# Reformer

## Overview

The Reformer model was proposed in the paper [Reformer: The Efficient Transformer](https://arxiv.org/abs/2001.04451.pdf) by Nikita Kitaev, Łukasz Kaiser, Anselm Levskaya.

The abstract from the paper is the following:

*Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can

be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of

Transformers. For one, we replace dot-product attention by one that uses locality-sensitive hashing, changing its

complexity from O(L^2) to O(Llog(L)), where L is the length of the sequence. Furthermore, we use reversible residual

layers instead of the standard residuals, which allows storing activations only once in the training process instead of

N times, where N is the number of layers. The resulting model, the Reformer, performs on par with Transformer models

while being much more memory-efficient and much faster on long sequences.*

This model was contributed by [patrickvonplaten](https://huggingface.co/patrickvonplaten). The Authors' code can be

found [here](https://github.com/google/trax/tree/master/trax/models/reformer).

## Usage tips

- Reformer does **not** work with *torch.nn.DataParallel* due to a bug in PyTorch, see [issue #36035](https://github.com/pytorch/pytorch/issues/36035).

- Use Axial position encoding (see below for more details). It’s a mechanism to avoid having a huge positional encoding matrix (when the sequence length is very big) by factorizing it into smaller matrices.

- Replace traditional attention by LSH (local-sensitive hashing) attention (see below for more details). It’s a technique to avoid computing the full product query-key in the attention layers.

- Avoid storing the intermediate results of each layer by using reversible transformer layers to obtain them during the backward pass (subtracting the residuals from the input of the next layer gives them back) or recomputing them for results inside a given layer (less efficient than storing them but saves memory).

- Compute the feedforward operations by chunks and not on the whole batch.

### Axial Positional Encodings

Axial Positional Encodings were first implemented in Google's [trax library](https://github.com/google/trax/blob/4d99ad4965bab1deba227539758d59f0df0fef48/trax/layers/research/position_encodings.py#L29)

and developed by the authors of this model's paper. In models that are treating very long input sequences, the

conventional position id encodings store an embedings vector of size \\(d\\) being the `config.hidden_size` for

every position \\(i, \ldots, n_s\\), with \\(n_s\\) being `config.max_embedding_size`. This means that having

a sequence length of \\(n_s = 2^{19} \approx 0.5M\\) and a `config.hidden_size` of \\(d = 2^{10} \approx 1000\\)

would result in a position encoding matrix:

$$X_{i,j}, \text{ with } i \in \left[1,\ldots, d\right] \text{ and } j \in \left[1,\ldots, n_s\right]$$

which alone has over 500M parameters to store. Axial positional encodings factorize \\(X_{i,j}\\) into two matrices:

$$X^{1}_{i,j}, \text{ with } i \in \left[1,\ldots, d^1\right] \text{ and } j \in \left[1,\ldots, n_s^1\right]$$

and

$$X^{2}_{i,j}, \text{ with } i \in \left[1,\ldots, d^2\right] \text{ and } j \in \left[1,\ldots, n_s^2\right]$$

with:

$$d = d^1 + d^2 \text{ and } n_s = n_s^1 \times n_s^2 .$$

Therefore the following holds:

$$X_{i,j} = \begin{cases}

X^{1}_{i, k}, & \text{if }\ i < d^1 \text{ with } k = j \mod n_s^1 \\

X^{2}_{i - d^1, l}, & \text{if } i \ge d^1 \text{ with } l = \lfloor\frac{j}{n_s^1}\rfloor

\end{cases}$$

Intuitively, this means that a position embedding vector \\(x_j \in \mathbb{R}^{d}\\) is now the composition of two

factorized embedding vectors: \\(x^1_{k, l} + x^2_{l, k}\\), where as the `config.max_embedding_size` dimension

\\(j\\) is factorized into \\(k \text{ and } l\\). This design ensures that each position embedding vector

\\(x_j\\) is unique.

Using the above example again, axial position encoding with \\(d^1 = 2^9, d^2 = 2^9, n_s^1 = 2^9, n_s^2 = 2^{10}\\)

can drastically reduced the number of parameters from 500 000 000 to \\(2^{18} + 2^{19} \approx 780 000\\) parameters, this means 85% less memory usage.

In practice, the parameter `config.axial_pos_embds_dim` is set to a tuple \\((d^1, d^2)\\) which sum has to be

equal to `config.hidden_size` and `config.axial_pos_shape` is set to a tuple \\((n_s^1, n_s^2)\\) which

product has to be equal to `config.max_embedding_size`, which during training has to be equal to the *sequence

length* of the `input_ids`.

### LSH Self Attention

In Locality sensitive hashing (LSH) self attention the key and query projection weights are tied. Therefore, the key

query embedding vectors are also tied. LSH self attention uses the locality sensitive hashing mechanism proposed in

[Practical and Optimal LSH for Angular Distance](https://arxiv.org/abs/1509.02897) to assign each of the tied key

query embedding vectors to one of `config.num_buckets` possible buckets. The premise is that the more "similar"

key query embedding vectors (in terms of *cosine similarity*) are to each other, the more likely they are assigned to

the same bucket.

The accuracy of the LSH mechanism can be improved by increasing `config.num_hashes` or directly the argument

`num_hashes` of the forward function so that the output of the LSH self attention better approximates the output

of the "normal" full self attention. The buckets are then sorted and chunked into query key embedding vector chunks

each of length `config.lsh_chunk_length`. For each chunk, the query embedding vectors attend to its key vectors

(which are tied to themselves) and to the key embedding vectors of `config.lsh_num_chunks_before` previous

neighboring chunks and `config.lsh_num_chunks_after` following neighboring chunks.

For more information, see the [original Paper](https://arxiv.org/abs/2001.04451) or this great [blog post](https://www.pragmatic.ml/reformer-deep-dive/).

Note that `config.num_buckets` can also be factorized into a list \\((n_{\text{buckets}}^1,

n_{\text{buckets}}^2)\\). This way instead of assigning the query key embedding vectors to one of \\((1,\ldots,

n_{\text{buckets}})\\) they are assigned to one of \\((1-1,\ldots, n_{\text{buckets}}^1-1, \ldots,

1-n_{\text{buckets}}^2, \ldots, n_{\text{buckets}}^1-n_{\text{buckets}}^2)\\). This is crucial for very long sequences to

save memory.

When training a model from scratch, it is recommended to leave `config.num_buckets=None`, so that depending on the

sequence length a good value for `num_buckets` is calculated on the fly. This value will then automatically be

saved in the config and should be reused for inference.

Using LSH self attention, the memory and time complexity of the query-key matmul operation can be reduced from

\\(\mathcal{O}(n_s \times n_s)\\) to \\(\mathcal{O}(n_s \times \log(n_s))\\), which usually represents the memory

and time bottleneck in a transformer model, with \\(n_s\\) being the sequence length.

### Local Self Attention

Local self attention is essentially a "normal" self attention layer with key, query and value projections, but is

chunked so that in each chunk of length `config.local_chunk_length` the query embedding vectors only attends to

the key embedding vectors in its chunk and to the key embedding vectors of `config.local_num_chunks_before`

previous neighboring chunks and `config.local_num_chunks_after` following neighboring chunks.

Using Local self attention, the memory and time complexity of the query-key matmul operation can be reduced from

\\(\mathcal{O}(n_s \times n_s)\\) to \\(\mathcal{O}(n_s \times \log(n_s))\\), which usually represents the memory

and time bottleneck in a transformer model, with \\(n_s\\) being the sequence length.

### Training

During training, we must ensure that the sequence length is set to a value that can be divided by the least common

multiple of `config.lsh_chunk_length` and `config.local_chunk_length` and that the parameters of the Axial

Positional Encodings are correctly set as described above. Reformer is very memory efficient so that the model can

easily be trained on sequences as long as 64000 tokens.

For training, the [`ReformerModelWithLMHead`] should be used as follows:

thon

input_ids = tokenizer.encode("This is a sentence from the training data", return_tensors="pt")

loss = model(input_ids, labels=input_ids)[0]

## Resources

- [Text classification task guide](../tasks/sequence_classification)

- [Question answering task guide](../tasks/question_answering)

- [Causal language modeling task guide](../tasks/language_modeling)

- [Masked language modeling task guide](../tasks/masked_language_modeling)

## ReformerConfig

[[autodoc]] ReformerConfig

## ReformerTokenizer

[[autodoc]] ReformerTokenizer

    - save_vocabulary

## ReformerTokenizerFast

[[autodoc]] ReformerTokenizerFast

## ReformerModel

[[autodoc]] ReformerModel

    - forward

## ReformerModelWithLMHead

[[autodoc]] ReformerModelWithLMHead

    - forward

## ReformerForMaskedLM

[[autodoc]] ReformerForMaskedLM

    - forward

## ReformerForSequenceClassification

[[autodoc]] ReformerForSequenceClassification

    - forward

## ReformerForQuestionAnswering

[[autodoc]] ReformerForQuestionAnswering

    - forward