconditioner_list,
+            quantized_dtype_for_second_moment_preconditioner_buffers(),
+        )
+
+    def _maybe_dequantize_matrices_with_dtype(statistics_list, quantized_dtype):
+        if quantized_dtype != jnp.float32:
+            return [s.to_float() for s in statistics_list]
+        else:
+            return statistics_list
+
+    def _quantize_diagonal_statistics(diagonal_statistics):
+        return QuantizedValue.from_float_value(diagonal_statistics, jnp.float32)
+
+    def _quantize_momentum(momentum_statistics):
+        return QuantizedValue.from_float_value(
+            momentum_statistics,
+            quantized_dtype_for_momentum_buffers(momentum_statistics),
+        )
+
+    def preconditioner_from_params(param):
+        """Returns a Preconditioner object for given param."""
+        return Preconditioner(
+            param,
+            block_size,
+            merge_small_dims_block_size,
+            best_effort_shape_interpretation,
+            precondtioner_type,
+        )
+
+    def sharded_init_fn(params):
+        """Returns optimizer state (for PJIT mode).
+
+        Args:
+          params: the parameters that should be updated.
+        """
+        params_flat, treedef = jax.tree_flatten(params)
+        # Find max size to pad to.
+        max_size = 0
+        for param in params_flat:
+            preconditioner = preconditioner_from_params(param)
+            if not _skip_preconditioning(param):
+                shapes = preconditioner.shapes_for_preconditioners()
+                sizes = [s[0] for s in shapes]
+                max_size = max(max(sizes), max_size)
+
+        padded_statistics = []
+        padded_preconditioners = []
+        local_stats_flat = []
+        exponents = []
+        for param in params_flat:
+            preconditioner = preconditioner_from_params(param)
+            shapes = preconditioner.shapes_for_preconditioners()
+            sizes = []
+
+            statistics = []
+            preconditioners = []
+            index_start = len(padded_statistics)
+            if not _skip_preconditioning(param):
+                sizes = [s[0] for s in shapes]
+                shapes = preconditioner.shapes_for_preconditioners()
+                statistics = [
+                    matrix_epsilon * jnp.eye(max_size, dtype=jnp.float32)
+                    for s in shapes
+                ]
+                preconditioners = [jnp.eye(max_size, dtype=jnp.float32) for s in shapes]
+                padded_statistics.extend(statistics)
+                padded_preconditioners.extend(preconditioners)
+                exponent = (
+                    preconditioner.exponent_for_preconditioner()
+                    if exponent_override == 0
+                    else exponent_override
+                )
+                exponents.extend([exponent] * len(shapes))
+
+            diagonal_statistics = _quantize_diagonal_statistics(jnp.zeros_like(param))
+            diagonal_momentum = _quantize_momentum(jnp.zeros_like(param))
+            momentum = _quantize_momentum(jnp.zeros_like(param))
+
+            local_stats_flat.append(
+                LocalShardedParameterStats(
+                    diagonal_statistics,
+                    diagonal_momentum,
+                    momentum,
+                    init_training_metrics(len(sizes)),
+                    index_start,
+                    sizes,
+                )
+            )
+
+        local_stats = jax.tree_unflatten(treedef, local_stats_flat)
+        to_pad = -len(padded_statistics) % num_devices_for_pjit
+        if max_size == 0:
+            to_pad = num_devices_for_pjit
+            max_size = block_size
+            stat_dtype = jnp.float32
+        else:
+            stat_dtype = padded_statistics[0].dtype
+        # Pad the statistics and preconditioner matrices to be a multiple of
+        # num devices.
+        # TODO(rohananil): Relax to only the size of the mesh axis where the dim
+        # is split on.
+        padded_statistics.extend(
+            [jnp.eye(max_size, dtype=stat_dtype) for _ in range(to_pad)]
+        )
+        padded_preconditioners.extend(
+            [jnp.eye(max_size, dtype=stat_dtype) for _ in range(to_pad)]
+        )
+        exponents.extend([1 for _ in range(to_pad)])
+        global_stats = GlobalShardedParameterStats(
+            jnp.stack(padded_statistics),
+            jnp.stack(padded_preconditioners),
+            jnp.stack(exponents),
+        )
+        return ShampooState(
+            count=jnp.zeros([], jnp.int32),
+            stats=ShardedShampooStats(global_stats, local_stats),
+        )
+
+    def _max_statistics_size_from_params(params):
+        max_size = 0
+        for param in params:
+            param_clone = jnp.zeros(param.shape, dtype=param.dtype)
+            preconditioner = preconditioner_from_params(param_clone)
+            if not _skip_preconditioning(param):
+                shapes = preconditioner.shapes_for_preconditioners()
+                sizes = [s[0] for s in shapes]
+                max_size = max(max(sizes), max_size)
+        return max_size
+
+    def _remove_leading_sharding_annotation(pspec):
+        """Mapping from N-d to (N-1)-d, used for quantization, factoring etc."""
+        # None and PSpec(None) are valid PSpecs.
+        if pspec and len(pspec) > 1:
+            return pjit.PartitionSpec(*pspec[1:])
+        else:
+            return []
+
+    def sharded_init_partition_spec_fn(
+        params, params_partition_spec, partition_spec_for_statistics
+    ):
+        """Returns a parallel state tree with PartitionSpec associated with state.
+
+
+        Args:
+          params: A pytree with params.
+          params_partition_spec: A pytree with PartitionSpec for params.
+          partition_spec_for_statistics: PartitionSpec for the statistics.
+        """
+        # Parallel lists of spec, and params.
+        param_pspec_flat, _ = jax.tree_flatten(
+            params_partition_spec, is_leaf=lambda x: x is None
+        )
+        params_flat, treedef = jax.tree_flatten(params)
+        assert param_pspec_flat
+        assert params_flat
+        # Step is replicated across cores.
+        # None means cores.
+        local_stats_flat = []
+        num_statistics = 0
+        for param, param_pspec in zip(params_flat, param_pspec_flat):
+            param_clone = jnp.zeros(param.shape, dtype=param.dtype)
+            preconditioner = preconditioner_from_params(param_clone)
+            shapes = preconditioner.shapes_for_preconditioners()
+            sizes = []
+
+            index_start = num_statistics
+            if not _skip_preconditioning(param):
+                sizes = [s[0] for s in shapes]
+                shapes = preconditioner.shapes_for_preconditioners()
+                num_statistics += len(shapes)
+
+            qdtype = quantized_dtype_for_momentum_buffers(param)
+            m1_pspec = param_pspec
+            m2_pspec = param_pspec
+            m1_scale_pspec = []
+            m2_scale_pspec = []
+            if qdtype != jnp.float32:
+                m1_scale_pspec = _remove_leading_sharding_annotation(m1_pspec)
+                m2_scale_pspec = _remove_leading_sharding_annotation(m2_pspec)
+
+            local_stats_flat.append(
+                LocalShardedParameterStats(
+                    QuantizedValue(
+                        param_pspec, [], [], jnp.float32, False, list(param.shape)
+                    ),
+                    QuantizedValue(
+                        m1_pspec, [], m1_scale_pspec, qdtype, False, list(param.shape)
+                    ),
+                    QuantizedValue(
+                        m2_pspec, [], m2_scale_pspec, qdtype, False, list(param.shape)
+                    ),
+                    init_training_metrics_pspec(),
+                    index_start,
+                    sizes,
+                )
+            )
+
+        local_stats = jax.tree_unflatten(treedef, local_stats_flat)
+        global_stats = GlobalShardedParameterStats(
+            partition_spec_for_statistics,
+            partition_spec_for_statistics,
+            pjit.PartitionSpec(),
+        )
+        count_pspec = pjit.PartitionSpec()
+        return ShampooState(
+            count=count_pspec, stats=ShardedShampooStats(global_stats, local_stats)
+        )
+
+    def sharded_init_shape_and_dtype_fn(params):
+        """Returns a parallel state tree with shape, dtype associated with state.
+
+
+        Args:
+          params: A pytree with params.
+        """
+        # Parallel lists of spec, and params.
+        params_flat, treedef = jax.tree_flatten(params)
+        assert params_flat
+        # Step is replicated across cores.
+        # None means cores.
+        local_stats_flat = []
+        num_statistics = 0
+        for param in params_flat:
+            param_clone = jnp.zeros(param.shape, dtype=param.dtype)
+            preconditioner = preconditioner_from_params(param_clone)
+            shapes = preconditioner.shapes_for_preconditioners()
+            sizes = []
+
+            index_start = num_statistics
+            if not _skip_preconditioning(param):
+                sizes = [s[0] for s in shapes]
+                shapes = preconditioner.shapes_for_preconditioners()
+                num_statistics += len(shapes)
+
+            qdtype = quantized_dtype_for_momentum_buffers(param)
+            m1_shape_and_dtype = [list(param.shape), param.dtype]
+            m2_shape_and_dtype = [list(param.shape), param.dtype]
+            m1_scale_shape_and_dtype = []
+            m2_scale_shape_and_dtype = []
+            if qdtype != jnp.float32:
+                m1_scale_shape_and_dtype = [list(param.shape)[1:], qdtype]
+                m2_scale_shape_and_dtype = [list(param.shape)[1:], qdtype]
+
+            diagonal_statistics_shape_and_dtype = [list(param.shape), param.dtype]
+            local_stats_flat.append(
+                LocalShardedParameterStats(
+                    QuantizedValue(
+                        diagonal_statistics_shape_and_dtype,
+                        [],
+                        [],
+                        jnp.float32,
+                        False,
+                        list(param.shape),
+                    ),
+                    QuantizedValue(
+                        m1_shape_and_dtype,
+                        [],
+                        m1_scale_shape_and_dtype,
+                        qdtype,
+                        False,
+                        list(param.shape),
+                    ),
+                    QuantizedValue(
+                        m2_shape_and_dtype,
+                        [],
+                        m2_scale_shape_and_dtype,
+                        qdtype,
+                        False,
+                        list(param.shape),
+                    ),
+                    init_training_metrics_shapes(len(sizes)),
+                    index_start,
+                    sizes,
+                )
+            )
+
+        local_stats = jax.tree_unflatten(treedef, local_stats_flat)
+        max_statistics_size = _max_statistics_size_from_params(params_flat)
+        to_pad = -num_statistics % num_devices_for_pjit
+        num_statistics += to_pad
+        if num_statistics == 0:
+            num_statistics = num_devices_for_pjit
+            max_statistics_size = block_size
+        statistics_shape = [num_statistics, max_statistics_size, max_statistics_size]
+        global_stats = GlobalShardedParameterStats(
+            [statistics_shape, jnp.float32],
+            [statistics_shape, jnp.float32],
+            [[num_statistics], jnp.int32],
+        )
+        return ShampooState(
+            count=[[], jnp.float32],
+            stats=ShardedShampooStats(global_stats, local_stats),
+        )
+
+    def sharded_update_fn(grads, state, params):
+        """Transform the input gradient and update all statistics in sharded mode.
+
+        Args:
+          grads: the gradient tensors for the parameters.
+          state: a named tuple containing the state of the optimizer
+          params: the parameters that should be updated.
+
+        Returns:
+          A tuple containing the new parameters and the new optimizer state.
+        """
+        params_flat, treedef = jax.tree_flatten(params)
+        grads_flat = treedef.flatten_up_to(grads)
+
+        global_stats = state.stats.global_stats
+        local_stats_flat = treedef.flatten_up_to(state.stats.local_stats)
+        stats_flat = [
+            _convert_to_parameter_stats(global_stats, local_stat)
+            for local_stat in local_stats_flat
+        ]
+        new_stats_flat = jax.tree_map(
+            lambda g, s, p: _compute_stats(g, s, p, state.count),
+            grads_flat,
+            stats_flat,
+            params_flat,
+        )
+
+        outputs = jax.tree_map(
+            lambda g, s, p: _transform_grad(g, s, p, state.count),
+            grads_flat,
+            new_stats_flat,
+            params_flat,
+        )
+        updates_flat, new_stats_flat = list(zip(*outputs)) if outputs else ((), ())
+
+        updates = jax.tree_unflatten(treedef, updates_flat)
+        # Create new local_stats
+        new_local_stats_flat = [
+            _convert_from_parameter_stats(new_stat, local_stat)
+            for new_stat, local_stat in zip(new_stats_flat, local_stats_flat)
+        ]
+
+        max_size = global_stats.statistics.shape[1]
+        new_padded_statistics = []
+        for stat in new_stats_flat:
+            new_padded_statistics.extend(
+                [pad_square_matrix(stat, max_size) for stat in stat.statistics]
+            )
+
+        # Create global stats
+        # TODO(rohananil): Preconditioner is not updated every step, so cost of
+        # stack/pad can be obviated away.
+        # Pad the statistics and preconditioner matrices to be a multiple of
+        # num devices.
+        # TODO(rohananil): Relax to only the size of the mesh axis where the dim
+        # is split on.
+        to_pad = -len(new_padded_statistics) % num_devices_for_pjit
+        if not new_padded_statistics:
+            to_pad = num_devices_for_pjit
+            stat_dtype = jnp.float32
+        else:
+            stat_dtype = new_padded_statistics[0].dtype
+
+        new_padded_statistics.extend(
+            [jnp.eye(max_size, dtype=stat_dtype) for _ in range(to_pad)]
+        )
+        new_stacked_padded_statistics = jnp.stack(new_padded_statistics)
+        new_stacked_padded_statistics = pjit.with_sharding_constraint(
+            new_stacked_padded_statistics, statistics_partition_spec
+        )
+
+        def _internal_inverse_pth_root_all():
+            preconditioners, errors = _matrix_inverse_pth_root_pjit(
+                new_stacked_padded_statistics,
+                global_stats.exponents,
+                statistics_partition_spec,
+            )
+            return preconditioners, errors
+
+        if preconditioning_compute_steps == 1:
+            new_preconditioners, errors = _internal_inverse_pth_root_all()
+        else:
+            # Passing statistics instead of preconditioners as they are similarly
+            # shaped tensors. Note statistics will be ignored as we are passing in
+            # a large init value for error.
+            preconditioners_init = new_stacked_padded_statistics
+            n = new_stacked_padded_statistics.shape[0]
+            errors_init = jnp.ones([n], jnp.float32) * inverse_failure_threshold
+            init_state = [preconditioners_init, errors_init]
+            perform_step = state.count % preconditioning_compute_steps == 0
+            new_preconditioners, errors = efficient_cond(
+                perform_step, _internal_inverse_pth_root_all, init_state
+            )
+
+        new_local_stats_flat = _add_error_into_local_stats(
+            new_local_stats_flat, errors, inverse_failure_threshold
+        )
+        new_local_stats = jax.tree_unflatten(treedef, new_local_stats_flat)
+        errors = errors.reshape((-1, 1, 1))
+        predicate = jnp.logical_or(
+            jnp.isnan(errors), errors >= inverse_failure_threshold
+        ).astype(new_preconditioners.dtype)
+        # TODO(rohananil): Check for numerical instabilities.
+        new_conditional_preconditioners = (
+            predicate * global_stats.preconditioners
+            + (1.0 - predicate) * new_preconditioners
+        )
+        new_global_stats = GlobalShardedParameterStats(
+            new_stacked_padded_statistics,
+            new_conditional_preconditioners,
+            global_stats.exponents,
+        )
+        new_shampoo_state = ShampooState(
+            count=state.count + 1,
+            stats=ShardedShampooStats(new_global_stats, new_local_stats),
+        )
+        return updates, new_shampoo_state
+
+    def init_fn(params):
+        """Initialise the optimiser's state."""
+
+        def _init(param):
+            preconditioner = preconditioner_from_params(param)
+            statistics = []
+            preconditioners = []
+            if not _skip_preconditioning(param):
+                shapes = preconditioner.shapes_for_preconditioners()
+                statistics = [
+                    matrix_epsilon * jnp.eye(s[0], dtype=jnp.float32) for s in shapes
+                ]
+                preconditioners = [jnp.eye(s[0], dtype=jnp.float32) for s in shapes]
+
+            diagonal_statistics = []
+            if _graft_type_has_diagonal_statistics():
+                diagonal_statistics = jnp.zeros_like(param)
+
+            diagonal_momentum = _quantize_momentum(jnp.zeros_like(param))
+            momentum = _quantize_momentum(jnp.zeros_like(param))
+
+            return ParameterStats(
+                _quantize_diagonal_statistics(diagonal_statistics),
+                _maybe_quantize_statistics(statistics),
+                _maybe_quantize_preconditioners(preconditioners),
+                diagonal_momentum,
+                momentum,
+                init_training_metrics(len(statistics)),
+            )
+
+        return ShampooState(
+            count=jnp.zeros([], jnp.int32), stats=jax.tree_map(_init, params)
+        )
+
+    def _skip_preconditioning(param):
+        return len(param.shape) < skip_preconditioning_rank_lt or any(
+            [s > skip_preconditioning_dim_size_gt for s in param.shape]
+        )
+
+    def _compute_stats(grad, state, param, step):
+        """Compute per-parameter statistics."""
+        preconditioner = preconditioner_from_params(param)
+        new_statistics = [[]] * len(state.statistics)
+        w1 = beta2
+        w2 = beta2 if beta2 == 1.0 else (1.0 - beta2)
+        if not _skip_preconditioning(param):
+
+            def compute_updated_statistics():
+                return preconditioner.updated_statistics_from_grad(
+                    state.statistics,
+                    grad,
+                    w1=w1,
+                    w2=w2,
+                    to_float=_to_float,
+                    from_float=lambda x: _maybe_quantize_statistics([x])[0],
+                    precision=tensordot_precision,
+                )
+
+            if statistics_compute_steps > 1:
+                perform_step = step % statistics_compute_steps == 0
+                init_state = state.statistics
+                new_statistics = list(
+                    efficient_cond(perform_step, compute_updated_statistics, init_state)
+                )
+            else:
+                new_statistics = compute_updated_statistics()
+        return ParameterStats(
+            state.diagonal_statistics,
+            new_statistics,
+            state.preconditioners,
+            state.diagonal_momentum,
+            state.momentum,
+            state.training_metrics,
+        )
+
+    mi_pth_root = functools.partial(
+        matrix_inverse_pth_root,
+        ridge_epsilon=matrix_epsilon,
+        precision=precision,
+        relative_matrix_epsilon=relative_matrix_epsilon,
+        lobpcg_topk_precondition=lobpcg_topk_precondition,
+        lobpcg_max_iter=lobpcg_max_iter,
+    )
+
+    def _matrix_inverse_pth_root_vmap(xs, ps):
+        return jax.vmap(mi_pth_root)(xs, ps)
+
+    def _quantized_matrix_inverse_pth_root_vmap(qxs, qds, qbs, ps):
+        def _quantized_to_float(qx, qd, qb):
+            qv = QuantizedValue(qx, qd, qb, qx.dtype, True, list(qx.shape))
+            return qv.to_float()
+
+        def matrix_inverse_pth_root_wrapper(qx, qd, qb, p):
+            v = _quantized_to_float(qx, qd, qb)
+            preconditioner, error = mi_pth_root(v, p)
+            qp = QuantizedValue.from_float_value(preconditioner, qx.dtype, True)
+            return qp.quantized, qp.diagonal, qp.bucket_size, error
+
+        return jax.vmap(matrix_inverse_pth_root_wrapper)(qxs, qds, qbs, ps)
+
+    def _matrix_inverse_pth_root_pjit(xs, ps, statistics_partition_spec=None):
+        # Partition the concatenated statistics matrix across all cores.
+        pspec_for_partition = preconditioner_partition_spec
+        partitioned_xs = pjit.with_sharding_constraint(xs, pspec_for_partition)
+        if preconditioner_partition_spec:
+            partitioned_ps_spec = pjit.PartitionSpec(preconditioner_partition_spec[0])
+        else:
+            partitioned_ps_spec = None
+        partitioned_ps = pjit.with_sharding_constraint(ps, partitioned_ps_spec)
+        # Run matrix inverse pth root on each shard.
+        partitioned_preconditioners, partitioned_errors = _matrix_inverse_pth_root_vmap(
+            partitioned_xs, partitioned_ps
+        )
+        # Reshard output to have the same PSpec as input. This is required to avoid
+        # vmap seeing the full set of statistics.
+        partitioned_preconditioners = pjit.with_sharding_constraint(
+            partitioned_preconditioners, pspec_for_partition
+        )
+        # Recombine the outputs at each core.
+        preconditioners = pjit.with_sharding_constraint(
+            partitioned_preconditioners, statistics_partition_spec
+        )
+        errors = pjit.with_sharding_constraint(partitioned_errors, pjit.PartitionSpec())
+        return preconditioners, errors
+
+    def _pmap_compute_preconditioners(
+        states,
+        step,
+        statistics,
+        num_statistics_per_state,
+        original_shapes,
+        exponents,
+        max_size,
+        prev_preconditioners,
+    ):
+        """Computes preconditioners for given statistics in states in PMAP mode.
+
+        Args:
+          states: A list of optimizer states.
+          step: Current step number
+          statistics: A list of statistics for all variables (for every dim)
+          num_statistics_per_state: Number of statistis per state to reconstruct
+            output states.
+          original_shapes: A list of shapes of the statistics.
+          exponents: Exponent power to use for inverse-pth roots.
+          max_size: Maximum dim of the statistics to pad.
+          prev_preconditioners: Previously available preconditioner.
+
+        Returns:
+          New optimizer states after computing the preconditioner.
+        """
+        if batch_axis_name:
+            num_devices = lax.psum(1, batch_axis_name)
+        else:
+            num_devices = 1
+        num_statistics = len(statistics)
+        # Pad statistics and exponents to next multiple of num_devices.
+        packed_statistics = [pad_square_matrix(stat, max_size) for stat in statistics]
+        to_pad = -num_statistics % num_devices
+        packed_statistics.extend(
+            [jnp.eye(max_size, dtype=packed_statistics[0].dtype) for _ in range(to_pad)]
+        )
+        exponents.extend([1 for _ in range(to_pad)])
+
+        if not packed_statistics:
+            return states
+
+        all_statistics = batch(packed_statistics, num_devices)
+        all_exponents = batch(exponents, num_devices)
+
+        def _internal_inverse_pth_root_all():
+            if batch_axis_name:
+                current_replica = lax.axis_index(batch_axis_name)
+                preconditioners, errors = _matrix_inverse_pth_root_vmap(
+                    all_statistics[current_replica], all_exponents[current_replica]
+                )
+                preconditioners = jax.lax.all_gather(preconditioners, batch_axis_name)
+                errors = jax.lax.all_gather(errors, batch_axis_name)
+                preconditioners_flat = unbatch(preconditioners)
+                errors_flat = unbatch(errors)
+            else:
+                preconditioners, errors = _matrix_inverse_pth_root_vmap(
+                    all_statistics[0], all_exponents[0]
+                )
+                preconditioners_flat = unbatch(jnp.stack([preconditioners]))
+                errors_flat = unbatch(jnp.stack([errors]))
+
+            return preconditioners_flat, errors_flat
+
+        if preconditioning_compute_steps == 1:
+            preconditioners_flat, errors_flat = _internal_inverse_pth_root_all()
+        else:
+            # Passing statistics instead of preconditioners as they are similarly
+            # shaped tensors. Note statistics will be ignored as we are passing in
+            # a large init value for error.
+            preconditioners_init = packed_statistics
+            errors_init = [inverse_failure_threshold] * len(packed_statistics)
+            init_state = [preconditioners_init, errors_init]
+            perform_step = step % preconditioning_compute_steps == 0
+            preconditioners_flat, errors_flat = efficient_cond(
+                perform_step, _internal_inverse_pth_root_all, init_state
+            )
+
+        def _skip(error):
+            condition = jnp.logical_or(
+                jnp.isnan(error), error >= inverse_failure_threshold
+            )
+            return condition.astype(error.dtype)
+
+        def _select_preconditioner(error, new_p, old_p):
+            return lax.cond(
+                _skip(error), lambda _: old_p, lambda _: new_p, operand=None
+            )
+
+        new_preconditioners_flat = []
+        new_errors_flat = []
+        for p, shape, prev_p, error in zip(
+            preconditioners_flat, original_shapes, prev_preconditioners, errors_flat
+        ):
+            new_preconditioners_flat.append(
+                _select_preconditioner(error, p[: shape[0], : shape[1]], prev_p)
+            )
+            new_errors_flat.append(error)
+
+        assert len(states) == len(num_statistics_per_state)
+        assert len(new_preconditioners_flat) == num_statistics
+        assert len(new_errors_flat) == num_statistics
+
+        # Add back empty preconditioners so we that we can set the optimizer state.
+        preconditioners_for_states = []
+        idx = 0
+        errors_for_states = []
+        for num_statistics, state in zip(num_statistics_per_state, states):
+            if num_statistics == 0:
+                preconditioners_for_states.append([])
+                errors_for_states.append(jnp.array(0, jnp.float32))
+            else:
+                preconditioners_for_state = new_preconditioners_flat[
+                    idx : idx + num_statistics
+                ]
+                assert len(state.statistics) == len(preconditioners_for_state)
+                preconditioners_for_states.append(preconditioners_for_state)
+
+                errors_for_state = jnp.stack(
+                    new_errors_flat[idx : idx + num_statistics]
+                )
+                assert len(state.statistics) == len(errors_for_state)
+                errors_for_states.append(errors_for_state)
+
+                idx += num_statistics
+        new_states = []
+        for state, new_preconditioners, new_errors in zip(
+            states, preconditioners_for_states, errors_for_states
+        ):
+            if state.statistics:
+                new_errors = jnp.where(
+                    jnp.logical_and(
+                        new_errors > 0.0, new_errors != inverse_failure_threshold
+                    ),
+                    new_errors,
+                    state.training_metrics.inverse_pth_root_errors,
+                )
+            new_training_metrics = TrainingMetrics(new_errors)
+            new_states.append(
+                ParameterStats(
+                    state.diagonal_statistics,
+                    state.statistics,
+                    new_preconditioners,
+                    state.diagonal_momentum,
+                    state.momentum,
+                    new_training_metrics,
+                )
+            )
+
+        return new_states
+
+    def _pmap_quantized_compute_preconditioners(
+        states,
+        step,
+        statistics,
+        num_statistics_per_state,
+        original_shapes,
+        exponents,
+        max_size,
+        prev_preconditioners,
+    ):
+        """Computes preconditioners for given statistics in states in PMAP mode.
+
+        For quantization, each statistic is represented by three values:
+          quantized matrix, diagonal, and bucket sizes, we run inverse pth-roots
+          without ever recreating the original matrix in f32.
+
+        Args:
+          states: A list of optimizer states.
+          step: Current step number
+          statistics: A list of statistics for all variables (for every dim)
+          num_statistics_per_state: Number of statistis per state to reconstruct
+            output states.
+          original_shapes: A list of shapes of the statistics.
+          exponents: Exponent power to use for inverse-pth roots.
+          max_size: Maximum dim of the statistics to pad.
+          prev_preconditioners: Previously available preconditioner.
+
+        Returns:
+          New optimizer states after computing the preconditioner.
+        """
+        num_devices = lax.psum(1, batch_axis_name)
+        num_statistics = len(statistics)
+        quantized_dtype = quantized_dtype_for_second_moment_statistics_buffers()
+        # Complexity here is around: shapes needing be statically shaped,
+        # our custom quantization type requires a different type of packing.
+
+        # Parallel tensors:
+        # quantized [dxd]
+        # diagonals [d] f32
+        # bucket_sizes [d] f32
+        packed_quantized_statistics = [
+            pad_square_matrix(stat.quantized, max_size) for stat in statistics
+        ]
+        packed_quantized_diagonals = [
+            pad_vector(stat.diagonal, max_size) for stat in statistics
+        ]
+        packed_quantized_bucket_sizes = [
+            pad_vector(stat.bucket_size, max_size) for stat in statistics
+        ]
+
+        to_pad = -num_statistics % num_devices
+        padded_eye = jnp.eye(max_size, dtype=jnp.float32)
+        quantized_eye = QuantizedValue.from_float_value(
+            padded_eye, quantized_dtype, True
+        )
+        packed_quantized_statistics.extend(
+            [quantized_eye.quantized for _ in range(to_pad)]
+        )
+        packed_quantized_diagonals.extend(
+            [quantized_eye.diagonal for _ in range(to_pad)]
+        )
+        packed_quantized_bucket_sizes.extend(
+            [quantized_eye.bucket_size for _ in range(to_pad)]
+        )
+        exponents.extend([1 for _ in range(to_pad)])
+
+        if not packed_quantized_statistics:
+            return states
+
+        all_quantized_statistics = batch(packed_quantized_statistics, num_devices)
+        all_quantized_diagonals = batch(packed_quantized_diagonals, num_devices)
+        all_quantized_bucket_sizes = batch(packed_quantized_bucket_sizes, num_devices)
+        all_exponents = batch(exponents, num_devices)
+
+        def _internal_inverse_pth_root_all():
+            current_replica = lax.axis_index(batch_axis_name)
+            (
+                quantized_preconditioners,
+                quantized_diagonals,
+                quantized_bucket_sizes,
+                errors,
+            ) = _quantized_matrix_inverse_pth_root_vmap(
+                all_quantized_statistics[current_replica],
+                all_quantized_diagonals[current_replica],
+                all_quantized_bucket_sizes[current_replica],
+                all_exponents[current_replica],
+            )
+            quantized_preconditioners = jax.lax.all_gather(
+                quantized_preconditioners, batch_axis_name
+            )
+            quantized_diagonals = jax.lax.all_gather(
+                quantized_diagonals, batch_axis_name
+            )
+            quantized_bucket_sizes = jax.lax.all_gather(
+                quantized_bucket_sizes, batch_axis_name
+            )
+            errors = jax.lax.all_gather(errors, batch_axis_name)
+            quantized_preconditioners_flat = unbatch(quantized_preconditioners)
+            quantized_diagonals_flat = unbatch(quantized_diagonals)
+            quantized_bucket_sizes_flat = unbatch(quantized_bucket_sizes)
+            errors_flat = unbatch(errors)
+            return (
+                quantized_preconditioners_flat,
+                quantized_diagonals_flat,
+                quantized_bucket_sizes_flat,
+                errors_flat,
+            )
+
+        if preconditioning_compute_steps == 1:
+            (
+                quantized_preconditioners_flat,
+                quantized_diagonals_flat,
+                quantized_bucket_sizes_flat,
+                errors_flat,
+            ) = _internal_inverse_pth_root_all()
+        else:
+            # Passing statistics instead of preconditioners as they are similarly
+            # shaped tensors. Note statistics will be ignored as we are passing in
+            # a large init value for error.
+            quantized_preconditioners_init = packed_quantized_statistics
+            quantized_diagonals_init = packed_quantized_diagonals
+            quantized_bucket_sizes_init = packed_quantized_bucket_sizes
+            errors_init = [inverse_failure_threshold] * len(
+                quantized_preconditioners_init
+            )
+            init_state = [
+                quantized_preconditioners_init,
+                quantized_diagonals_init,
+                quantized_bucket_sizes_init,
+                errors_init,
+            ]
+            perform_step = step % preconditioning_compute_steps == 0
+            (
+                quantized_preconditioners_flat,
+                quantized_diagonals_flat,
+                quantized_bucket_sizes_flat,
+                errors_flat,
+            ) = efficient_cond(perform_step, _internal_inverse_pth_root_all, init_state)
+
+        def _skip(error):
+            condition = jnp.logical_or(
+                jnp.isnan(error), error >= inverse_failure_threshold
+            )
+            return condition.astype(error.dtype)
+
+        def _select_preconditioner(error, new_p, old_p):
+            return lax.cond(
+                _skip(error), lambda _: old_p, lambda _: new_p, operand=None
+            )
+
+        new_quantized_preconditioners_flat = []
+        new_quantized_diagonals_flat = []
+        new_quantized_bucket_sizes_flat = []
+        new_errors_flat = []
+        for p, d, b, shape, prev_p, error in zip(
+            quantized_preconditioners_flat,
+            quantized_diagonals_flat,
+            quantized_bucket_sizes_flat,
+            original_shapes,
+            prev_preconditioners,
+            errors_flat,
+        ):
+            new_quantized_preconditioners_flat.append(
+                _select_preconditioner(
+                    error, p[: shape[0], : shape[1]], prev_p.quantized
+                )
+            )
+            new_quantized_diagonals_flat.append(
+                _select_preconditioner(error, d[: shape[0]], prev_p.diagonal)
+            )
+            new_quantized_bucket_sizes_flat.append(
+                _select_preconditioner(error, b[: shape[0]], prev_p.bucket_size)
+            )
+            new_errors_flat.append(error)
+
+        assert len(states) == len(num_statistics_per_state)
+        assert len(new_quantized_preconditioners_flat) == num_statistics
+        assert len(new_quantized_diagonals_flat) == num_statistics
+        assert len(new_quantized_bucket_sizes_flat) == num_statistics
+
+        # Add back empty preconditioners so we that we can set the optimizer state.
+        preconditioners_for_states = []
+        errors_for_states = []
+        idx = 0
+        for num_statistics, state in zip(num_statistics_per_state, states):
+            if num_statistics == 0:
+                preconditioners_for_states.append([])
+                errors_for_states.append(jnp.array(0, jnp.float32))
+            else:
+                quantized_preconditioners_for_state = (
+                    new_quantized_preconditioners_flat[idx : idx + num_statistics]
+                )
+                quantized_diagonals_for_state = new_quantized_diagonals_flat[
+                    idx : idx + num_statistics
+                ]
+                quantized_bucket_sizes_for_state = new_quantized_bucket_sizes_flat[
+                    idx : idx + num_statistics
+                ]
+                errors_for_state = jnp.stack(
+                    new_errors_flat[idx : idx + num_statistics]
+                )
+
+                assert len(state.statistics) == len(quantized_preconditioners_for_state)
+                assert len(state.statistics) == len(quantized_diagonals_for_state)
+                assert len(state.statistics) == len(quantized_bucket_sizes_for_state)
+                assert len(state.statistics) == len(errors_for_state)
+
+                quantized_preconditioners = []
+                for qv, qd, qb in zip(
+                    quantized_preconditioners_for_state,
+                    quantized_diagonals_for_state,
+                    quantized_bucket_sizes_for_state,
+                ):
+                    quantized_preconditioners.append(
+                        QuantizedValue(qv, qd, qb, qv.dtype, True, list(qv.shape))
+                    )
+                preconditioners_for_states.append(quantized_preconditioners)
+                errors_for_states.append(errors_for_state)
+                idx += num_statistics
+        new_states = []
+        for state, new_preconditioners, new_errors in zip(
+            states, preconditioners_for_states, errors_for_states
+        ):
+            if state.statistics:
+                new_errors = jnp.where(
+                    jnp.logical_and(
+                        new_errors > 0.0, new_errors != inverse_failure_threshold
+                    ),
+                    new_errors,
+                    state.training_metrics.inverse_pth_root_errors,
+                )
+            new_training_metrics = TrainingMetrics(new_errors)
+            new_states.append(
+                ParameterStats(
+                    state.diagonal_statistics,
+                    state.statistics,
+                    new_preconditioners,
+                    state.diagonal_momentum,
+                    state.momentum,
+                    new_training_metrics,
+                )
+            )
+
+        return new_states
+
+    def _pjit_compute_preconditioners(
+        states,
+        step,
+        statistics,
+        num_statistics_per_state,
+        original_shapes,
+        exponents,
+        max_size,
+        prev_preconditioners,
+    ):
+        """Computes preconditioners for given statistics in states in PJIT mode.
+
+        Args:
+          states: A list of optimizer states.
+          step: Current step number
+          statistics: A list of statistics for all variables (for every dim)
+          num_statistics_per_state: Number of statistis per state to reconstruct
+            output states.
+          original_shapes: A list of shapes of the statistics.
+          exponents: Exponent power to use for inverse-pth roots.
+          max_size: Maximum dim of the statistics to pad.
+          prev_preconditioners: Previously available preconditioner.
+
+        Returns:
+          New optimizer states after computing the preconditioner.
+        """
+        num_statistics = len(statistics)
+        to_pad = -num_statistics % num_devices_for_pjit
+        padded_statistics = [pad_square_matrix(stat, max_size) for stat in statistics]
+        padded_statistics.extend(
+            [jnp.eye(max_size, dtype=padded_statistics[0].dtype) for _ in range(to_pad)]
+        )
+        exponents.extend([1 for _ in range(to_pad)])
+        all_statistics = jnp.stack(padded_statistics)
+        all_exponents = jnp.stack(exponents)
+
+        def _internal_inverse_pth_root_all():
+            preconditioners, errors = _matrix_inverse_pth_root_pjit(
+                all_statistics, all_exponents
+            )
+            b1 = preconditioners.shape[0]
+
+            def split(batched_values):
+                return [
+                    jnp.squeeze(v)
+                    for v in jnp.split(batched_values, indices_or_sections=b1, axis=0)
+                ]
+
+            return split(preconditioners), split(errors)
+
+        if preconditioning_compute_steps == 1:
+            preconditioners_flat, errors_flat = _internal_inverse_pth_root_all()
+        else:
+            # Passing statistics instead of preconditioners as they are similarly
+            # shaped tensors. Note statistics will be ignored as we are passing in
+            # a large init value for error.
+            preconditioners_init = padded_statistics
+            errors_init = [inverse_failure_threshold] * len(padded_statistics)
+            init_state = [preconditioners_init, errors_init]
+            perform_step = step % preconditioning_compute_steps == 0
+            preconditioners_flat, errors_flat = efficient_cond(
+                perform_step, _internal_inverse_pth_root_all, init_state
+            )
+
+        def _skip(error):
+            condition = jnp.logical_or(
+                jnp.isnan(error), error >= inverse_failure_threshold
+            )
+            return condition.astype(error.dtype)
+
+        def _select_preconditioner(error, new_p, old_p):
+            return lax.cond(
+                _skip(error), lambda _: old_p, lambda _: new_p, operand=None
+            )
+
+        new_preconditioners_flat = []
+        new_errors_flat = []
+        for p, shape, prev_p, error in zip(
+            preconditioners_flat, original_shapes, prev_preconditioners, errors_flat
+        ):
+            new_preconditioners_flat.append(
+                _select_preconditioner(error, p[: shape[0], : shape[1]], prev_p)
+            )
+            new_errors_flat.append(error)
+
+        assert len(states) == len(num_statistics_per_state)
+        assert len(new_preconditioners_flat) == num_statistics
+
+        # Add back empty preconditioners so we that we can set the optimizer state.
+        preconditioners_for_states = []
+        errors_for_states = []
+        idx = 0
+        for num_statistics, state in zip(num_statistics_per_state, states):
+            if num_statistics == 0:
+                preconditioners_for_states.append([])
+                errors_for_states.append(jnp.array(0, jnp.float32))
+            else:
+                preconditioners_for_state = new_preconditioners_flat[
+                    idx : idx + num_statistics
+                ]
+                assert len(state.statistics) == len(preconditioners_for_state)
+                preconditioners_for_states.append(preconditioners_for_state)
+
+                errors_for_state = jnp.stack(
+                    new_errors_flat[idx : idx + num_statistics]
+                )
+                assert len(state.statistics) == len(errors_for_state)
+                errors_for_states.append(errors_for_state)
+                idx += num_statistics
+
+        new_states = []
+        for state, new_preconditioners, new_errors in zip(
+            states, preconditioners_for_states, errors_for_states
+        ):
+            if state.statistics:
+                new_errors = jnp.where(
+                    jnp.logical_and(
+                        new_errors > 0.0, new_errors != inverse_failure_threshold
+                    ),
+                    new_errors,
+                    state.training_metrics.inverse_pth_root_errors,
+                )
+            new_training_metrics = TrainingMetrics(new_errors)
+            new_states.append(
+                ParameterStats(
+                    state.diagonal_statistics,
+                    state.statistics,
+                    new_preconditioners,
+                    state.diagonal_momentum,
+                    state.momentum,
+                    new_training_metrics,
+                )
+            )
+
+        return new_states
+
+    def _compute_preconditioners(states, params, step):
+        """Computes preconditioners for given statistics in states.
+
+        Args:
+          states: A list of optimizer states.
+          params: A list of params.
+          step: Current step number
+
+        Returns:
+          New optimizer states after computing the preconditioner.
+        """
+        statistics = []
+        num_statistics_per_state = []
+        original_shapes = []
+        exponents = []
+        max_size = 0
+        prev_preconditioners = []
+
+        for state, param in zip(states, params):
+            num_statistics = len(state.statistics)
+            num_statistics_per_state.append(num_statistics)
+            original_shapes_for_state = []
+            if num_statistics > 0:
+                preconditioner = preconditioner_from_params(param)
+                for statistic in state.statistics:
+                    exponents.append(
+                        preconditioner.exponent_for_preconditioner()
+                        if exponent_override == 0
+                        else exponent_override
+                    )
+                    original_shapes_for_state.append(statistic.shape)
+                    max_size = max(max_size, statistic.shape[0])
+
+                statistics.extend(state.statistics)
+                prev_preconditioners.extend(state.preconditioners)
+                original_shapes.extend(original_shapes_for_state)
+
+        if not shard_optimizer_states:
+            # Quantization is only enabled if batch_axis_name is not set.
+            quantized_dtype = quantized_dtype_for_second_moment_statistics_buffers()
+
+            if quantized_dtype == jnp.float32:
+                return _pmap_compute_preconditioners(
+                    states,
+                    step,
+                    statistics,
+                    num_statistics_per_state,
+                    original_shapes,
+                    exponents,
+                    max_size,
+                    prev_preconditioners,
+                )
+            else:
+                return _pmap_quantized_compute_preconditioners(
+                    states,
+                    step,
+                    statistics,
+                    num_statistics_per_state,
+                    original_shapes,
+                    exponents,
+                    max_size,
+                    prev_preconditioners,
+                )
+
+        else:
+            return _pjit_compute_preconditioners(
+                states,
+                step,
+                statistics,
+                num_statistics_per_state,
+                original_shapes,
+                exponents,
+                max_size,
+                prev_preconditioners,
+            )
+
+    def _transform_grad(grad, state, param, step):
+        """Transform per-parameter gradients."""
+        preconditioner = preconditioner_from_params(param)
+        sgd_update = grad
+        new_diagonal_statistics = state.diagonal_statistics.to_float()
+
+        if (
+            graft_type == GraftingType.ADAGRAD
+            or graft_type == GraftingType.ADAGRAD_NORMALIZED
+        ):
+            scaled_grad = grad
+            if graft_type == GraftingType.ADAGRAD_NORMALIZED:
+                scaled_grad = grad / (jnp.linalg.norm(grad) + 1e-16)
+
+            new_diagonal_statistics = state.diagonal_statistics.to_float() + jnp.square(
+                scaled_grad
+            )
+            adagrad_update = scaled_grad / (
+                jnp.sqrt(new_diagonal_statistics) + diagonal_epsilon
+            )
+            grafting_update = adagrad_update
+        elif (
+            graft_type == GraftingType.RMSPROP
+            or graft_type == GraftingType.RMSPROP_NORMALIZED
+        ):
+            scaled_grad = grad
+            if graft_type == GraftingType.RMSPROP_NORMALIZED:
+                scaled_grad = grad / (jnp.linalg.norm(grad) + 1e-16)
+
+            w1 = beta2
+            w2 = beta2 if beta2 == 1.0 else (1.0 - beta2)
+
+            new_diagonal_statistics = (
+                w1 * state.diagonal_statistics.to_float() + w2 * jnp.square(scaled_grad)
+            )
+            rmsprop_update = scaled_grad / (
+                jnp.sqrt(new_diagonal_statistics) + diagonal_epsilon
+            )
+
+            if clip_by_scaled_gradient_norm:
+                scaled_grad_norm = jnp.linalg.norm(rmsprop_update) / (
+                    jnp.sqrt(float(rmsprop_update.size))
+                )
+                clipping_denom = jnp.maximum(
+                    1.0, scaled_grad_norm / clip_by_scaled_gradient_norm
+                )
+                rmsprop_update /= clipping_denom
+
+            grafting_update = rmsprop_update
+        elif graft_type == GraftingType.SGD:
+            grafting_update = sgd_update
+        else:
+            grafting_update = jnp.ones_like(sgd_update) * jnp.sign(sgd_update)
+
+        lr = learning_rate
+        if callable(learning_rate):
+            lr = learning_rate(step)
+
+        preconditioner_multiplier = lr if not decoupled_learning_rate else 1.0
+        grafting_update = grafting_update * preconditioner_multiplier
+
+        precond_grad = grad
+        if not _skip_preconditioning(param):
+            precond_grad = preconditioner.preconditioned_grad(
+                precond_grad, _maybe_dequantize_preconditioners(state.preconditioners)
+            )
+        else:
+            precond_grad = grafting_update
+
+        grafting_update_norm = jnp.linalg.norm(grafting_update)
+        precond_grad_norm = jnp.linalg.norm(precond_grad)
+
+        multiplier = grafting_update_norm / (precond_grad_norm + 1e-16)
+        shampoo_update = precond_grad * multiplier
+
+        shampoo_update_with_wd = shampoo_update
+        grafting_update_with_wd = grafting_update
+
+        if weight_decay != 0 and not decoupled_weight_decay:
+            shampoo_update_with_wd = shampoo_update + weight_decay * param
+            grafting_update_with_wd = grafting_update + weight_decay * param
+
+        w = (1.0 - beta1) if moving_average_for_momentum else 1.0
+
+        shampoo_update_with_wd_momentum = (
+            state.momentum.to_float() * beta1 + w * shampoo_update_with_wd
+        )
+
+        grafting_update_with_wd_momentum = (
+            state.diagonal_momentum.to_float() * beta1 + w * grafting_update_with_wd
+        )
+
+        run_shampoo = (step >= start_preconditioning_step).astype(
+            grafting_update_with_wd_momentum.dtype
+        )
+
+        momentum_update = (
+            run_shampoo * shampoo_update_with_wd_momentum
+            + (1.0 - run_shampoo) * grafting_update_with_wd_momentum
+        )
+
+        wd_update = (
+            run_shampoo * shampoo_update_with_wd
+            + (1.0 - run_shampoo) * grafting_update_with_wd
+        )
+
+        nesterov_momentum_update = momentum_update
+
+        if nesterov:
+            nesterov_momentum_update = w * wd_update + beta1 * momentum_update
+
+        if weight_decay != 0 and decoupled_weight_decay:
+            nesterov_momentum_update = (
+                nesterov_momentum_update + lr * weight_decay * param
+            )
+
+        momentum_multiplier = lr if decoupled_learning_rate else 1.0
+        transformed_update = -1.0 * momentum_multiplier * nesterov_momentum_update
+
+        new_diagonal_momentum = grafting_update_with_wd_momentum
+        new_momentum = shampoo_update_with_wd_momentum
+
+        param_stats = ParameterStats(
+            _quantize_diagonal_statistics(new_diagonal_statistics),
+            state.statistics,
+            state.preconditioners,
+            _quantize_momentum(new_diagonal_momentum),
+            _quantize_momentum(new_momentum),
+            state.training_metrics,
+        )
+
+        return transformed_update, param_stats
+
+    def update_fn(grads, state, params):
+        """Transform the input gradient and update all statistics.
+
+        Args:
+          grads: the gradient tensors for the parameters
+            and any custom gradients for preconditioners.
+          state: a named tuple containing the state of the optimizer
+          params: the parameters that should be updated.
+
+        Returns:
+          A tuple containing the new parameters and the new optimizer state.
+        """
+        params_flat, treedef = jax.tree_flatten(params)
+        stats_flat = treedef.flatten_up_to(state.stats)
+        grads_flat = treedef.flatten_up_to(grads)
+        stats_grads = grads_flat
+
+        new_stats_flat = jax.tree_map(
+            lambda g, s, p: _compute_stats(g, s, p, state.count),
+            stats_grads,
+            stats_flat,
+            params_flat,
+        )
+
+        new_stats_flat = _compute_preconditioners(
+            new_stats_flat, params_flat, state.count
+        )
+        outputs = jax.tree_map(
+            lambda g, s, p: _transform_grad(g, s, p, state.count),
+            grads_flat,
+            new_stats_flat,
+            params_flat,
+        )
+        updates_flat, new_stats_flat = list(zip(*outputs)) if outputs else ((), ())
+
+        updates = jax.tree_unflatten(treedef, updates_flat)
+        new_stats = jax.tree_unflatten(treedef, new_stats_flat)
+
+        new_state = ShampooState(count=state.count + 1, stats=new_stats)
+        return updates, new_state
+
+    if shard_optimizer_states:
+        # Hijacks the init_fn signature so we can return an OptState with
+        # appropriate init_fns.
+        opt_init_fn = sharded_init_fn
+
+        def _init_fns(unused_params):
+            return InitFnState(
+                init_fn=opt_init_fn,
+                pspec_fn=sharded_init_partition_spec_fn,
+                shape_and_dtype_fn=sharded_init_shape_and_dtype_fn,
+            )
+
+        opt_update_fn = sharded_update_fn
+        return optax.GradientTransformation(_init_fns, opt_update_fn)
+    else:
+        return optax.GradientTransformation(init_fn, update_fn)

tools/train/scalable_shampoo/quantization_utils.py

@@ -0,0 +1,123 @@
+# coding=utf-8
+# Copyright 2022 The Google Research Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Helper routines for quantization."""
+
+from typing import Any
+
+import chex
+import jax.numpy as jnp
+from flax import struct
+
+
+# pylint:disable=no-value-for-parameter
+@struct.dataclass
+class QuantizedValue:
+    """State associated with quantized value."""
+
+    quantized: chex.Array
+    diagonal: chex.Array  # Diagonal (if extract_diagonal is set)
+    bucket_size: chex.Array
+    quantized_dtype: jnp.dtype = struct.field(
+        pytree_node=False
+    )  # Dtype for the quantized value.
+    extract_diagonal: bool = struct.field(pytree_node=False)  # In case its centered.
+    shape: Any = struct.field(pytree_node=False)  # Shape of the tensor.
+
+    @classmethod
+    def from_float_value(cls, fvalue, quantized_dtype, extract_diagonal=False):
+        if isinstance(fvalue, list) and not fvalue:
+            return QuantizedValue([], [], [], quantized_dtype, extract_diagonal, [])
+        quantized, diagonal_fvalue, bucket_size = QuantizedValue.quantize(
+            fvalue, quantized_dtype, extract_diagonal
+        )
+        return QuantizedValue(
+            quantized,
+            diagonal_fvalue,
+            bucket_size,
+            quantized_dtype,
+            extract_diagonal,
+            list(quantized.shape),
+        )
+
+    # Quantization is from Lingvo JAX optimizers.
+    # We extend it for int16 quantization of PSD matrices.
+    @classmethod
+    def quantize(cls, fvalue, quantized_dtype, extract_diagonal=False):
+        """Returns quantized value and the bucket."""
+        if quantized_dtype == jnp.float32:
+            return fvalue, [], []
+        elif quantized_dtype == jnp.bfloat16:
+            return fvalue.astype(jnp.bfloat16), [], []
+
+        float_dtype = fvalue.dtype
+        if quantized_dtype == jnp.int8:
+            # value -128 is not used.
+            num_buckets = jnp.array(127.0, dtype=float_dtype)
+        elif quantized_dtype == jnp.int16:
+            # value -32768 is not used.
+            num_buckets = jnp.array(32767.0, dtype=float_dtype)
+        else:
+            raise ValueError(f"Quantized dtype {quantized_dtype} not supported.")
+        # max value is mapped to num_buckets
+
+        if extract_diagonal and fvalue.ndim != 2:
+            raise ValueError(
+                f"Input array {fvalue} must be 2D to work with extract_diagonal."
+            )
+
+        diagonal_fvalue = []
+        if extract_diagonal:
+            diagonal_fvalue = jnp.diag(fvalue)
+            # Remove the diagonal entries.
+            fvalue = fvalue - jnp.diag(diagonal_fvalue)
+
+        # TODO(rohananil): Extend this by making use of information about the blocks
+        # SM3 style which will be useful for diagonal statistics
+        # We first decide the scale.
+        if fvalue.ndim < 1:
+            raise ValueError(
+                f"Input array {fvalue} must have a strictly positive number of dimensions."
+            )
+
+        max_abs = jnp.max(jnp.abs(fvalue), axis=0)
+        bucket_size = max_abs / num_buckets
+        bs_expanded = bucket_size[jnp.newaxis, Ellipsis]
+        # To avoid divide by 0.0
+        bs_nonzero = jnp.where(
+            bs_expanded > 0.0, bs_expanded, jnp.ones_like(bs_expanded)
+        )
+        ratio = fvalue / bs_nonzero
+        # We use rounding to remove bias.
+        quantized = jnp.round(ratio)
+        return quantized.astype(quantized_dtype), diagonal_fvalue, bucket_size
+
+    def to_float(self):
+        """Returns the float value."""
+        if isinstance(self.quantized, list) and not self.quantized:
+            return self.quantized
+
+        if self.quantized_dtype == jnp.float32:
+            return self.quantized
+
+        if self.quantized_dtype == jnp.bfloat16:
+            return self.quantized.astype(jnp.float32)
+
+        float_dtype = self.bucket_size.dtype
+        bucket_size = self.bucket_size[jnp.newaxis, Ellipsis]
+        val = self.quantized.astype(float_dtype) * bucket_size
+        if self.extract_diagonal:
+            val += jnp.diag(self.diagonal)
+        return val

tools/train/scalable_shampoo/sm3.py

@@ -0,0 +1,176 @@
+# coding=utf-8
+# Copyright 2022 The Google Research Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# An implementation of SM3 from:
+#
+# Memory-Efficient Adaptive Optimization, https://arxiv.org/pdf/1901.11150.pdf
+# Rohan Anil, Vineet Gupta, Tomer Koren, Yoram Singer
+#
+# Author: Rohan Anil (rohananil at google dot com)
+#
+
+"""SM3 Implementation."""
+
+import functools
+from typing import Any, NamedTuple
+
+import chex
+import jax
+import jax.numpy as jnp
+import optax
+
+from .quantization_utils import QuantizedValue
+
+
+class SM3State(NamedTuple):
+    count: chex.Array
+    stats: Any
+
+
+# Per parameter optimizer state used in data-parallel training.
+class ParameterStats(NamedTuple):
+    """State associated to each parameter of the model being trained."""
+
+    diagonal_statistics: chex.Array  # Accumulator for diagonal preconditioner
+    diagonal_momentum: QuantizedValue  # Momentum for the diagonal preconditioner
+
+
+def sm3(
+    learning_rate, beta1=0.9, beta2=0.999, diagonal_epsilon=1e-10, normalize_grads=False
+):
+    """SM3 optimizer.
+
+    Memory-Efficient Adaptive Optimization, Rohan Anil, Vineet Gupta, Tomer Koren,
+      Yoram Singer
+
+    https://arxiv.org/abs/1901.11150
+
+    Args:
+      learning_rate: the step size used to update the parameters.
+      beta1: momentum parameter.
+      beta2: second moment averaging parameter.
+      diagonal_epsilon: epsilon for sm3
+      normalize_grads: Whether to normalize grads. Author finds it useful when
+        grads are high variance.
+
+    Returns:
+      a GradientTransformation.
+    """
+
+    def _quantize_momentum(momentum_statistics):
+        return QuantizedValue.from_float_value(momentum_statistics, jnp.int8)
+
+    def init_fn(params):
+        """Initialise the optimiser's state."""
+
+        def _init(param):
+            accumulators = [jnp.zeros([s]) for s in param.shape]
+            momentum = _quantize_momentum(jnp.zeros_like(param))
+            return ParameterStats(accumulators, momentum)
+
+        return SM3State(
+            count=jnp.zeros([], jnp.int32), stats=jax.tree_map(_init, params)
+        )
+
+    def _get_expanded_shape(shape, i):
+        rank = len(shape)
+        # Replaces a `shape` of [M, N, K] with 1 in all dimensions except for i.
+        # For eg: i = 1 returns [1, N, 1].
+        return [1] * i + [shape[i]] + [1] * (rank - i - 1)
+
+    def _moving_averages(grad, accumulators):
+        w = (1.0 - beta2) if beta2 != 1.0 else 1.0
+        if grad.ndim < 2:
+            return beta2 * accumulators[0] + w * grad**2
+        else:
+            min_accumulator = functools.reduce(jnp.minimum, accumulators)
+            return beta2 * min_accumulator + w * grad**2
+
+    def _moving_averages_momentum(grad, momentum):
+        w = (1.0 - beta1) if beta1 != 1.0 else 1.0
+        return beta1 * momentum.to_float() + w * grad
+
+    def _sketch_diagonal_statistics(grad, updated_diagonal_statistics):
+        all_diagonal_statistics = []
+        for i in range(grad.ndim):
+            axes = list(range(i)) + list(range(i + 1, grad.ndim))
+            dim_diagonal_statistics = jnp.max(updated_diagonal_statistics, axis=axes)
+            all_diagonal_statistics.append(dim_diagonal_statistics)
+        if grad.ndim == 1:
+            all_diagonal_statistics[0] = updated_diagonal_statistics
+        return all_diagonal_statistics
+
+    def update_fn(updates, state, params=None):
+        del params
+        stats = state.stats
+        if normalize_grads:
+            updates = jax.tree_map(lambda g: g / (jnp.linalg.norm(g) + 1e-16), updates)
+        # Reshape all vectors into N-d tensors to compute min over them.
+        # [n], [m] -> [n, 1], [1, m]
+        expanded_diagonal_statistics = jax.tree_map(
+            lambda grad, state: [  # pylint:disable=g-long-lambda
+                jnp.reshape(
+                    state.diagonal_statistics[i], _get_expanded_shape(grad.shape, i)
+                )
+                for i in range(grad.ndim)
+            ],
+            updates,
+            stats,
+        )
+
+        # Compute new diagonal statistics
+        new_diagonal_statistics = jax.tree_map(
+            _moving_averages, updates, expanded_diagonal_statistics
+        )
+
+        # Compute preconditioners (1/sqrt(s)) where s is the statistics.
+        new_preconditioners = jax.tree_map(
+            lambda t: 1.0 / jnp.sqrt(t + diagonal_epsilon), new_diagonal_statistics
+        )
+        preconditioned_grads = jax.tree_map(
+            lambda g, p: g * p, updates, new_preconditioners
+        )
+
+        # Compute updated momentum (also handle quantization)
+        updated_momentum = jax.tree_map(
+            lambda preconditioned_grad, state: _moving_averages_momentum(  # pylint:disable=g-long-lambda
+                preconditioned_grad, state.diagonal_momentum
+            ),
+            preconditioned_grads,
+            stats,
+        )
+
+        # Update diagonal statistics.
+        updated_diagonal_statistics = jax.tree_map(
+            _sketch_diagonal_statistics, updates, new_diagonal_statistics
+        )
+
+        # Update momentum.
+        new_sm3_stats = jax.tree_map(
+            lambda momentum, diagonal_stats: ParameterStats(  # pylint:disable=g-long-lambda
+                diagonal_stats, _quantize_momentum(momentum)
+            ),
+            updated_momentum,
+            updated_diagonal_statistics,
+        )
+
+        lr = learning_rate
+        if callable(learning_rate):
+            lr = learning_rate(state.count)
+
+        new_updates = jax.tree_map(lambda pg: -lr * pg, updated_momentum)
+        return new_updates, SM3State(count=state.count + 1, stats=new_sm3_stats)
+
+    return optax.GradientTransformation(init_fn, update_fn)

tools/train/scalable_shampoo/symmetric_matrices/symmetric_matrices.py

@@ -0,0 +1,441 @@
+# coding=utf-8
+# Copyright 2022 The Google Research Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""JAX Ops for symmetric matrices used by the Shampoo optimizer."""
+
+import functools
+from typing import Any, List, Optional, Sequence, Union
+
+import jax
+import jax.numpy as jnp
+import numpy as np
+from flax import struct
+from jax import lax
+
+
+@struct.dataclass
+class SlicedSymmetricMatrix:
+    """A symmetric matrix represented by lower-triangular block row slices.
+
+    For example, the symmetric matrix M = [[a, b^T], [b, c]] would be represented
+    by the block rows a and [b, c].
+
+    The matrix may be batched, in which case each entry of block_rows may have
+    dimension greater than 2. The last two dimensions represent the rows and cols.
+    """
+
+    block_rows: List[jnp.ndarray]
+
+
+def product_with_transpose(
+    mat1,
+    mat2,
+    axes,
+    precision=lax.Precision.DEFAULT,
+):
+    """Returns mat1 * mat2^T for two matrices (possibly batched).
+
+    The rows and columns are the last two dimensions for each matrix.
+
+    Args:
+      mat1: First matrix.
+      mat2: Second matrix.
+      axes: The axes over which to apply the product.
+      precision: JAX precision to use for the multiplication.
+    """
+    return jnp.tensordot(a=mat1, b=mat2, axes=axes, precision=precision)
+
+
+@functools.partial(jax.jit, static_argnames=("block_size", "axes", "precision"))
+def sliced_transposed_product(
+    mat,
+    block_size,
+    axes=(-1,),
+    precision=lax.Precision.DEFAULT,
+):
+    """Returns the blocked slices representing a symmetric contraction.
+
+    Specifically, the output is a contraction of the input mat with itself, in the
+    specified axes.
+
+    Args:
+      mat: The matrix for which we will compute a contraction with itself.
+      block_size: The size of row blocks to compute.
+      axes: Axes to use for the contraction.
+      precision: The precision to use in each computation.
+
+    Raises:
+      ValueError: Raised when the specified block size does not evenly divide
+        the number of rows of the input mat.
+    """
+    rank = len(mat.shape)
+
+    def _make_axis_positive(ax):
+        assert -rank <= ax < rank
+        return ax + rank if ax < 0 else ax
+
+    positive_axes = [_make_axis_positive(ax) for ax in axes]
+    assert len(positive_axes) == len(axes)
+    remaining_axes = set(range(rank)) - set(positive_axes)
+    assert len(remaining_axes) == 1
+    remaining_ax = remaining_axes.pop()
+
+    num_rows = mat.shape[remaining_ax]
+    if num_rows % block_size != 0:
+        raise ValueError(
+            "The row dimension must be divisible by block_size. "
+            f"Instead got row dimension={num_rows} and block_size={block_size}."
+        )
+
+    block_rows = []
+    for i in range(num_rows // block_size):
+        start_indices = [0] * rank
+        start_indices[remaining_ax] = i * block_size
+
+        slice_sizes = list(mat.shape)
+        slice_sizes[remaining_ax] = block_size
+
+        slice_sizes_full = list(mat.shape)
+        slice_sizes_full[remaining_ax] = (i + 1) * block_size
+
+        block_rows.append(
+            product_with_transpose(
+                lax.dynamic_slice(
+                    mat, start_indices=start_indices, slice_sizes=slice_sizes
+                ),
+                lax.dynamic_slice(
+                    mat, start_indices=[0] * rank, slice_sizes=slice_sizes_full
+                ),
+                axes=(axes, axes),
+                precision=precision,
+            )
+        )
+
+    return SlicedSymmetricMatrix(block_rows=block_rows)
+
+
+@functools.partial(jax.jit, static_argnames=("block_size", "axes", "precision"))
+def sliced_transposed_product_concat(
+    mat,
+    block_size,
+    axes=(-1,),
+    precision=lax.Precision.DEFAULT,
+):
+    """Returns the concatenated slices representing mat*mat^T.
+
+    Args:
+      mat: The matrix for which we will compute mat*mat^T. It does not need to be
+        square, and may be batched.
+      block_size: The size of row blocks to compute.
+      axes: Axes to use for the contraction.
+      precision: The precision to use in each computation.
+
+    Raises:
+      ValueError: Raised when the specified block size does not evenly divide
+        the number of rows of the input mat.
+    """
+    sliced_symmetric_matrix = sliced_transposed_product(
+        mat=mat, block_size=block_size, axes=axes, precision=precision
+    )
+    return jnp.concatenate(sliced_symmetric_matrix.block_rows, axis=-1)
+
+
+@jax.jit
+def materialize_matrix(symmetric_matrix):
+    """Returns a materialized symmetric matrix.
+
+    Args:
+      symmetric_matrix: the matrix represented by lower-triangular block slices.
+    """
+    block_rows = symmetric_matrix.block_rows
+    block_size = block_rows[0].shape[-2]
+    num_blocks = len(block_rows)
+
+    # Slice the lower-triangular and diagonal blocks into blocks.
+    blocks = [
+        [
+            block_row[Ellipsis, i * block_size : (i + 1) * block_size]
+            for i in range(k + 1)
+        ]
+        for k, block_row in enumerate(block_rows)
+    ]
+
+    # Generate the (off-diagonal) upper-triangular blocks.
+    off_diags = [[] for _ in range(num_blocks - 1)]
+    for k, block_row in enumerate(block_rows[1:]):
+        for i in range(k + 1):
+            off_diags[i].append(
+                jnp.swapaxes(
+                    a=block_row[Ellipsis, i * block_size : (i + 1) * block_size],
+                    axis1=-1,
+                    axis2=-2,
+                )
+            )
+
+    return jnp.block(
+        [row + row_t for row, row_t in zip(blocks[:-1], off_diags)] + [blocks[-1]]
+    )
+
+
+@functools.partial(jax.jit, static_argnames="num_blocks")
+def materialize_matrix_from_concat(
+    block_rows_concat,
+    num_blocks=None,
+):
+    """Returns a materialized symmetric matrix from concatenated slices.
+
+    Args:
+      block_rows_concat: The matrix represented as the concatenated
+        lower-triangular blocks.
+      num_blocks: The number of block-rows used to represent the symmetric matrix.
+        If not specified, it is inferred from the shape of block_rows_concat.
+    """
+    if num_blocks is None:
+        num_blocks = find_num_blocks(block_rows_concat)
+
+    block_size = block_rows_concat.shape[-2]
+
+    block_rows = [
+        block_rows_concat[
+            Ellipsis,
+            (k * (k + 1))
+            // 2
+            * block_size : (((k + 1) * (k + 2)) // 2 + 1)
+            * block_size,
+        ]
+        for k in range(num_blocks)
+    ]
+
+    return materialize_matrix(SlicedSymmetricMatrix(block_rows=block_rows))
+
+
+@functools.partial(jax.jit, static_argnames=("alpha", "beta", "axes"))
+def update_sliced_rows(
+    symmetric_matrix,
+    mat,
+    alpha,
+    beta,
+    axes=(-1,),
+):
+    """Implements the blocked equivalent of SYRK.
+
+    Specifically, the symmetric matrix (represented using lower-triangular block
+    rows) is updated using the sliced product of mat.
+
+    Args:
+      symmetric_matrix: The symmetric matrix to update.
+      mat: The matrix to use for the update = mat * mat^T. The number of rows
+        should match that of symmetric_matrix.
+      alpha: The weight for the update.
+      beta: The weight for the original symmetric matrix.
+      axes: Axes to use for the contraction of the update.
+
+    Returns:
+      The updated rows of alpha * mat * mat^T + beta * symmetric_matrix.
+    """
+    block_size = symmetric_matrix.block_rows[0].shape[-2]
+    sym_prod = sliced_transposed_product(mat=mat, block_size=block_size, axes=axes)
+    return SlicedSymmetricMatrix(
+        block_rows=[
+            update * alpha + row * beta
+            for update, row in zip(sym_prod.block_rows, symmetric_matrix.block_rows)
+        ]
+    )
+
+
+def num_blocks_from_total_blocks(total_blocks):
+    """Returns the number of blocks (i.e.
+
+    block rows) from the total blocks.
+
+    This is the inverse of the function x -> x*(x+1)/2.
+
+    For example, the matrix M = [[A, B^T], [B, C]] may be represented using a
+    total of 3 blocks ([A, B, C]). The number of corresponding block rows is 2.
+
+    Args:
+      total_blocks: The total blocks used to represent the matrix.
+    """
+    num_blocks = np.round((np.sqrt(8 * total_blocks + 1) - 1) / 2).astype(np.int32)
+    if (num_blocks * (num_blocks + 1)) / 2 != total_blocks:
+        raise ValueError(
+            f"total_blocks={total_blocks} does not correspond to "
+            "a symmetric matrix. It must have the form total_blocks = x*(x+1)/2."
+        )
+    return num_blocks
+
+
+def find_num_blocks(block_rows_concat):
+    """Returns the number of (row) blocks representing the concatenated matrix.
+
+    For example, an input with dimensions [256, 2560] represents 10 square blocks,
+    which matches 4 lower-triangular block rows (1+2+3+4). So this function will
+    return 4.
+
+    Use ordinary numpy functions here so that the returned value is static.
+
+    Args:
+      block_rows_concat: The concatenated block array.
+
+    Raises:
+      ValueError: When the dimensions of the matrix do not correspond to a lower
+      triangular block representation.
+    """
+    # Compute the number of square blocks used to represent the matrix.
+    total_blocks = block_rows_concat.shape[-1] / block_rows_concat.shape[-2]
+    # Determine the number of block rows by inverting y = x*(x+1)/2.
+    return num_blocks_from_total_blocks(total_blocks)
+
+
+@functools.partial(jax.jit, static_argnames="block_size")
+def slice_symmetric_matrix(
+    mat,
+    block_size,
+):
+    """Returns sliced row blocks.
+
+    Args:
+      mat: A symmetric matrix.
+      block_size: The size of the row slices.
+    """
+    num_rows = mat.shape[-2]
+    num_cols = mat.shape[-1]
+    if num_rows != num_cols:
+        raise ValueError("mat is not square.")
+    if num_rows % block_size != 0:
+        raise ValueError(
+            f"block size does not evenly divide rows. num_rows={num_rows}, block_size={block_size}"
+        )
+    return SlicedSymmetricMatrix(
+        block_rows=[
+            mat[
+                Ellipsis,
+                i * block_size : (i + 1) * block_size,
+                0 : (i + 1) * block_size,
+            ]
+            for i in range(num_rows // block_size)
+        ]
+    )
+
+
+@functools.partial(jax.jit, static_argnames="block_size")
+def slice_symmetric_matrix_concat(
+    mat,
+    block_size,
+):
+    """Returns the concatenated sliced row blocks.
+
+    Args:
+      mat: A symmetric matrix.
+      block_size: The size of the row slices.
+    """
+    sliced_symmetric_matrix = slice_symmetric_matrix(mat=mat, block_size=block_size)
+    return jnp.concatenate(sliced_symmetric_matrix.block_rows, axis=-1)
+
+
+def sliced_matrix_diag(mat):
+    """Returns the diagonal of the symmetric matrix.
+
+    Args:
+      mat: The symmetric matrix represented in concatenated block form.
+    """
+    rows, cols = mat.shape
+    total_blocks = cols // rows
+    num_blocks = num_blocks_from_total_blocks(total_blocks)
+    diags = []
+    for i in range(num_blocks):
+        last_index = rows * ((i + 2) * (i + 1)) // 2
+        first_index = last_index - rows
+        diags.append(jnp.diag(mat[Ellipsis, first_index:last_index]))
+    return jnp.concatenate(diags, axis=-1)
+
+
+def diag_as_concat(diag, block_size):
+    """Returns the representation of a diagonal matrix in symmetric block form.
+
+    Args:
+      diag: The 1D array for the diagonals.
+      block_size: The size of blocks to use. Must divide the length of diag.
+    """
+    assert len(diag.shape) == 1  # diag must be 1D.
+    assert len(diag) % block_size == 0
+    num_diag_blocks = len(diag) // block_size
+    blocks = []
+    for i in range(num_diag_blocks):
+        blocks.append(jnp.zeros(shape=(block_size, block_size * i), dtype=diag.dtype))
+        blocks.append(jnp.diag(diag[i * block_size : (i + 1) * block_size]))
+    return jnp.concatenate(blocks, axis=-1)
+
+
+def row_abs_maxes(mat):
+    """Returns the max of the absolute values of the rows of the full matrix.
+
+    For example the symmetric matrix M = [[1, 6], [6, 2]] is represented using
+    mat = [1, 6, 2] with block_size = 1. In this case the function returns the
+    aboslute row maxes of the original symmetric matrix, [6, 6].
+
+    Args:
+      mat: The symmetric matrix represented as the concatenated blocks.
+    """
+    rows, cols = mat.shape
+
+    # Find col and row max for each block.
+    col_maxes = []
+    row_maxes = []
+    for i in range(cols // rows):
+        block = jnp.abs(mat[Ellipsis, i * rows : (i + 1) * rows])
+        col_maxes.append(jnp.max(block, axis=1))
+        row_maxes.append(jnp.max(block, axis=0))
+
+    # global row max from block maxes.
+    num_blocks = num_blocks_from_total_blocks(cols // rows)
+    maxes = []
+    for i in range(num_blocks):
+        maxes.append(
+            jnp.concatenate(
+                row_maxes[(i * (i + 1) // 2) : ((i + 2) * (i + 1) // 2)]
+                + [
+                    col_maxes[((j + 1) * (j + 2)) // 2 - (j - i + 1)]
+                    for j in range(i + 1, num_blocks)
+                ],
+                axis=-1,
+            )
+        )
+
+    return jnp.max(jnp.stack(maxes), axis=0)
+
+
+def times_vector(mat, vec):
+    """Returns the symmetric block-concatenated matrix multiplied by a vector.
+
+    Specifically, each value in the vector is multiplied by a row of the full
+    matrix. That is, the vector is broadcast and multiplied element-wise. Note
+    this would be the transpose of full_mat * vec if full_mat represented the full
+    symmetric matrix.
+
+    Args:
+      mat: The symmetric matrix represented as the concatenated blocks.
+      vec: The vector, having the same dimension as the materialized matrix.
+    """
+    rows, cols = mat.shape
+    num_blocks = num_blocks_from_total_blocks(cols // rows)
+    multiplied = []
+    for i in range(num_blocks):
+        mat_block = mat[
+            Ellipsis, rows * ((i + 1) * i) // 2 : rows * ((i + 1) * (i + 2)) // 2
+        ]
+        vec_block = vec[Ellipsis, rows * i : rows * (i + 1)]
+        multiplied.append(jnp.einsum("...ij,...i->ij", mat_block, vec_block))
+    return jnp.concatenate(multiplied, axis=-1)

tools/train/sweep.yaml

@@ -0,0 +1,49 @@
+program: train.py
+project: dalle-mini
+method: random
+metric:
+  name: eval/loss
+  goal: minimize
+parameters:
+  optim:
+    value: distributed_shampoo
+  learning_rate:
+    distribution: log_uniform
+    # from exp(min) to exp(max)
+    min: -9.2
+    max: -6.9
+  tokenizer_name:
+    value: boris/dalle-mini-tokenizer
+  config_name:
+    value: ./config/mini
+  dtype:
+    value: bfloat16
+  dataset_repo_or_path:
+    value: ./data
+  per_device_train_batch_size:
+    value: 64
+  per_device_eval_batch_size:
+    value: 64
+  gradient_accumulation_steps:
+    value: 1
+  warmup_steps:
+    value: 1000
+  num_train_epochs:
+    value: 1
+  max_train_samples:
+    value: 1000000
+  logging_steps:
+    value: 40
+  eval_steps:
+    value: 200
+
+command:
+  - python3
+  - ${program}
+  - "--streaming"
+  - "--output_dir"
+  - "./output"
+  - "--overwrite_output_dir"
+  - "--do_train"
+  - "--do_eval"
+  - ${args}

tools/train/train.py

@@ -0,0 +1,1740 @@
+#!/usr/bin/env python
+# coding=utf-8
+# Copyright 2021-2022 The HuggingFace & DALL·E Mini team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+Training DALL·E Mini.
+Script adapted from run_summarization_flax.py
+"""
+
+import io
+import logging
+import os
+import sys
+import tempfile
+import time
+from dataclasses import asdict, dataclass, field
+from functools import partial
+from pathlib import Path
+from typing import Any, Callable, NamedTuple, Optional
+
+import datasets
+import flax
+import jax
+import jax.numpy as jnp
+import jaxlib
+import numpy as np
+import optax
+import transformers
+import wandb
+from datasets import Dataset
+from flax import core, struct, traverse_util
+from flax.core.frozen_dict import FrozenDict, freeze, unfreeze
+from flax.serialization import from_bytes, to_bytes
+from flax.training.common_utils import onehot
+from jax.experimental import PartitionSpec, maps
+from jax.experimental.compilation_cache import compilation_cache as cc
+from jax.experimental.pjit import pjit, with_sharding_constraint
+from scalable_shampoo.distributed_shampoo import GraftingType, distributed_shampoo
+from tqdm import tqdm
+from transformers import HfArgumentParser
+
+import dalle_mini
+from dalle_mini.data import Dataset
+from dalle_mini.model import (
+    DalleBart,
+    DalleBartConfig,
+    DalleBartTokenizer,
+    set_partitions,
+)
+
+try:
+    from google.cloud import storage
+except:
+    storage = None
+
+logger = logging.getLogger(__name__)
+
+cc.initialize_cache("jax_cache")
+
+
+@dataclass
+class ModelArguments:
+    """
+    Arguments pertaining to which model/config/tokenizer we are going to fine-tune, or train from scratch.
+    """
+
+    model_name_or_path: Optional[str] = field(
+        default=None,
+        metadata={
+            "help": "The model checkpoint for weights initialization. "
+            "Don't set if you want to train a model from scratch. "
+            "W&B artifact references are supported in addition to the sources supported by `PreTrainedModel`."
+        },
+    )
+    config_name: Optional[str] = field(
+        default=None,
+        metadata={
+            "help": "Pretrained config name or path if not the same as model_name_or_path"
+        },
+    )
+    tokenizer_name: Optional[str] = field(
+        default=None,
+        metadata={
+            "help": "Pretrained tokenizer name or path if not the same as model_name_or_path"
+        },
+    )
+    dtype: Optional[str] = field(
+        default="float32",
+        metadata={
+            "help": "Floating-point format in which the computations will be performed (not the model weights). Choose one of `[float32, float16, bfloat16]`."
+        },
+    )
+    restore_state: Optional[bool] = field(
+        default=False,
+        metadata={
+            "help": "Restore optimizer and training state. Can be True (will retrieve associated wandb artifact), a local directory or a Google bucket path."
+        },
+    )
+    dropout: Optional[float] = field(
+        default=None,
+        metadata={"help": "Dropout rate. Overwrites config."},
+    )
+    activation_dropout: Optional[float] = field(
+        default=None,
+        metadata={"help": "Activation dropout rate. Overwrites config."},
+    )
+    attention_dropout: Optional[float] = field(
+        default=None,
+        metadata={"help": "Attention dropout rate. Overwrites config."},
+    )
+
+    def __post_init__(self):
+        if self.tokenizer_name is None:
+            self.tokenizer_name = self.model_name_or_path
+            assert (
+                self.tokenizer_name is not None
+            ), "Tokenizer name or model name/path needs to be specified"
+        if self.restore_state:
+            assert self.model_name_or_path is not None and (
+                "/model-" in self.model_name_or_path
+            ), "Restoring state only available with W&B artifact reference"
+
+    def get_metadata(self):
+        if self.model_name_or_path is not None and ":" in self.model_name_or_path:
+            if jax.process_index() == 0:
+                artifact = wandb.run.use_artifact(self.model_name_or_path)
+            else:
+                artifact = wandb.Api().artifact(self.model_name_or_path)
+            return artifact.metadata
+        else:
+            return dict()
+
+    def get_opt_state(self):
+        with tempfile.TemporaryDirectory() as tmp_dir:  # avoid multiple artifact copies
+            if self.restore_state is True:
+                # wandb artifact
+                state_artifact = self.model_name_or_path.replace(
+                    "/model-", "/state-", 1
+                )
+                if jax.process_index() == 0:
+                    artifact = wandb.run.use_artifact(state_artifact)
+                else:
+                    artifact = wandb.Api().artifact(state_artifact)
+                if artifact.metadata.get("bucket_path"):
+                    # we will read directly file contents
+                    self.restore_state = artifact.metadata["bucket_path"]
+                else:
+                    artifact_dir = artifact.download(tmp_dir)
+                    self.restore_state = str(Path(artifact_dir) / "opt_state.msgpack")
+
+            if self.restore_state.startswith("gs://"):
+                bucket_path = Path(self.restore_state[5:]) / "opt_state.msgpack"
+                bucket, blob_name = str(bucket_path).split("/", 1)
+                assert (
+                    storage is not None
+                ), 'Could not find google.storage. Install with "pip install google-cloud-storage"'
+                client = storage.Client()
+                bucket = client.bucket(bucket)
+                blob = bucket.blob(blob_name)
+                return blob.download_as_bytes()
+
+            with Path(self.restore_state).open("rb") as f:
+                return f.read()
+
+
+@dataclass
+class DataTrainingArguments:
+    """
+    Arguments pertaining to what data we are going to input our model for training and eval.
+    """
+
+    text_column: Optional[str] = field(
+        default="caption",
+        metadata={
+            "help": "The name of the column in the datasets containing the full texts (for summarization)."
+        },
+    )
+    encoding_column: Optional[str] = field(
+        default="encoding",
+        metadata={
+            "help": "The name of the column in the datasets containing the image encodings."
+        },
+    )
+    dataset_repo_or_path: str = field(
+        default=None,
+        metadata={"help": "The dataset repository containing encoded files."},
+    )
+    train_file: Optional[str] = field(
+        default=None,
+        metadata={
+            "help": "The input training data file (glob & braceexpand acceptable)."
+        },
+    )
+    validation_file: Optional[str] = field(
+        default=None,
+        metadata={
+            "help": "An optional input evaluation data file (glob & braceexpand acceptable)."
+        },
+    )
+    # data loading should not be a bottleneck so we use "streaming" mode by default
+    streaming: Optional[bool] = field(
+        default=True,
+        metadata={"help": "Whether to stream the dataset."},
+    )
+    use_auth_token: Optional[bool] = field(
+        default=False,
+        metadata={
+            "help": "Whether to use the authentication token for private datasets."
+        },
+    )
+    shard_by_host: Optional[bool] = field(
+        default=False,
+        metadata={
+            "help": "Whether to shard data files by host in multi-host environments."
+        },
+    )
+    blank_caption_prob: Optional[float] = field(
+        default=0.0,
+        metadata={
+            "help": "Probability of removing some captions for classifier-free guidance."
+        },
+    )
+    clip_score_column: Optional[str] = field(
+        default="clip_score",
+        metadata={"help": "Column that containts clip score for filtering."},
+    )
+    min_clip_score: Optional[float] = field(
+        default=None,
+        metadata={"help": "Minimum clip score required."},
+    )
+    max_clip_score: Optional[float] = field(
+        default=None,
+        metadata={"help": "Maximum clip score required."},
+    )
+    filter_column: Optional[str] = field(
+        default=None,
+        metadata={"help": "Column that containts classes to be filtered."},
+    )
+    filter_value: Optional[str] = field(
+        default=None,
+        metadata={"help": "Class value to be kept during filtering."},
+    )
+    multi_eval_ds: Optional[bool] = field(
+        default=False,
+        metadata={
+            "help": "Whether to look for multiple validation datasets (local support only)."
+        },
+    )
+    max_train_samples: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "For debugging purposes or quicker training, truncate the number of training examples."
+        },
+    )
+    max_eval_samples: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "For debugging purposes or quicker training, truncate the number of evaluation examples."
+        },
+    )
+    preprocessing_num_workers: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "The number of processes to use for the preprocessing. Not used in streaming mode."
+        },
+    )
+    overwrite_cache: bool = field(
+        default=False,
+        metadata={
+            "help": "Overwrite the cached training and evaluation sets. Not used in streaming mode."
+        },
+    )
+    # default seed of None ensures we don't repeat the same items if script was interrupted during an epoch
+    seed_dataset: int = field(
+        default=None,
+        metadata={
+            "help": "Random seed for the dataset that will be set at the beginning of training."
+        },
+    )
+
+    def __post_init__(self):
+        if self.dataset_repo_or_path is None:
+            raise ValueError("Need a dataset repository or path.")
+
+
+@dataclass
+class TrainingArguments:
+    """
+    Arguments pertaining to training parameters.
+    """
+
+    output_dir: str = field(
+        metadata={
+            "help": "The output directory where the model predictions and checkpoints will be written."
+        },
+    )
+    overwrite_output_dir: bool = field(
+        default=False,
+        metadata={
+            "help": (
+                "Overwrite the content of the output directory. "
+                "Use this to continue training if output_dir points to a checkpoint directory."
+            )
+        },
+    )
+
+    do_train: bool = field(default=False, metadata={"help": "Whether to run training."})
+    do_eval: bool = field(
+        default=False, metadata={"help": "Whether to run eval on the validation set."}
+    )
+
+    per_device_train_batch_size: int = field(
+        default=8,
+        metadata={"help": "Batch size per data parallel device for training."},
+    )
+    per_device_eval_batch_size: Optional[int] = field(
+        default=None,
+        metadata={
+            "help": "Batch size per data parallel device for evaluation. Same as training batch size if not set."
+        },
+    )
+
+    gradient_accumulation_steps: int = field(
+        default=1,
+        metadata={
+            "help": "Number of updates steps to accumulate before performing an update pass."
+        },
+    )
+    gradient_checkpointing: bool = field(
+        default=False, metadata={"help": "Use gradient checkpointing."}
+    )
+
+    learning_rate: float = field(
+        default=5e-5, metadata={"help": "The initial learning rate."}
+    )
+    optim: str = field(
+        default="distributed_shampoo",
+        metadata={
+            "help": 'The optimizer to use. Can be "distributed_shampoo" (default), "adam" or "adafactor"'
+        },
+    )
+    weight_decay: float = field(
+        default=0.0, metadata={"help": "Weight decay applied to parameters."}
+    )
+    beta1: float = field(
+        default=0.9,
+        metadata={"help": "Beta1 for Adam & Distributed Shampoo."},
+    )
+    beta2: float = field(
+        default=0.999,
+        metadata={"help": "Beta2 for for Adam & Distributed Shampoo."},
+    )
+    adam_epsilon: float = field(
+        default=1e-8, metadata={"help": "Epsilon for AdamW optimizer."}
+    )
+    max_grad_norm: float = field(
+        default=1.0, metadata={"help": "Max gradient norm for Adafactor."}
+    )
+    block_size: int = field(
+        default=1024,
+        metadata={"help": "Chunked size for large layers with Distributed Shampoo."},
+    )
+    preconditioning_compute_steps: int = field(
+        default=10, metadata={"help": "Number of steps to update preconditioner."}
+    )
+    skip_preconditioning_dim_size_gt: int = field(
+        default=4096,
+        metadata={"help": "Max size for preconditioning with Distributed Shampoo."},
+    )
+    graft_type: str = field(
+        default="rmsprop_normalized",
+        metadata={
+            "help": "The type of grafting to use. Can be 'rmsprop_normalized' (default), 'rmsprop', 'adagrad', 'adagrad_normalized', 'sgd' or 'sqrt_n'"
+        },
+    )
+    nesterov: bool = field(
+        default=False,
+        metadata={"help": "Use Nesterov momentum for Distributed Shampoo."},
+    )
+    optim_quantized: bool = field(
+        default=False,
+        metadata={
+            "help": "Whether to quantize optimizer (only supported with Distributed Shampoo)."
+        },
+    )
+    shard_shampoo_across: str = field(
+        default="dp",
+        metadata={
+            "help": "Whether to shard the optimizer across data devices (dp), model devices (mp) or both (2d)."
+        },
+    )
+
+    num_train_epochs: int = field(
+        default=3, metadata={"help": "Total number of training epochs to perform."}
+    )
+
+    warmup_steps: int = field(
+        default=0, metadata={"help": "Linear warmup over warmup_steps."}
+    )
+    lr_decay: str = field(
+        default=None,
+        metadata={
+            "help": "Decay to be used in the learning rate scheduler. Can be None (default), linear or exponential."
+        },
+    )
+    lr_transition_steps: int = field(
+        default=None,
+        metadata={
+            "help": "Number of transition steps associated with learning rate decay when using exponential decay."
+        },
+    )
+    lr_decay_rate: float = field(
+        default=None,
+        metadata={
+            "help": "Decay rate associated with learning rate when using exponential decay."
+        },
+    )
+    lr_staircase: bool = field(
+        default=False,
+        metadata={
+            "help": "Whether to use staircase or continuous learning rate when using exponential decay."
+        },
+    )
+    lr_offset: int = field(
+        default=0,
+        metadata={"help": "Number of steps to offset learning rate and keep it at 0."},
+    )
+    logging_steps: int = field(
+        default=40, metadata={"help": "Log every X updates steps."}
+    )
+    eval_steps: int = field(
+        default=400, metadata={"help": "Run an evaluation every X steps."}
+    )
+    save_steps: int = field(
+        default=4000, metadata={"help": "Save checkpoint every X updates steps."}
+    )
+    log_model: bool = field(
+        default=False,
+        metadata={"help": "Log model to wandb at `save_steps` frequency."},
+    )
+    log_norm_steps: int = field(
+        default=True,
+        metadata={"help": "Log parameters and gradients norm at this frequency."},
+    )
+    log_histogram_steps: int = field(
+        default=False,
+        metadata={
+            "help": "Log parameters and gradients histograms at this frequency. Slows down training."
+        },
+    )
+
+    seed_model: int = field(
+        default=42,
+        metadata={
+            "help": "Random seed for the model that will be set at the beginning of training."
+        },
+    )
+
+    embeddings_only: bool = field(
+        default=False, metadata={"help": "Train only embedding layers."}
+    )
+    init_embeddings: bool = field(
+        default=False,
+        metadata={"help": "When training embedding layers, initialize them."},
+    )
+
+    wandb_entity: Optional[str] = field(
+        default=None,
+        metadata={"help": "The wandb entity to use (for teams)."},
+    )
+    wandb_project: str = field(
+        default="dalle-mini",
+        metadata={"help": "The name of the wandb project."},
+    )
+    wandb_job_type: str = field(
+        default="Seq2Seq",
+        metadata={"help": "The name of the wandb job type."},
+    )
+
+    assert_TPU_available: bool = field(
+        default=False,
+        metadata={"help": "Verify that TPU is not in use."},
+    )
+
+    use_vmap_trick: bool = field(
+        default=True,
+        metadata={"help": "Verify that TPU is not in use."},
+    )
+
+    mp_devices: Optional[int] = field(
+        default=1,
+        metadata={
+            "help": "Number of devices required for model parallelism. The other dimension of available devices is used for data parallelism."
+        },
+    )
+
+    dp_devices: int = field(init=False)
+
+    def __post_init__(self):
+        if self.assert_TPU_available:
+            assert (
+                jax.local_device_count() == 8
+            ), "TPUs in use, please check running processes"
+        if self.output_dir.startswith("gs://"):
+            assert (
+                storage is not None
+            ), 'Could not find google.storage. Install with "pip install google-cloud-storage"'
+        assert self.optim in [
+            "distributed_shampoo",
+            "adam",
+            "adafactor",
+        ], f"Selected optimizer not supported: {self.optim}"
+        if self.optim == "adafactor" and self.weight_decay == 0:
+            self.weight_decay = None
+        assert self.graft_type in [
+            "rmsprop_normalized",
+            "rmsprop",
+            "adagrad",
+            "adagrad_normalized",
+            "sgd",
+            "sqrt_n",
+        ], f"Selected graft type not supported: {self.graft_type}"
+        assert self.lr_decay in [
+            None,
+            "linear",
+            "exponential",
+        ], f"Selected learning rate decay not supported: {self.lr_decay}"
+        if self.per_device_eval_batch_size is None:
+            self.per_device_eval_batch_size = self.per_device_train_batch_size
+        if self.log_norm_steps is True:
+            self.log_norm_steps = self.logging_steps
+        if not self.do_train:
+            self.num_train_epochs = 1
+        if (
+            os.path.exists(self.output_dir)
+            and os.listdir(self.output_dir)
+            and self.do_train
+            and not self.overwrite_output_dir
+        ):
+            raise ValueError(
+                f"Output directory ({self.output_dir}) already exists and is not empty."
+                "Use --overwrite_output_dir to overcome."
+            )
+        assert self.shard_shampoo_across in [
+            "dp",
+            "mp",
+            "2d",
+        ], f"Shard shampoo across {self.shard_shampoo_across} not supported."
+        assert (
+            self.mp_devices > 0
+        ), f"Number of devices for model parallelism must be > 0"
+        assert (
+            jax.device_count() % self.mp_devices == 0
+        ), f"Number of available devices ({jax.device_count()} must be divisible by number of devices used for model parallelism ({self.mp_devices})."
+        self.dp_devices = jax.device_count() // self.mp_devices
+
+
+def split_params(data):
+    """Split params between scanned and non-scanned"""
+    flat = traverse_util.flatten_dict(unfreeze(data))
+    split = {"standard": {}, "scanned_encoder": {}, "scanned_decoder": {}}
+    for k, v in flat.items():
+        if "FlaxBartEncoderLayers" in k:
+            split["scanned_encoder"][k] = v
+        elif "FlaxBartDecoderLayers" in k:
+            split["scanned_decoder"][k] = v
+        else:
+            split["standard"][k] = v
+    # remove empty keys
+    split = {k: v for k, v in split.items() if v}
+    for k, v in split.items():
+        split[k] = freeze(traverse_util.unflatten_dict(v))
+    return split
+
+
+def unsplit_params(data):
+    flat = {}
+    for k in ["standard", "scanned_encoder", "scanned_decoder"]:
+        if k in data:
+            flat.update(traverse_util.flatten_dict(unfreeze(data[k])))
+    return freeze(traverse_util.unflatten_dict(flat))
+
+
+def trainable_params(data, embeddings_only):
+    """Keep only trainable parameters"""
+
+    if not embeddings_only:
+        return data
+
+    data = unfreeze(data)
+    trainable = {
+        "lm_head": data["lm_head"],
+        "model": {
+            "decoder": {
+                layer: data["model"]["decoder"][layer]
+                for layer in [
+                    "embed_positions",
+                    "embed_tokens",
+                    "final_ln",
+                    "layernorm_embedding",
+                ]
+            }
+        },
+    }
+    return freeze(trainable)
+
+
+def init_embeddings(model, params):
+    """Reinitialize trainable embeddings"""
+    # Must match params in trainable_params() above
+    trainable_keypaths = [
+        "lm_head.kernel",
+        "model.decoder.embed_positions.embedding",
+        "model.decoder.embed_tokens.embedding",
+        "model.decoder.final_ln.bias",
+        "model.decoder.layernorm_embedding.bias",
+        "model.decoder.layernorm_embedding.scale",
+    ]
+
+    # Note: using private _missing_keys
+    init_keys = {tuple(k.split(".")) for k in trainable_keypaths}
+    model._missing_keys = init_keys
+    return model.init_weights(model.key, model.input_shape, params=params)
+
+
+def main():
+    # See all possible arguments by passing the --help flag to this script.
+    parser = HfArgumentParser(
+        (ModelArguments, DataTrainingArguments, TrainingArguments)
+    )
+    if len(sys.argv) == 2 and sys.argv[1].endswith(".json"):
+        # If we pass only one argument to the script and it's the path to a json file,
+        # let's parse it to get our arguments.
+        model_args, data_args, training_args = parser.parse_json_file(
+            json_file=os.path.abspath(sys.argv[1])
+        )
+    else:
+        model_args, data_args, training_args = parser.parse_args_into_dataclasses()
+
+    # check arguments
+    if training_args.mp_devices > jax.local_device_count():
+        assert (
+            data_args.seed_dataset is not None
+        ), "Seed dataset must be provided when model is split over multiple hosts"
+
+    # Make one log on every process with the configuration for debugging.
+    logging.basicConfig(
+        format="%(asctime)s - %(levelname)s - %(name)s - %(message)s",
+        datefmt="%m/%d/%Y %H:%M:%S",
+        level=logging.INFO,
+    )
+    # Setup logging, we only want one process per machine to log things on the screen.
+    logger.setLevel(logging.INFO if jax.process_index() == 0 else logging.ERROR)
+    if jax.process_index() == 0:
+        datasets.utils.logging.set_verbosity_warning()
+        transformers.utils.logging.set_verbosity_info()
+    else:
+        datasets.utils.logging.set_verbosity_error()
+        transformers.utils.logging.set_verbosity_error()
+
+    # Set the verbosity to info of the Transformers logger (on main process only):
+    logger.info(f"Training/evaluation parameters {training_args}")
+
+    # Load dataset
+    dataset = Dataset(
+        **asdict(data_args),
+        do_train=training_args.do_train,
+        do_eval=training_args.do_eval,
+    )
+
+    logger.info(f"Local TPUs: {jax.local_device_count()}")
+    logger.info(f"Global TPUs: {jax.device_count()}")
+
+    # Set up wandb run
+    if jax.process_index() == 0:
+        wandb.init(
+            entity=training_args.wandb_entity,
+            project=training_args.wandb_project,
+            job_type=training_args.wandb_job_type,
+            config=parser.parse_args(),
+        )
+
+    # Set up our new model config
+    config_args = {
+        k: getattr(model_args, k)
+        for k in ["dropout", "activation_dropout", "attention_dropout"]
+        if getattr(model_args, k) is not None
+    }
+    config_args["gradient_checkpointing"] = training_args.gradient_checkpointing
+    if model_args.config_name:
+        config = DalleBartConfig.from_pretrained(model_args.config_name)
+    else:
+        config = None
+
+    # Load or create new model
+    if model_args.model_name_or_path:
+        model, params = DalleBart.from_pretrained(
+            model_args.model_name_or_path,
+            config=config,
+            seed=training_args.seed_model,
+            dtype=getattr(jnp, model_args.dtype),
+            _do_init=False,
+        )
+        if training_args.embeddings_only and training_args.init_embeddings:
+            params = init_embeddings(model, params)
+    else:
+        model = DalleBart(
+            config,
+            seed=training_args.seed_model,
+            dtype=getattr(jnp, model_args.dtype),
+            _do_init=False,
+        )
+        params = None
+    for k, v in config_args.items():
+        setattr(model.config, k, v)
+    params_shape = model.params_shape_tree
+
+    # get model metadata
+    model_metadata = model_args.get_metadata()
+
+    # get PartitionSpec for model params (required to be a dict)
+    param_spec = set_partitions(params_shape, model.config.use_scan)
+    params_shape = freeze(params_shape)
+    if params is not None:
+        params = freeze(params)
+
+    # Load tokenizer
+    tokenizer = DalleBartTokenizer.from_pretrained(
+        model_args.tokenizer_name, use_fast=True
+    )
+
+    # Preprocessing the datasets.
+    # We need to normalize and tokenize inputs and targets.
+    dataset.preprocess(tokenizer=tokenizer, config=model.config)
+
+    # Initialize our training
+    dropout_rng = jax.random.PRNGKey(training_args.seed_model)
+
+    # Store some constant
+    num_epochs = training_args.num_train_epochs
+    # batch size
+    batch_size_per_node_per_grad_step = (
+        training_args.per_device_train_batch_size
+        * jax.local_device_count()
+        // training_args.mp_devices
+    )
+    batch_size_per_node = (
+        batch_size_per_node_per_grad_step * training_args.gradient_accumulation_steps
+    )
+    batch_size_per_step = batch_size_per_node * jax.process_count()
+    eval_batch_size_per_node = (
+        training_args.per_device_eval_batch_size
+        * jax.local_device_count()
+        // training_args.mp_devices
+    )
+    eval_batch_size_per_step = eval_batch_size_per_node * jax.process_count()
+    len_train_dataset, len_eval_dataset = dataset.length
+    steps_per_epoch = (
+        len_train_dataset // batch_size_per_node
+        if len_train_dataset is not None
+        else None
+    )
+    num_train_steps = (
+        steps_per_epoch * num_epochs if steps_per_epoch is not None else None
+    )
+    num_params = model.num_params(params_shape)
+
+    logger.info("***** Running training *****")
+    logger.info(f"  Num examples = {len_train_dataset}")
+    logger.info(f"  Num Epochs = {num_epochs}")
+    logger.info(
+        f"  Batch size per dp device = {training_args.per_device_train_batch_size}"
+    )
+    logger.info(f"  Number of devices = {jax.device_count()}")
+    logger.info(
+        f"  Gradient accumulation steps = {training_args.gradient_accumulation_steps}"
+    )
+    logger.info(f"  Batch size per update = {batch_size_per_step}")
+    logger.info(f"  Model parameters = {num_params:,}")
+
+    # set up wandb run
+    if jax.process_index() == 0:
+        # set default x-axis as 'train/step'
+        wandb.define_metric("*", step_metric="train/step")
+
+        # add interesting config parameters
+        wandb.config.update(
+            {
+                "len_train_dataset": len_train_dataset,
+                "len_eval_dataset": len_eval_dataset,
+                "batch_size_per_step": batch_size_per_step,
+                "num_params": num_params,
+                "model_config": model.config.to_dict(),
+                "num_devices": jax.device_count(),
+                "versions": {
+                    "jax": jax.__version__,
+                    "jaxlib": jaxlib.__version__,
+                    "flax": flax.__version__,
+                    "transformers": transformers.__version__,
+                    "datasets": datasets.__version__,
+                    "wandb": wandb.__version__,
+                    "dalle_mini": dalle_mini.__version__,
+                },
+            }
+        )
+
+    # Create learning rate schedule
+    def create_learning_rate_fn() -> Callable[[int], jnp.array]:
+        """Create the learning rate function."""
+        warmup_fn = optax.linear_schedule(
+            init_value=0.0,
+            end_value=training_args.learning_rate,
+            transition_steps=training_args.warmup_steps + 1,  # ensure not 0
+        )
+        last_boundary = training_args.warmup_steps
+        # offset step when resuming
+        if training_args.lr_offset:
+            warmup_fn = optax.join_schedules(
+                schedules=[optax.constant_schedule(0.0), warmup_fn],
+                boundaries=[training_args.lr_offset],
+            )
+            last_boundary += training_args.lr_offset
+        if training_args.lr_decay is None:
+            return warmup_fn
+        elif training_args.lr_decay == "linear":
+            assert (
+                num_train_steps is not None
+            ), "linear decay requires knowing the dataset length"
+            decay_fn = optax.linear_schedule(
+                init_value=training_args.learning_rate,
+                end_value=0,
+                transition_steps=num_train_steps - training_args.warmup_steps,
+            )
+        elif training_args.lr_decay == "exponential":
+            decay_fn = optax.exponential_decay(
+                init_value=training_args.learning_rate,
+                transition_steps=training_args.lr_transition_steps,
+                decay_rate=training_args.lr_decay_rate,
+                staircase=training_args.lr_staircase,
+            )
+        schedule_fn = optax.join_schedules(
+            schedules=[warmup_fn, decay_fn],
+            boundaries=[last_boundary],
+        )
+        return schedule_fn
+
+    learning_rate_fn = create_learning_rate_fn()
+
+    # create optimizer
+    trainable_params_shape = trainable_params(
+        params_shape, training_args.embeddings_only
+    )
+    if training_args.optim == "distributed_shampoo":
+        # parameters from https://github.com/tensorflow/lingvo/blob/03ee9d7cd50764b0424c7c863733c91fc0b053ec/lingvo/jax/optimizers.py#L729
+        graft_type = {
+            "sgd": GraftingType.SGD,
+            "adagrad": GraftingType.ADAGRAD,
+            "rmsprop": GraftingType.RMSPROP,
+            "rmsprop_normalized": GraftingType.RMSPROP_NORMALIZED,
+            "sqrt_n": GraftingType.SQRT_N,
+            "adagrad_normalized": GraftingType.ADAGRAD_NORMALIZED,
+        }[training_args.graft_type]
+        statistics_partition_spec = (
+            PartitionSpec(None, training_args.shard_shampoo_across, None)
+            if training_args.shard_shampoo_across != "2d"
+            else PartitionSpec(None, "dp", "mp")
+        )
+        opt = distributed_shampoo(
+            learning_rate_fn,
+            block_size=training_args.block_size,
+            beta1=training_args.beta1,
+            beta2=training_args.beta2,
+            diagonal_epsilon=1e-10,
+            matrix_epsilon=1e-6,
+            weight_decay=training_args.weight_decay,
+            start_preconditioning_step=max(
+                training_args.preconditioning_compute_steps + 1, 101
+            ),
+            preconditioning_compute_steps=training_args.preconditioning_compute_steps,
+            statistics_compute_steps=1,
+            best_effort_shape_interpretation=True,
+            graft_type=graft_type,
+            nesterov=training_args.nesterov,
+            exponent_override=0,
+            statistics_partition_spec=statistics_partition_spec,
+            preconditioner_partition_spec=PartitionSpec(
+                training_args.shard_shampoo_across, None, None
+            )
+            if training_args.shard_shampoo_across != "2d"
+            else PartitionSpec(
+                "mp" if training_args.mp_devices > training_args.dp_devices else "dp",
+                None,
+                None,
+            ),
+            num_devices_for_pjit=training_args.dp_devices,
+            shard_optimizer_states=True,
+            inverse_failure_threshold=0.1,
+            moving_average_for_momentum=True,
+            skip_preconditioning_dim_size_gt=training_args.skip_preconditioning_dim_size_gt,
+            clip_by_scaled_gradient_norm=None,
+            precision=jax.lax.Precision.HIGHEST,
+            best_effort_memory_usage_reduction=training_args.optim_quantized,
+        )
+        # get the real optimizer and helper functions
+        update_fn = opt.update
+
+        optimizer = {}
+        opt_fn = {}
+        for k, p in split_params(trainable_params_shape).items():
+            if "scanned" in k:
+                p = jax.eval_shape(
+                    lambda x: jax.tree_util.tree_map(lambda y: y[0], x), p
+                )
+            optimizer[k] = opt.init(p)
+            opt_fn[k] = NamedTuple("opt_fn", pspec_fn=Any, shape_and_dtype_fn=Any)(
+                optimizer[k].pspec_fn, optimizer[k].shape_and_dtype_fn
+            )
+            optimizer[k] = optax.GradientTransformation(optimizer[k].init_fn, update_fn)
+
+    elif training_args.optim == "adam":
+        optimizer = optax.adamw(
+            learning_rate=learning_rate_fn,
+            b1=training_args.beta1,
+            b2=training_args.beta2,
+            eps=training_args.adam_epsilon,
+            weight_decay=training_args.weight_decay,
+        )
+        optimizer = {k: optimizer for k in split_params(trainable_params_shape)}
+
+    elif training_args.optim == "adafactor":
+        # We use the default parameters here to initialize adafactor,
+        # For more details about the parameters please check https://github.com/deepmind/optax/blob/ed02befef9bf81cbbf236be3d2b0e032e9ed4a40/optax/_src/alias.py#L74
+        optimizer = optax.adafactor(
+            learning_rate=learning_rate_fn,
+            clipping_threshold=training_args.max_grad_norm,
+            weight_decay_rate=training_args.weight_decay,
+        )
+        optimizer = {k: optimizer for k in split_params(trainable_params_shape)}
+
+    # get PartitionSpec for optimizer state
+    def get_opt_state_spec_and_shape():
+        # get opt_state shape without actual init
+        opt_state_shape = {}
+        for k, p in split_params(trainable_params_shape).items():
+            if "scanned" not in k:
+                opt_state_shape[k] = jax.eval_shape(optimizer[k].init, p)
+            else:
+                opt_state_shape[k] = jax.eval_shape(jax.vmap(optimizer[k].init), p)
+
+        if training_args.optim == "adafactor":
+            # factorized state must be replicated (rank different than params)
+            opt_state_spec = {k: None for k in split_params(trainable_params_shape)}
+
+        elif training_args.optim in ["adam", "distributed_shampoo"]:
+
+            def _opt_state_spec_per_leaf(x, spec):
+                if isinstance(x, FrozenDict):
+                    # variables with same structure as params
+                    return spec
+                else:
+                    # other variables such as count
+                    return None
+
+            split_spec = split_params(set_partitions(trainable_params_shape, False))
+            opt_state_spec = {}
+            for k, p in split_params(trainable_params_shape).items():
+                if "scanned" in k:
+                    p = jax.eval_shape(
+                        lambda x: jax.tree_util.tree_map(lambda y: y[0], x), p
+                    )
+                if training_args.optim == "adam":
+                    opt_state_spec[k] = jax.tree_util.tree_map(
+                        partial(_opt_state_spec_per_leaf, spec=split_spec[k]),
+                        opt_state_shape[k],
+                        # return None spec for empty elements
+                        is_leaf=lambda x: isinstance(x, (FrozenDict, optax.EmptyState)),
+                    )
+                elif training_args.optim == "distributed_shampoo":
+                    opt_state_spec[k] = opt_fn[k].pspec_fn(
+                        p,
+                        split_spec[k],
+                        statistics_partition_spec,
+                    )
+                # add dimension for scanned params
+                if "scanned" in k:
+                    opt_state_spec[k] = jax.tree_util.tree_map(
+                        lambda x: PartitionSpec(*(None,) + x)
+                        if x is not None
+                        else None,
+                        opt_state_spec[k],
+                        is_leaf=lambda x: isinstance(x, PartitionSpec),
+                    )
+
+        else:
+            raise NotImplementedError
+        return freeze(opt_state_spec), freeze(opt_state_shape)
+
+    opt_state_spec, opt_state_shape = get_opt_state_spec_and_shape()
+
+    # create a mesh
+    mesh_shape = (training_args.dp_devices, training_args.mp_devices)
+    devices = np.asarray(jax.devices()).reshape(*mesh_shape)
+    mesh = maps.Mesh(devices, ("dp", "mp"))
+    logger.info(f"  Mesh shape: {mesh_shape}")
+
+    # define TrainState
+    class TrainState(struct.PyTreeNode):
+        step: int
+        params: core.FrozenDict[str, Any]
+        opt_state: optax.OptState
+        apply_fn: Callable = struct.field(pytree_node=False)
+        tx: optax.GradientTransformation = struct.field(pytree_node=False)
+        dropout_rng: jnp.ndarray = None
+        epoch: int = 0
+        train_time: float = 0.0  # total time the model trained
+        train_samples: int = 0  # number of samples seen
+
+        def apply_gradients(self, *, grads, **kwargs):
+            grads = split_params(trainable_params(grads, training_args.embeddings_only))
+            params = split_params(
+                trainable_params(self.params, training_args.embeddings_only)
+            )
+            opt_state = {}
+            # we loop over keys: "standard", "scanned_encoder", "scanned_decoder"
+            for k, param in params.items():
+                update_fn = self.tx[k].update
+                if "scanned" in k:
+                    update_fn = jax.vmap(update_fn, in_axes=(0, 0, 0), out_axes=(0, 0))
+                updates, new_opt_state = update_fn(grads[k], self.opt_state[k], param)
+                params[k] = optax.apply_updates(param, updates)
+                opt_state[k] = new_opt_state
+            params = unsplit_params(params)
+            # merge with non-trainable params
+            params, new_params = traverse_util.flatten_dict(
+                unfreeze(self.params)
+            ), traverse_util.flatten_dict(unfreeze(params))
+            params.update(new_params)
+            params = freeze(traverse_util.unflatten_dict(params))
+
+            return self.replace(
+                step=self.step + 1,
+                params=params,
+                opt_state=freeze(opt_state),
+                **kwargs,
+            )
+
+        @classmethod
+        def create(cls, *, apply_fn, params, tx, **kwargs):
+            opt_state = {}
+            for k, p in split_params(
+                trainable_params(params, training_args.embeddings_only)
+            ).items():
+                init_fn = tx[k].init
+                if "scanned" in k:
+                    init_fn = jax.vmap(init_fn)
+                opt_state[k] = init_fn(p)
+            return cls(
+                step=0,
+                apply_fn=apply_fn,
+                params=params,
+                tx=tx,
+                opt_state=freeze(opt_state),
+                **kwargs,
+            )
+
+    # define state spec
+    state_spec = TrainState(
+        params=param_spec,
+        opt_state=opt_state_spec,
+        dropout_rng=None,
+        step=None,
+        epoch=None,
+        train_time=None,
+        train_samples=None,
+        apply_fn=model.__call__,
+        tx=optimizer,
+    )
+
+    # init params if not available yet
+    def maybe_init_params(params):
+        if params is not None:
+            # model params are correctly loaded
+            return params
+        else:
+            # params have not been initialized yet
+            return model.init_weights(model.key, model.input_shape)
+
+    with mesh:
+        logger.info("  Creating state")
+
+        # restore metadata
+        attr_state = {}
+        keys = ["train_time", "train_samples"]
+        if model_args.restore_state:
+            keys += ["step", "epoch"]
+        attr_state = {k: v for k, v in model_metadata.items() if k in keys}
+
+        if not model_args.restore_state:
+
+            def init_state(params):
+                return TrainState.create(
+                    apply_fn=model.__call__,
+                    tx=optimizer,
+                    params=maybe_init_params(params),
+                    dropout_rng=dropout_rng,
+                    **attr_state,
+                )
+
+            state = pjit(
+                init_state,
+                in_axis_resources=(param_spec,)
+                if model_args.model_name_or_path
+                else None,
+                out_axis_resources=state_spec,
+                donate_argnums=(0,),
+            )(params)
+
+        else:
+            # load opt_state
+            opt_state = from_bytes(opt_state_shape, model_args.get_opt_state())
+
+            def restore_state(params, opt_state):
+                return TrainState(
+                    apply_fn=model.__call__,
+                    tx=optimizer,
+                    params=params,
+                    opt_state=opt_state,
+                    dropout_rng=dropout_rng,
+                    **attr_state,
+                )
+
+            state = pjit(
+                restore_state,
+                in_axis_resources=(
+                    param_spec,
+                    opt_state_spec,
+                ),
+                out_axis_resources=state_spec,
+                donate_argnums=(0, 1),
+            )(params, opt_state)
+
+            # remove opt_state from CPU
+            del opt_state
+
+    # free CPU memory
+    del params, opt_state_spec, opt_state_shape
+
+    # define batch specs
+    batch_spec = PartitionSpec("dp")
+    grad_batch_spec = PartitionSpec(None, "dp")
+
+    # define loss
+    def loss_fn(logits, labels):
+        loss = optax.softmax_cross_entropy(logits, onehot(labels, logits.shape[-1]))
+        loss = loss.mean()
+        return loss
+
+    # "vmap trick" avoids a crash when mp_devices > 1 (not sure why it happens)
+    # lead to better perf: see https://wandb.ai/dalle-mini/dalle-mini/reports/JAX-pmap-vs-pjit--VmlldzoxNDg1ODA2
+    use_vmap_trick = training_args.use_vmap_trick
+
+    # make grad_param_spec for vmap
+    if use_vmap_trick:
+        grad_param_spec = jax.tree_util.tree_map(
+            lambda x: PartitionSpec(*("dp",) + (x if x is not None else (None,))),
+            param_spec,
+        )
+
+    # Define gradient update step fn
+    def train_step(state, batch, train_time):
+        # get a minibatch (one gradient accumulation slice)
+        def get_minibatch(batch, grad_idx):
+            return jax.tree_util.tree_map(
+                lambda x: jax.lax.dynamic_index_in_dim(x, grad_idx, keepdims=False),
+                batch,
+            )
+
+        def compute_loss(params, minibatch, dropout_rng):
+            # minibatch has dim (batch_size, ...)
+            minibatch, labels = minibatch.pop("labels")
+            logits = state.apply_fn(
+                **minibatch, params=params, dropout_rng=dropout_rng, train=True
+            )[0]
+            return loss_fn(logits, labels)
+
+        grad_fn = jax.value_and_grad(compute_loss)
+
+        def loss_and_grad(grad_idx, dropout_rng):
+            # minibatch at grad_idx for gradient accumulation (None otherwise)
+            minibatch = (
+                get_minibatch(batch, grad_idx) if grad_idx is not None else batch
+            )
+            # ensure it is sharded properly
+            minibatch = with_sharding_constraint(minibatch, batch_spec)
+            # only 1 single rng per grad step, let us handle larger batch size (not sure why)
+            dropout_rng, _ = jax.random.split(dropout_rng)
+
+            if use_vmap_trick:
+                # "vmap trick", calculate loss and grads independently per dp_device
+                loss, grads = jax.vmap(
+                    grad_fn, in_axes=(None, 0, None), out_axes=(0, 0)
+                )(state.params, minibatch, dropout_rng)
+                # ensure they are sharded correctly
+                loss = with_sharding_constraint(loss, batch_spec)
+                grads = with_sharding_constraint(grads, grad_param_spec)
+                # average across all devices
+                # Note: we could average per device only after gradient accumulation, right before params update
+                loss, grads = jax.tree_util.tree_map(
+                    lambda x: jnp.mean(x, axis=0), (loss, grads)
+                )
+            else:
+                # "vmap trick" does not work in multi-hosts and requires too much hbm
+                loss, grads = grad_fn(state.params, minibatch, dropout_rng)
+            # ensure grads are sharded
+            grads = with_sharding_constraint(grads, param_spec)
+            # return loss and grads
+            return loss, grads, dropout_rng
+
+        if training_args.gradient_accumulation_steps == 1:
+            loss, grads, dropout_rng = loss_and_grad(None, state.dropout_rng)
+        else:
+            # create initial state for cumul_minibatch_step loop
+            init_minibatch_step = (
+                0.0,
+                with_sharding_constraint(
+                    jax.tree_util.tree_map(jnp.zeros_like, state.params), param_spec
+                ),
+                state.dropout_rng,
+            )
+
+            # accumulate gradients
+            def cumul_minibatch_step(grad_idx, cumul_loss_grad_dropout):
+                cumul_loss, cumul_grads, dropout_rng = cumul_loss_grad_dropout
+                loss, grads, dropout_rng = loss_and_grad(grad_idx, dropout_rng)
+                cumul_loss, cumul_grads = jax.tree_util.tree_map(
+                    jnp.add, (cumul_loss, cumul_grads), (loss, grads)
+                )
+                cumul_grads = with_sharding_constraint(cumul_grads, param_spec)
+                return cumul_loss, cumul_grads, dropout_rng
+
+            # loop over gradients
+            loss, grads, dropout_rng = jax.lax.fori_loop(
+                0,
+                training_args.gradient_accumulation_steps,
+                cumul_minibatch_step,
+                init_minibatch_step,
+            )
+            grads = with_sharding_constraint(grads, param_spec)
+            # sum -> mean
+            loss, grads = jax.tree_util.tree_map(
+                lambda x: x / training_args.gradient_accumulation_steps, (loss, grads)
+            )
+
+        grads = with_sharding_constraint(grads, param_spec)
+
+        # update state
+        state = state.apply_gradients(
+            grads=grads,
+            dropout_rng=dropout_rng,
+            train_time=train_time,
+            train_samples=state.train_samples + batch_size_per_step,
+        )
+
+        metrics = {
+            "loss": loss,
+            "learning_rate": learning_rate_fn(state.step),
+        }
+
+        def maybe_fn(fn, val, zeros, freq):
+            """Call fn only if it is a logging step"""
+            return jax.lax.cond(
+                state.step % freq == 0,
+                fn,
+                lambda _: zeros,
+                val,
+            )
+
+        # log additional metrics
+        params = trainable_params(state.params, training_args.embeddings_only)
+        grads = trainable_params(grads, training_args.embeddings_only)
+        if training_args.log_norm_steps:
+            zeros_norm = jax.tree_util.tree_map(lambda _: jnp.float32(0), params)
+
+            def norm(val):
+                return jax.tree_util.tree_map(lambda x: jnp.linalg.norm(x), val)
+
+            gradients_norm = maybe_fn(
+                norm, grads, zeros_norm, training_args.log_norm_steps
+            )
+            params_norm = maybe_fn(
+                norm, params, zeros_norm, training_args.log_norm_steps
+            )
+
+            metrics.update(
+                {
+                    "gradients_norm": gradients_norm,
+                    "params_norm": params_norm,
+                }
+            )
+
+        if training_args.log_histogram_steps:
+            zeros_hist = jax.tree_util.tree_map(
+                lambda _: jnp.histogram(jnp.zeros(1), density=True), params
+            )
+
+            def histogram(val):
+                return jax.tree_util.tree_map(
+                    lambda x: jnp.histogram(x, density=True), val
+                )
+
+            gradients_hist = maybe_fn(
+                histogram, grads, zeros_hist, training_args.log_histogram_steps
+            )
+            params_hist = maybe_fn(
+                histogram, params, zeros_hist, training_args.log_histogram_steps
+            )
+
+            metrics.update(
+                {
+                    "params_hist": params_hist,
+                    "gradients_hist": gradients_hist,
+                }
+            )
+
+        return state, metrics
+
+    # Define eval fn
+    eval_model = (
+        model
+        if model_args.dtype == "float32"
+        else DalleBart(
+            model.config,
+            seed=training_args.seed_model,
+            dtype=jnp.float32,
+            _do_init=False,
+        )
+    )
+
+    def eval_step(state, batch):
+        def compute_eval_loss(batch):
+            batch, labels = batch.pop("labels")
+            logits = eval_model(**batch, params=state.params, train=False)[0]
+            return loss_fn(logits, labels)
+
+        if use_vmap_trick:
+            loss = jax.vmap(compute_eval_loss)(batch)
+            # ensure they are sharded correctly
+            loss = with_sharding_constraint(loss, batch_spec)
+            # average across all devices
+            loss = jnp.mean(loss)
+        else:
+            loss = compute_eval_loss(batch)
+
+        return loss
+
+    # Create parallel version of the train and eval step
+    p_train_step = pjit(
+        train_step,
+        in_axis_resources=(
+            state_spec,
+            grad_batch_spec
+            if training_args.gradient_accumulation_steps > 1
+            else batch_spec,
+            None,
+        ),
+        out_axis_resources=(state_spec, None),
+        donate_argnums=(0,),
+    )
+    p_eval_step = pjit(
+        eval_step,
+        in_axis_resources=(state_spec, batch_spec),
+        out_axis_resources=None,
+    )
+
+    # define metrics logger
+    class MetricsLogger:
+        def __init__(self, step):
+            # keep state
+            self.state_dict = {}
+            # estimate speed
+            self.step = step
+            self.time = time.perf_counter()
+            self.offset_time = 0.0
+
+        def update_state_metrics(self, state):
+            """Update internal state metrics (logged at each call to be used as x-axis)"""
+            self.state_dict = {
+                f'train/{k.split("_")[-1]}': state[k]
+                for k in ["step", "epoch", "train_time", "train_samples"]
+            }
+            # timing metrics
+            new_step = int(state["step"])
+            new_time = time.perf_counter()
+            if new_step > self.step:
+                # remove time for eval & save
+                delta_time = new_time - self.time - self.offset_time
+                self.offset_time = 0
+                time_per_step = delta_time / (new_step - self.step)
+                self.step = new_step
+                self.time = new_time
+                self.log_time("train_per_step", time_per_step, offset=False)
+                self.log_time("train_per_log", delta_time, offset=False)
+
+        def log_time(self, key, duration, offset=True):
+            if jax.process_index() == 0:
+                wandb.log({f"time/{key}": duration, **self.state_dict})
+            if offset:
+                self.offset_time += duration
+
+        def log(self, metrics, prefix=None):
+            if jax.process_index() == 0:
+                log_metrics = {}
+                for k, v in metrics.items():
+                    if "_norm" in k:
+                        if self.step % training_args.log_norm_steps == 0:
+                            log_metrics[f"{k}/"] = unfreeze(v)
+                    elif "_hist" in k:
+                        if self.step % training_args.log_histogram_steps == 0:
+                            v = jax.tree_util.tree_map(
+                                lambda x: jax.device_get(x), unfreeze(v)
+                            )
+                            v = jax.tree_util.tree_map(
+                                lambda x: wandb.Histogram(np_histogram=x),
+                                v,
+                                is_leaf=lambda x: isinstance(x, tuple),
+                            )
+                            log_metrics[f"{k}/"] = v
+                    else:
+                        if prefix is not None:
+                            k = f"{prefix}/{k}"
+                        log_metrics[k] = v
+                wandb.log({**log_metrics, **self.state_dict})
+
+    # keep local copy of state
+    local_state = {
+        k: jax.device_get(getattr(state, k)).item()
+        for k in ["step", "epoch", "train_time", "train_samples"]
+    }
+    # init variables
+    start_time = time.perf_counter() - local_state["train_time"]
+    train_metrics = None
+    evaluation_ran = False
+    save_model_ran = False
+    metrics_logger = MetricsLogger(local_state["step"])
+    epochs = tqdm(
+        range(local_state["epoch"], num_epochs),
+        desc=f"Epoch ... (1/{num_epochs})",
+        position=0,
+        disable=jax.process_index() > 0,
+    )
+
+    def run_evaluation():
+        # ======================== Evaluating ==============================
+        if training_args.do_eval:
+            start_eval_time = time.perf_counter()
+            # get validation datasets
+            val_datasets = list(
+                dataset.other_eval_datasets.keys()
+                if hasattr(dataset, "other_eval_datasets")
+                else []
+            )
+            val_datasets += ["eval"]
+            for val_dataset in val_datasets:
+                eval_loader = dataset.dataloader(
+                    val_dataset,
+                    eval_batch_size_per_step
+                    * max(1, training_args.mp_devices // jax.local_device_count()),
+                )
+                eval_steps = (
+                    len_eval_dataset // eval_batch_size_per_step
+                    if len_eval_dataset is not None
+                    else None
+                )
+                eval_loss = []
+                for batch in tqdm(
+                    eval_loader,
+                    desc="Evaluating...",
+                    position=2,
+                    leave=False,
+                    total=eval_steps,
+                    disable=jax.process_index() > 0,
+                ):
+                    # need to keep only eval_batch_size_per_node items relevant to the node
+                    batch = jax.tree_util.tree_map(
+                        lambda x: x.reshape(
+                            (jax.process_count(), eval_batch_size_per_node)
+                            + x.shape[1:]
+                        ),
+                        batch,
+                    )
+                    batch = jax.tree_util.tree_map(
+                        lambda x: x[jax.process_index()], batch
+                    )
+
+                    # add dp dimension when using "vmap trick"
+                    if use_vmap_trick:
+                        bs_shape = (
+                            jax.local_device_count() // training_args.mp_devices,
+                            training_args.per_device_eval_batch_size,
+                        )
+                        batch = jax.tree_util.tree_map(
+                            lambda x: x.reshape(bs_shape + x.shape[1:]), batch
+                        )
+
+                    # freeze batch to pass safely to jax transforms
+                    batch = freeze(batch)
+                    # accumulate losses async
+                    eval_loss.append(p_eval_step(state, batch))
+
+                # get the mean of the loss
+                eval_loss = jnp.stack(eval_loss)
+                eval_loss = jnp.mean(eval_loss)
+                eval_metrics = {"loss": eval_loss}
+
+                # log metrics
+                metrics_logger.log(eval_metrics, prefix=val_dataset)
+
+                # Print metrics and update progress bar
+                desc = f"Epoch... ({epoch + 1}/{num_epochs} | {val_dataset} Loss: {eval_metrics['loss']})"
+                epochs.write(desc)
+                epochs.desc = desc
+
+            # log time
+            metrics_logger.log_time("eval", time.perf_counter() - start_eval_time)
+
+            return eval_metrics
+
+    def run_save_model(state, eval_metrics=None):
+        if jax.process_index() == 0:
+            start_save_time = time.perf_counter()
+            output_dir = training_args.output_dir
+            use_bucket = output_dir.startswith("gs://")
+            if use_bucket:
+                bucket_path = Path(output_dir[5:]) / wandb.run.id / f"step_{state.step}"
+                bucket, dir_path = str(bucket_path).split("/", 1)
+                tmp_dir = tempfile.TemporaryDirectory()
+                output_dir = tmp_dir.name
+
+            # save model
+            params = jax.device_get(state.params)
+            model.save_pretrained(
+                output_dir,
+                params=params,
+            )
+
+            # save tokenizer
+            tokenizer.save_pretrained(output_dir)
+
+            # copy to bucket
+            if use_bucket:
+                client = storage.Client()
+                bucket = client.bucket(bucket)
+                for filename in Path(output_dir).glob("*"):
+                    blob_name = str(Path(dir_path) / "model" / filename.name)
+                    blob = bucket.blob(blob_name)
+                    blob.upload_from_filename(str(filename))
+                tmp_dir.cleanup()
+
+            # save state
+            opt_state = jax.device_get(state.opt_state)
+            if use_bucket:
+                blob_name = str(Path(dir_path) / "state" / "opt_state.msgpack")
+                blob = bucket.blob(blob_name)
+                blob.upload_from_file(io.BytesIO(to_bytes(opt_state)))
+            else:
+                with (Path(output_dir) / "opt_state.msgpack").open("wb") as f:
+                    f.write(to_bytes(opt_state))
+
+            # save to W&B
+            if training_args.log_model:
+                # save some space
+                c = wandb.wandb_sdk.wandb_artifacts.get_artifacts_cache()
+                c.cleanup(wandb.util.from_human_size("20GB"))
+
+                metadata = {
+                    k: jax.device_get(getattr(state, k)).item()
+                    for k in ["step", "epoch", "train_time", "train_samples"]
+                }
+                metadata["num_params"] = num_params
+                if eval_metrics is not None:
+                    metadata["eval"] = eval_metrics
+
+                # create model artifact
+                if use_bucket:
+                    metadata["bucket_path"] = f"gs://{bucket_path}/model"
+                artifact = wandb.Artifact(
+                    name=f"model-{wandb.run.id}",
+                    type="DalleBart_model",
+                    metadata=metadata,
+                )
+                if use_bucket:
+                    artifact.add_reference(metadata["bucket_path"])
+                else:
+                    for filename in [
+                        "config.json",
+                        "flax_model.msgpack",
+                        "merges.txt",
+                        "special_tokens_map.json",
+                        "tokenizer.json",
+                        "tokenizer_config.json",
+                        "vocab.json",
+                    ]:
+                        artifact.add_file(
+                            f"{Path(training_args.output_dir) / filename}"
+                        )
+                wandb.run.log_artifact(artifact)
+
+                # create state artifact
+                if use_bucket:
+                    metadata["bucket_path"] = f"gs://{bucket_path}/state"
+                artifact_state = wandb.Artifact(
+                    name=f"state-{wandb.run.id}",
+                    type="DalleBart_state",
+                    metadata=metadata,
+                )
+                if use_bucket:
+                    artifact_state.add_reference(metadata["bucket_path"])
+                else:
+                    artifact_state.add_file(
+                        f"{Path(training_args.output_dir) / 'opt_state.msgpack'}"
+                    )
+                wandb.run.log_artifact(artifact_state)
+            metrics_logger.log_time("save_model", time.perf_counter() - start_save_time)
+
+    logger.info("  Ready to start training")
+    with mesh:
+        for epoch in epochs:
+            state = state.replace(epoch=epoch)
+            local_state["epoch"] = epoch
+            # ======================== Training ================================
+            metrics_logger.update_state_metrics(local_state)
+            metrics_logger.log({})
+
+            if training_args.do_train:
+                # load data - may be replicated on multiple nodes
+                node_groups = max(
+                    1, training_args.mp_devices // jax.local_device_count()
+                )
+                loader_bs = batch_size_per_node * node_groups
+                train_loader = dataset.dataloader(
+                    "train",
+                    loader_bs,
+                    epoch,
+                )
+                # train
+                for batch in tqdm(
+                    train_loader,
+                    desc="Training...",
+                    position=1,
+                    leave=False,
+                    total=steps_per_epoch,
+                    disable=jax.process_index() > 0,
+                ):
+                    # calculate delta time (we have a lag of one step but it's ok)
+                    train_time = time.perf_counter() - start_time
+
+                    # reset control variables
+                    evaluation_ran = False
+                    save_model_ran = False
+
+                    # set correct shape to batch
+                    # - add grad_step dim if gradient_accumulation_steps > 1
+                    bs_shape = (
+                        (batch_size_per_node_per_grad_step * node_groups,)
+                        if not use_vmap_trick
+                        else (
+                            jax.local_device_count()
+                            * node_groups
+                            // training_args.mp_devices,  # local dp devices
+                            training_args.per_device_train_batch_size,
+                        )
+                    )
+                    if training_args.gradient_accumulation_steps > 1:
+                        # reshape data into (gradient_accumulation_steps, batch_per_node, ...)
+                        # to avoid any data redistribution when sharding
+                        bs_shape = (
+                            training_args.gradient_accumulation_steps,
+                        ) + bs_shape
+
+                    # reshape batch
+                    batch = jax.tree_util.tree_map(
+                        lambda x: x.reshape(bs_shape + x.shape[1:]),
+                        batch,
+                    )
+                    # freeze batch to pass safely to jax transforms
+                    batch = freeze(batch)
+
+                    # train step
+                    state, train_metrics = p_train_step(state, batch, train_time)
+                    local_state["step"] += 1
+                    local_state["train_time"] = train_time
+                    local_state["train_samples"] += batch_size_per_step
+
+                    if (
+                        local_state["step"] % training_args.logging_steps == 0
+                        and jax.process_index() == 0
+                    ):
+                        metrics_logger.update_state_metrics(local_state)
+                        metrics_logger.log(train_metrics, prefix="train")
+
+                    eval_metrics = None
+                    if local_state["step"] % training_args.eval_steps == 0:
+                        eval_metrics = run_evaluation()
+                        evaluation_ran = True
+
+                    if local_state["step"] % training_args.save_steps == 0:
+                        run_save_model(state, eval_metrics)
+                        save_model_ran = True
+
+                # log final train metrics
+                if train_metrics is not None:
+                    metrics_logger.update_state_metrics(local_state)
+                    metrics_logger.log(train_metrics, prefix="train")
+
+                    epochs.write(
+                        f"Epoch... ({epoch + 1}/{num_epochs} | Loss: {train_metrics['loss']}, Learning Rate: {train_metrics['learning_rate']})"
+                    )
+
+            # Final evaluation at the end of each epoch
+            if not evaluation_ran:
+                eval_metrics = run_evaluation()
+
+            # save checkpoint after each epoch
+            if not save_model_ran:
+                run_save_model(state, eval_metrics)
+
+
+if __name__ == "__main__":
+    main()