---
datasets:
- imagenet-1k
library_name: timm
license: apache-2.0
pipeline_tag: image-classification
metrics:
- accuracy
tags:
- ResNet
- CNN
- PDE
---

# Model Card for Model ID

Based on a class of partial differential equations called **quasi-linear hyperbolic systems** [[Liu et al, 2023](https://github.com/liuyao12/ConvNets-PDE-perspective)], the QLNet breaks into uncharted waters of ConvNet model space marked by the use of (element-wise) multiplication in lieu of ReLU as the primary nonlinearity. It achieves comparable performance as ResNet50 on ImageNet-1k (acc=**78.61**), demonstrating that it has the same level of capacity/expressivity, and deserves more analysis and study (hyper-paremeter tuning, optimizer, etc.) by the academic community.


![](https://huggingface.co/liuyao/QLNet/resolve/main/PDE_perspective.jpeg)

One notable feature is that the architecture (trained or not) admits a *continuous* symmetry in its parameters. Check out the [notebook](https://colab.research.google.com/#fileId=https://huggingface.co/liuyao/QLNet/blob/main/QLNet_symmetry.ipynb) for a demo that makes a particular transformation on the weights while leaving the output *unchanged*.

FAQ (as the author imagines):

- Q: Who needs another ConvNet, when the SOTA for ImageNet-1k is now in the low 80s with models of comparable size?
- A: Aside from lack of resources to perform extensive experiments, the real answer is that the new symmetry has the potential to be exploited (e.g., symmetry-aware optimization). The non-activation nonlinearity does have more "naturalness" (coordinate independence) that is innate in many equations in mathematics and physics. Activation is but a legacy from the early days of models inspired by *biological* neural networks.
- Q: Multiplication is too simple, someone must have tried it?
- A: Perhaps. My bet is whoever tried it soon found the model fail to train with standard ReLU. Without the belief in the underlying PDE perspective, maybe it wasn't pushed to its limit.
- Q: Is it not similar to attention in Transformer?
- A: It is, indeed. It's natural to wonder if the activation functions in Transformer could be removed (or reduced) while still achieve comparable performance.
- Q: If the weight/parameter space has a symmetry (other than permutations), perhaps there's redundancy in the weights.
- A: The transformation in our demo indeed can be used to reduce the weights from the get-go. However, there are variants of the model that admit a much larger symmetry. It is also related to the phenomenon of "flat minima" found empirically in some conventional neural networks.

*This modelcard aims to be a base template for new models. It has been generated using [this raw template](https://github.com/huggingface/huggingface_hub/blob/main/src/huggingface_hub/templates/modelcard_template.md?plain=1).*


## Model Details

### Model Description

Instead of the `bottleneck` block of ResNet50 which consists of 1x1, 3x3, 1x1 in succession, this simplest version of QLNet does a 1x1, splits into two equal halves and **multiplies** them, then applies a 3x3 (depthwise), and a 1x1, *all without activation functions* except at the end of the block, where a "radial" activation function that we call `hardball` is applied.

```python
class QLNet(nn.Module):
  ...

  def forward(self, x):
    x0 = self.skip(x)
    x = self.conv1(x)  # 1x1
    C = x.size(1) // 2
    x = x[:, :C, :, :] * x[:, C:, :, :]
    x = self.conv2(x)  # 3x3 depthwise
    x = self.conv3(x)  # 1x1
    x += x0
    if self.act3 is not None:
        x = self.act3(x)
    return x
```

- **Developed by:** Yao Liu 刘杳
- **Model type:** Convolutional Neural Network (ConvNet)
- **License:** As academic work, it is free for all to use. It is a natural progression from the origianl ConvNet (of LeCun) and ResNet, with "depthwise" from MobileNet.
- **Finetuned from model:** N/A (*trained from scratch*)

### Model Sources [optional]

<!-- Provide the basic links for the model. -->

- **Repository:** [ConvNet from the PDE perspective](https://github.com/liuyao12/ConvNets-PDE-perspective)
- **Paper:** [A Novel ConvNet Architecture with a Continuous Symmetry](https://arxiv.org/abs/2308.01621)
- **Demo:** [More Information Needed]

## How to Get Started with the Model

Use the code below to get started with the model.

```python
import torch, timm
from qlnet import QLNet

model = QLNet()
model.load_state_dict(torch.load('qlnet-10m.pth.tar'))
model.eval()
```

## Training Details

### Training and Testing Data

ImageNet-1k

[More Information Needed]

### Training Procedure 

We use the training script in `timm`

```
python3 train.py ../datasets/imagenet/ --model resnet50 --num-classes 1000 --lr 0.1 --warmup-epochs 5 --epochs 240 --weight-decay 1e-4 --sched cosine --reprob 0.4 --recount 3 --remode pixel --aa rand-m7-mstd0.5-inc1 -b 192 -j 6 --amp --dist-bn reduce 
```

### Results

qlnet-10m: acc=78.608