x-transformers

x-transformers

A concise but fully-featured transformer, complete with a set of promising experimental features from various papers.

Install

$ pip install x-transformers

Usage

Full encoder / decoder

import torch
from x_transformers import XTransformer

model = XTransformer(
    dim = 512,
    enc_num_tokens = 256,
    enc_depth = 6,
    enc_heads = 8,
    enc_max_seq_len = 1024,
    dec_num_tokens = 256,
    dec_depth = 6,
    dec_heads = 8,
    dec_max_seq_len = 1024,
    tie_token_emb = True      # tie embeddings of encoder and decoder
)

src = torch.randint(0, 256, (1, 1024))
src_mask = torch.ones_like(src).bool()
tgt = torch.randint(0, 256, (1, 1024))

loss = model(src, tgt, mask = src_mask) # (1, 1024, 512)
loss.backward()

Decoder-only (GPT-like)

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8
    )
).cuda()

x = torch.randint(0, 256, (1, 1024)).cuda()

model(x) # (1, 1024, 20000)

GPT3 would be approximately the following (but you wouldn't be able to run it anyways)

gpt3 = TransformerWrapper(
    num_tokens = 50000,
    max_seq_len = 2048,
    attn_layers = Decoder(
        dim = 12288,
        depth = 96,
        heads = 96,
        attn_dim_head = 128
    )
).cuda()

Encoder-only (BERT-like)

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 12,
        heads = 8
    )
).cuda()

x = torch.randint(0, 256, (1, 1024)).cuda()
mask = torch.ones_like(x).bool()

model(x, mask = mask) # (1, 1024, 20000)

State of the art image classification (SimpleViT)

import torch
from x_transformers import ViTransformerWrapper, Encoder

model = ViTransformerWrapper(
    image_size = 256,
    patch_size = 32,
    num_classes = 1000,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8,
    )
)

img = torch.randn(1, 3, 256, 256)
model(img) # (1, 1000)

Image -> caption

import torch
from x_transformers import ViTransformerWrapper, TransformerWrapper, Encoder, Decoder

encoder = ViTransformerWrapper(
    image_size = 256,
    patch_size = 32,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8
    )
)

decoder = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        cross_attend = True
    )
)

img = torch.randn(1, 3, 256, 256)
caption = torch.randint(0, 20000, (1, 1024))

encoded = encoder(img, return_embeddings = True)
decoder(caption, context = encoded) # (1, 1024, 20000)

PaLI, state of the art language-vision model

import torch
from x_transformers import ViTransformerWrapper, XTransformer, Encoder

# PaLI composes of
# 1. vision transformer (ViTransformerWrapper) +
# 2. encoder-decoder transformer (XTransformer)

vit = ViTransformerWrapper(
    image_size = 256,
    patch_size = 32,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8
    )
)

pali = XTransformer(
    dim = 512,
    enc_num_tokens = 256,
    enc_depth = 6,
    enc_heads = 8,
    enc_max_seq_len = 1024,
    dec_num_tokens = 256,
    dec_depth = 6,
    dec_heads = 8,
    dec_max_seq_len = 1024
)

# training data

img = torch.randn(1, 3, 256, 256)               # images
prompt = torch.randint(0, 256, (1, 1024))       # prompt
prompt_mask = torch.ones(1, 1024).bool()        # prompt text mask
output_text = torch.randint(0, 256, (1, 1024))  # target output text

# train

img_embeds = vit(
    img,
    return_embeddings = True
)

loss = pali(
    prompt,
    output_text,
    mask = prompt_mask,
    src_prepend_embeds = img_embeds             # will preprend image embeddings to encoder text embeddings before attention
)

loss.backward()

# do the above for many steps on a 17B parameter model
# attention is all you need

Dropouts

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    emb_dropout = 0.1,         # dropout after embedding
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        layer_dropout = 0.1,   # stochastic depth - dropout entire layer
        attn_dropout = 0.1,    # dropout post-attention
        ff_dropout = 0.1       # feedforward dropout
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

Features

Flash Attention

What originally started off as a short paper from Markus Rabe culminated as a practical fused attention CUDA kernel, named Flash Attention by Tri Dao.

The technique processes the attention matrix in tiles, only keeping track of the running softmax and exponentiated weighted sums. By recomputing on the backwards pass in a tiled fashion, one is able to keep the memory linear with respect to sequence length. This allows a lot of recent models to be able to reach for longer context lengths without worrying about the memory bottleneck.

Other engineering decisions made by Tri Dao led to its enormous success, namely minimizing HBM accesses so that both the forwards and backwards outperform naive attention. In other words, flash attention is not only more memory efficient, but faster as well, making it a necessity for training transformers.

MetaAI has recently added the ability to use Tri Dao's CUDA kernel through the scaled_dot_product_attention function in Pytorch 2.0. (They also have a mem_efficient attention, which is identical to flash attention design, just that the tiles are traversed differently)

Llama was trained using Flash Attention. The only reason to avoid it is if you require operating on the attention matrix (dynamic positional bias, talking heads, residual attention).

You can use it in this repository by setting attn_flash to True and enjoy the immediate memory savings and increase in speed.

ex.

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_flash = True # just set this to True if you have pytorch 2.0 installed
    )
)

Augmenting Self-attention with Persistent Memory

https://arxiv.org/abs/1907.01470

Proposes adding learned memory key / values prior to attention. They were able to remove feedforwards altogether and attain similar performance to the original transformers. I have found that keeping the feedforwards and adding the memory key / values leads to even better performance.

from x_transformers import Decoder, Encoder

enc = Encoder(
    dim = 512,
    depth = 6,
    heads = 8,
    attn_num_mem_kv = 16 # 16 memory key / values
)

Memory Transformers

https://arxiv.org/abs/2006.11527

Proposes adding learned tokens, akin to CLS tokens, named memory tokens, that is passed through the attention layers alongside the input tokens. This setting is compatible with both encoder and decoder training.

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    num_memory_tokens = 20, # 20 memory tokens
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8
    )
)

Update: MetaAI researchers have found that adding memory tokens (they call them register tokens), alleviates outliers (which is suspected now to be a pathology of attention networks unable to attend to nothing).

Update 2: a hybrid architecture out of Nvidia named Hymba used memory tokens successfully in the autoregressive case, termed meta tokens in their paper.

Update 3: further corroborated by a paper trying to extend memory in attention networks, termed persistent memory

Transformers Without Tears

https://arxiv.org/abs/1910.05895

They experiment with alternatives to Layer normalization and found one that is both effective and simpler. Researchers have shared with me this leads to faster convergence.

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        use_scalenorm = True # set to True to use for all layers
    )
)

You can also use the l2 normalized embeddings proposed as part of fixnorm. I have found it leads to improved convergence, when paired with small initialization (proposed by BlinkDL). The small initialization will be taken care of as long as l2norm_embed is set to True

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    l2norm_embed = True,    # set this to True for l2 normalized embedding + small init
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8
    )
)

Along the same lines of l2 normalized embeddings, Huggingface's 175B parameter BLOOM also places a layernorm right after the embeddings and just before the tokens enter the attention layers. This was corroborated by Yandex's 100B parameter YaLM to stabilize training.

It is recommended you either have either l2norm_embed or post_emb_norm set to True but not both, as they probably serve the same purpose.

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    post_emb_norm = True,    # set this to True to layernorm summed token + pos embeddings
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8
    )
)

Root Mean Square Layer Normalization

https://arxiv.org/abs/1910.07467

The authors propose to replace layer normalization with a simpler alternative, without mean centering and the learned bias. An investigative paper found this to be the best performing normalization variant. It was also used in Deepmind's latest large language models, Retro and Gopher.

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        use_rmsnorm = True # set to true to use for all layers
    )
)

July 2023 A linear attention paper has experiments to show that removing the learned multiplicative gamma led to no performance degradation. This simplifies the RMS normalization to a satisfying l2norm(x) * sqrt(dim).

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        use_simple_rmsnorm = True # set to true to use for all layers
    )
)

GLU Variants Improve Transformer

https://arxiv.org/abs/2002.05202

Noam Shazeer paper that explores gating in the feedforward, finding that simple gating with GELU leads to significant improvements. This variant also showed up in the latest mT5 architecture. You should always turn this on (I may eventually turn it on by default).

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        ff_glu = True # set to true to use for all feedforwards
    )
)

The PaLM language model also chose to use the Swish GLU variant. You can turn this on by setting two flags

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        ff_swish = True, # set this to True
        ff_glu = True    # set to true to use for all feedforwards
    )
)

No Bias in Feedforward

Starting with PaLM, there begun a trend to remove biases from the transformer all together. Boris Dayma has run a number of experiments that showed removing biases from feedforwards led to increased throughput without any loss of accuracy. This was corroborated by yet another paper investigating transformer architecture variants.

You can turn off the feedforward bias as follows

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        ff_no_bias = True  # set this to True
    )
)

ReLU²

https://arxiv.org/abs/2109.08668

This paper used neural architecture search and found an activation, Relu Squared, that is both simpler and performs better than GELU, in the autoregressive language model setting. I have confirmed this in my independent experiments. However, if one were using the GLU variant from above, GELU still performs better. Pending further corroboration.

import torch
from x_transformers import TransformerWrapper, Decoder, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        ff_relu_squared = True
    )
)

Explicit Sparse Transformer: Concentrated Attention Through Explicit Selection

https://arxiv.org/abs/1912.11637

This paper proposes an efficient way to sparsify attention by zeroing all dot-product query/key values not within the top k values. The show that this cheap method was as effective as other more expensive operations like sparsemax or entmax15. This technique comes with the cost of an extra hyperparameter (the top k values to keep). The paper recommends a value of k = 8

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_sparse_topk = 8,                       # keep only the top 8 values before attention (softmax)
        attn_sparse_topk_straight_through = True    # straight through the original gradients
    )
)

An extreme case of topk value of 1, you can use the following

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_hard = True  # will only propagate the single value of the argmax of qk logit. offered in the case it addresses https://arxiv.org/abs/2410.01104
    )
)

Talking-Heads Attention

https://arxiv.org/abs/2003.02436

A Noam Shazeer paper that proposes mixing information between heads pre and post attention (softmax). This comes with the cost of extra memory and compute.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_pre_talking_heads = True,  # linear combination across pre-softmax attn logits across heads
        attn_post_talking_heads = True  # linear combination across post-softmax attn across heads
    )
)

One Write-Head Is All You Need

https://arxiv.org/abs/1911.02150

Yet another Noam Shazeer paper (he's a legend) that proposes to only have one head for the key / values, but multi-headed queries. This paper was largely ignored for a while, but recently validated at scale in AlphaCode as well as PaLM. It has the property of being memory efficient when decoding extremely large language models. You can use it with one keyword argument as shown below.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_one_kv_head = True
    )
)

This has been further generalized in a recent paper to allow for groups of query heads to attend to a single key / value head. You can use this by specifying the attn_kv_heads

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8,
        attn_kv_heads = 2 # say you want 4 query heads to attend to 1 key / value head
    )
)

Attention on Attention for Image Captioning

https://arxiv.org/abs/1908.06954

This paper proposes to add a gated linear unit at the end of the attention layer, further gated by the original queries. Although this is not widely used outside of visual question / answering, I suspect it should lead to improvements after seeing the success of the feedforward GLU variant.

Update: After some experimentation, I found this variant actually performs worse, but if it were to be modified to not concatenate the queries before gating, it performs much better. That is what we will be using in this repository.

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_on_attn = True  # gate output of attention layer, by queries
    )
)

Intra-attention Gating on Values

Alphafold2 had a peculiar variant of attention where they gate the aggregated values with the input, presumably to have the block have more control over the update.

A quick test shows a small but noticeable improvement, on about the same order as attention on attention.

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_gate_values = True  # gate aggregated values with the input
    )
)

Improving Transformer Models by Reordering their Sublayers

https://arxiv.org/abs/1911.03864

This paper proposes to break from the normal fixed pattern of alternating attention and feedforwards, but to have blocks of only attention at the beginning followed by blocks of feedforwards at the end. This was further corroborated by a paper by Nvidia that reduces the number of attention layers to be 1/3rd of the feedforwards without loss in performance.

The amount of interleaving is controlled by a "sandwich coefficient", which they found to be optimal at a value of 6.

You can experiment with this feature as shown below

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8,
        sandwich_coef = 6  # interleave attention and feedforwards with sandwich coefficient of 6
    )
)

Weight-tied Layers

In the early days of the cambrian explosion of BERT, a paper explored weight tying all the layers, the model named ALBERT. You can use it by setting weight_tie_layers = True

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 12,
        weight_tie_layers = True   # set this to True to weight tie all the layers
    )
)

If you wish to do something more sophisticated, say 3 layers, with each layer recurrent 4 times before onto the next (similar to this paper), that is possible as well. Be aware the layers_execute_order is 0-indexed

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        custom_layers = (
            'a', 'f',        # 3 sets of attention and feedforward
            'a', 'f',
            'a', 'f'
        ),
        layers_execute_order = (
            *((0, 1) * 4),   # each done 4 times before sequentially passed forward, but you can probably imagine some more interesting configurations...
            *((2, 3) * 4),
            *((4, 5) * 4),
        )
    )
)

Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View

https://arxiv.org/abs/1906.02762

The authors propose to view the success of transformers from a dynamical systems point of view, and then proposes an improvement based on mathematics of that POV. Specifically, they propose to place the attention layer in between two feedforward layers. This was adopted by a paper using transformers for speech recognition, the Conformer.

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8,
        macaron = True  # use macaron configuration
    )
)

T5's Simplified Relative Positional Encoding

https://arxiv.org/abs/1910.10683

T5 is one of the most successful encoder / decoder transformer architectures trained to date. They invented a new simplified relative positional encoding based on learned bias values that are added to the attention matrix pre-softmax. This bias is shared and injected into each attention layer. I have decided to include this because it offers a cheap way to have relative positional encoding (superior to absolute positional), and I have read papers that suggest having positional encoding added to each layer (vs only before the first) is beneficial.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        rel_pos_bias = True  # adds relative positional bias to all attention layers, a la T5
    )
)

Residual Attention

https://arxiv.org/abs/2012.11747

This paper from Google proposes residualizing the pre-attention scores across all layers. At the cost of no extra parameters, they show improvement on top of regular attention networks. If you turn on this setting, be aware that the best results in the paper used post-normalization, in which case a learning warmup will be needed. The authors also reported that they could use a higher learning rate and get even better gains in the same amount of steps. (In the paper they use 2e-4 vs 1e-4 for vanilla transformer)

import torch
from x_transformers import TransformerWrapper, Encoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Encoder(
        dim = 512,
        depth = 6,
        heads = 8,
        pre_norm = False,       # in the paper, residual attention had best results with post-layernorm
        residual_attn = True    # add residual attention
    )
)

I also tried residualizing cross attention and may have noticed an improvement in convergence. You can try it by setting the cross_residual_attn keyword to True

import torch
from x_transformers import XTransformer

model = XTransformer(
    dim = 512,
    enc_num_tokens = 256,
    enc_depth = 6,
    enc_heads = 8,
    enc_max_seq_len = 1024,
    dec_num_tokens = 256,
    dec_depth = 6,
    dec_heads = 8,
    dec_max_seq_len = 1024,
    dec_cross_residual_attn = True     # residualize cross attention
)

Transformer-XL recurrence

You can also do Transformer-XL recurrence, by simply passing in a max_mem_len in the TransformerWrapper class, and then making sure your Decoder has rel_pos_bias (or rotary_pos_emb) set to True.

Then, you can retrieve the memories at each step with the return_mems keyword and pass it to the next iteration.

import torch
from x_transformers import TransformerWrapper, Decoder

model_xl = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 512,
    max_mem_len = 2048,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        rel_pos_bias = True
    )
)

seg1 = torch.randint(0, 20000, (1, 512))
seg2 = torch.randint(0, 20000, (1, 512))
seg3 = torch.randint(0, 20000, (1, 512))

logits1, mems1  = model_xl(seg1, return_mems = True)
logits2, mems2  = model_xl(seg2, mems = mems1, return_mems = True)
logits3, mems3  = model_xl(seg3, mems = mems2, return_mems = True)

Setting up the logic for training and sampling from transformer xl can be a bit overwhelming. This repository offers a simple wrapper that should make this easy, with the XLAutoregressiveWrapper.

# pass in the above model_xl

xl_wrapper = XLAutoregressiveWrapper(model_xl)

seg = torch.randint(0, 20000, (1, 4096)).cuda()  # sequence exceeding max length, automatically segmented and memory managed

loss = xl_wrapper(seg)
loss.backward()

# then, after much training

prime = seg[:, :1024]   # if prime exceeds max length, memory will be caught up before generating

generated = xl_wrapper.generate(prime, 4096)  # (1, 4096)

Enhanced recurrence

This paper proposes a simple technique to enhance the range of Transformer-XL. They simply route the memory segment of a layer to the layer below it, for the next recurrent step. You can enable this by setting shift_mem_down = 1. You can also shift down arbitrary number of layers by setting this value to > 1.

import torch
from x_transformers import TransformerWrapper, Decoder

model_xl = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 512,
    max_mem_len = 2048,
    shift_mem_down = 1,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        rotary_pos_emb = True,
        rotate_num_heads = 4   # only rotate 4 out of the 8 attention heads
    )
)

seg1 = torch.randint(0, 20000, (1, 512))
seg2 = torch.randint(0, 20000, (1, 512))
seg3 = torch.randint(0, 20000, (1, 512))

logits1, mems1  = model_xl(seg1, return_mems = True)
logits2, mems2  = model_xl(seg2, mems = mems1, return_mems = True) # mems1 of layer N are automatically routed to the layer N-1

Gated residual

https://arxiv.org/abs/1910.06764

The authors propose gating the residual connections in the transformer network and demonstrate increased stability and performance for Transformer-XL in a variety of reinforcement learning tasks.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    max_mem_len = 2048,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 16,
        gate_residual = True
    )
)

Rotary Positional Embeddings

Developed in Beijing, this new technique quickly gained interest in the NLP circles. In short, it allows you to endow the transformer with relative positional embeddings at the cost of no learned parameters. You apply a rotary operation to the queries and keys prior to their dot product in attention. The big idea is injecting positions through rotations.

Highly recommend that you have this turned on whenever you are working on an ordered sequence.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        rotary_pos_emb = True  # turns on rotary positional embeddings
    )
)

Update (12/2022): Rotary embedding has since been hugely successful, widely adopted in many large language models, including the largest in the world, PaLM. However, it has been uncovered in the ALiBi paper that rotary embeddings cannot length extrapolate well. This was recently addressed in a Microsoft research paper. They propose a way to unobtrusively add the same decay as in ALiBi, and found that this resolves the extrapolation problem. You can use it in this repository by setting rotary_xpos = True. Like ALiBi, it would enforce the attention to be local. You can set the receptive field with rotary_xpos_scale_base value, which defaults to 512

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        rotary_xpos = True   # modified rotary to extrapolate well beyond length at which it was trained
    )
)

Dynamic Positional Bias

This technique bears roots from the field of vision transformers, where researchers are trying to have relative positions generalize to larger resolutions (without having to retrain the entire network). It was used in two recent papers, CrossFormer, as well as SwinV2.

Charles Foster first tried this for a language model, and found that it works. Later on Eric Engelhart produced experimental results that show the same type of extrapolation holds, even for 1d sequences.

Eric trained at sequence lengths of 128, and showed that it generalized well to 1024. In addition, he showed that linear positions was better than log (used in SwinV2), for language.

Linear distances

Log distances

Negative control - Sinusoidal

More of Eric's experimental results can be found here

You can use this type of relative position if you wish to train at smaller sequence lengths and have it generalize to longer ones, for both autoregressive and bidirectional models.

Update: First place RNA folding using dynamic positional bias

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 256,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        dynamic_pos_bias = True,                # set this to True
        dynamic_pos_bias_log_distance = False   # whether to use log distance, as in SwinV2
    )
)

ALiBi Positional Embedding

This paper proposes to simply apply a static linear bias to the attention matrix. The authors show this is not only effective as a relative positional encoding, but also allows the attention net to extrapolate to greater sequences length than what it was trained on, for autoregressive language models.

This repository also offers a bidirectional variant (nonsymmetric), proposed by the authors here. However, this is untested. If you need bidirectional length extrapolation, the safest option would be Dynamic Position Bias

Update: It may be that ALiBi enforces a strong local attention across the heads, and may hinder it from attending at distances greater than 1k. To avoid any issues with global message passing, I've decided to introduce another hyperparameter alibi_num_heads, so one can specify less heads for the ALiBi bias

Update: There are reports that ALiBi outperform Rotary embeddings for pretraining and downstream fine-tuning.

Update: New paper shows that no positional embedding can length extrapolate even than explicit ones

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        alibi_pos_bias = True, # turns on ALiBi positional embedding
        alibi_num_heads = 4    # only use ALiBi for 4 out of the 8 heads, so other 4 heads can still attend far distances
    )
)

Shifted Tokens

An independent researcher has found that shifting a subset of the feature dimension along the sequence dimension by 1 token helps with convergence (Time-mixing). I have tested this for the autoregressive case and can confirm that it leads to greatly improved convergence. This also lines up with the results of some papers in the vision domain.

To use it, simply set shift_tokens = 1 (or to whatever number of shifts you desire). The feature dimension will be divided by shift_tokens + 1 and then each chunk will be shifted [0, shift_tokens] respectively

Update: new experiments by @sdtblck suggests this may only work for character-level training

Update: after more experiments, it seems that in the context of BPE encoding, with rotary turned on, there is no benefit to shifting. for character-level training, shifting may still improve a tiny bit

Update: When doing BPE encoded tokens, it seems that shift of 2 will bottleneck the dimensions (divided by 5). It is recommended you always do a shift of 1, unless if you are working with character level.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        shift_tokens = 1
    )
)

If you want finer control over how much is shifted per block (whether attention or feedforward), simply pass in a tuple of size that is equal to the number of layers.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        shift_tokens = (1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0) # 12 blocks, attention and feedforward alternating, with progressively less shifting
    )
)

Sandwich Norm

This technique first made an appearance in the CoqView paper, a Chinese version of the famous text-to-image transformer DALL-E. They propose, when using pre-layernorm, to add an extra layernorm to all the branch outputs. I have found this to be very effective for a number of projects, when facing instability during training.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        sandwich_norm = True # set this to True
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

ResiDual

This Microsoft paper proposes yet another normalization configuration, combining both pre and post layernorm. They claim this hybridization reduces representation collapse (known to be an issue with pre-layernorm with increasing depth), while maintaining stability and reducing vanishing gradients (issues with post-layernorm). Initial experiments on my end show it to work no worse than pre-layernorm or sandwich norm. More study needed by the public to see if this is actually a winning technique.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        resi_dual = True,               # set this to True
        resi_dual_scale = 0.1           # in appendix, they said on fp16 the prenorm residual is prone to overflow. they claim by scaling it at each layer by a factor, it would prevent the overflow, and keep results the same (as layernorms are invariant to scaling of the input)
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

Normformer

This paper uncovers an issue with pre-norm transformers where gradients are mismatched between the early and later layers. They propose 4 changes, of which I will be offering 3.

The first change is to offer per head scaling after aggregating the values in attention. My experiments show a slight improvement in convergence.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_head_scale = True  # set this to True
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

The second change is an extra layernorm right after the activation in the feedforward. I have also verified a slight improvement, at the cost of extra compute.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        ff_post_act_ln = True # set this to True
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

For the residual scaling, you simply have to set scale_residual = True. I have noticed slight improvements, but occasional instability as well, so use with caution.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        scale_residual = True # set this to True
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

The last change is a layernorm right after the outwards projection in attention. This is actually identical to the sandwich norm proposed by the Coqview paper, so you can use this by simply setting sandwich_norm = True, although it would also add it to the feedforward layer.

Cosine Sim Attention

This paper proposes to l2 normalize the queries and keys along the head dimension before the dot product (cosine similarity), with the additional change of the scale being learned rather than static. The normalization prevents the attention operation from overflowing, and removes any need for numerical stability measures prior to softmax. Both are perennial problems when training transformers.

This was validated at scale recently by the training of a 3B parameter vision transformer. The SwinV2 paper also proposes to change the pre-layernorm to a post-layernorm for further stability.

I have validated that this works just as well as dot product attention in an autoregressive setting, if one were to initialize the temperature as proposed in the QK-norm paper (as a function of the sequence length).

This flavor of attention also has a connection to sparse distributed memory. [youtube talk]

Update: I have discovered a way to remove the learned temperature altogether, by grouping the feature dimension and doing l2-normalization on each group. This allows the queries and keys to have a similarity that is upper bounded by the number of groups. A group size of 8 or 16 was sufficient in my tests. Decided to name this technique "Grouped QK Normalization". The drawback is that I believe an attention head dimension 32 is too small to use this tactic (a dimension often used in vision)

Update 2: Tero Karras has successfully used cosine sim attention in a new paper.

You can use it as follows

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_qk_norm = True,       # set this to True
        attn_qk_norm_groups = 8    # number of groups in the feature dimension for l2norm, similarity scores will be bounded between [-group, group]. determines how sharp the attention can be
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

Another update: Simply scaling the cosine similarity (group of 1) with a fixed constant (10) may work too

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
        attn_qk_norm = True,       # set to True
        attn_qk_norm_scale = 10    # new scale on the similarity, with groups of 1
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

QK RMSNorm

Update: Google Brain has proven out something similar to cosine sim attention in a 22B parameter model. In their papers, they have analysis showing that the normalization resulted in not only extra stability, but also better results in the end (due to less need to adjust learning rate when increasing parameter count).

We are nearing the point of wiping out a source of transformer training instability with one simple intervention, in my opinion. The only slight difference in the paper is that they still have a learned scale across the feature dimension (per use of rmsnorm). Not sure how critical this is, but just to make sure we don't miss anything, I will include this here. You can use this by setting qk_norm_dim_scale = True

Update: Counterpoint from Tim Dettmers

Update 2: Counter to Tim's assertion that outliers are needed, and potentially even some solutions

Update 3: Used by 8B parameter LLM successfully

Update 4: a MetaAI group found that they can alleviate outliers by adding register tokens, also known as memory tokens from earlier literature (Burtsev et al). Perhaps what should be tried next is see if qk norm can be improved in the presence of memory tokens.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8,
        attn_qk_norm = True,
        attn_qk_norm_dim_scale = True # set this to True, in addition to `attn_qk_norm = True`
    )
)

x = torch.randint(0, 256, (1, 1024))
model(x)

Turning off absolute positional embedding

A number of papers have hinted that causal transformers (Decoder) can learn absolute positions in the absence of added embeddings of any sort. This was recently thoroughly investigated here. You can turn off the absolute positional embedding by setting use_abs_pos_emb = False in the TransformerWrapper

Given PaLM, the trend going forward may be to forgo absolute positional embedding (again, for causal transformers only), and add relative positional embeddings with RoPE, ALiBi, etc.

Update: This paper shows that in the absence of any engineered absolute or relative positional embeddings, decoders can generate implicit positions, and even length generalize better than solutions of the past. They were unaware of dynamic positional bias, however.

import torch
from x_transformers import TransformerWrapper, Decoder

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    use_abs_pos_emb = False,   # set this to False
    attn_layers = Decoder(
        dim = 512,
        depth = 6,
        heads = 8,
    )
)

x = torch.randint(0, 20000, (1, 1024))
model(x)

Forgetful Causal Mask

This paper shows convincing results that one can combine masking (from masked language modeling) with autoregressive training, leading to significantly better results.

You can use this by setting the mask_prob on the AutoregressiveWrapper class

import torch
from x_transformers import TransformerWrapper, Decoder, AutoregressiveWrapper

model = TransformerWrapper(
    num_tokens = 20000,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8
    )
)

model = AutoregressiveWrapper(
    model,
    mask_prob = 0.15  # in paper, they use 15%, same as BERT
).cuda()

# mock data

x = torch.randint(0, 20000, (1, 1024)).cuda()

# derive cross entropy loss, masking all taken care of

loss = model(x)
loss.backward()

Miscellaneous

Cross Attention

import torch
from x_transformers import Encoder, CrossAttender

enc = Encoder(dim = 512, depth = 6)
model = CrossAttender(dim = 512, depth = 6)

nodes = torch.randn(1, 1, 512)
node_masks = torch.ones(1, 1).bool()

neighbors = torch.randn(1, 5, 512)
neighbor_masks = torch.ones(1, 5).bool()

encoded_neighbors = enc(neighbors, mask = neighbor_masks)
model(nodes, context = encoded_neighbors, mask = node_masks, context_mask = neighbor_masks) # (1, 1, 512)

Continuous Embeddings

import torch
from x_transformers import ContinuousTransformerWrapper, Decoder

model = ContinuousTransformerWrapper(
    dim_in = 32,
    dim_out = 100,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8
    )
)

x = torch.randn((1, 1024, 32))
mask = torch.ones(1, 1024).bool()

model(x, mask = mask) # (1, 1024, 100)

You can also train a transformer that accepts continuous values autoregressively easily, in the same scheme as done successfully in this paper

import torch
from x_transformers import ContinuousTransformerWrapper, Decoder
from x_transformers import ContinuousAutoregressiveWrapper

model = ContinuousTransformerWrapper(
    dim_in = 777,
    dim_out = 777,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8
    )
)

# wrap it with the continuous autoregressive wrapper

model = ContinuousAutoregressiveWrapper(model)

# mock data

x = torch.randn((1, 1024, 777))
mask = torch.ones(1, 1024).bool()

# train on a lot of data above

loss = model(x, mask = mask)
loss.backward

# then generate

start_emb = torch.randn(1, 777)
generated = model.generate(start_emb, 17) # (17, 777)

xVal - Continuous and Discrete

This is promising work that resulted from the collaboration across many institutes (collectively known as Polymathic AI). They found that by offering a continuously scaled number token to the transformer, the transformer was able to generalize arithmetic and forecasting tasks better than the alternative encoding schemes.

This is corroborated by some prior work

import torch

from x_transformers import (
    Decoder,
    XValTransformerWrapper,
    XValAutoregressiveWrapper
)

model = XValTransformerWrapper(
    num_tokens = 4,
    numerical_token_id = 3,
    max_seq_len = 1024,
    attn_layers = Decoder(
        dim = 512,
        depth = 12,
        heads = 8
    )
)

# wrap it with the xval autoregressive wrapper

model = XValAutoregressiveWrapper(model)

# mock data

ids = torch.randint(0, 4, (1, 777))
nums = torch.randn(1, 777)

# train on a lot of data above

loss = model(ids, nums)
loss.backward()

# then generate

start_ids = torch.randint(0, 4, (1, 1))
start_nums = torch.randn(1, 1)

ids_out, num_out, is_number_mask = model.generate(start_ids, start_nums, 17)

# (1, 17), (1, 17), (1, 17)

# discrete, continuous, mask for discrete / continuous

Citations

@misc{vaswani2017attention,
    title   = {Attention Is All You Need},
    author  = {Ashish Vaswani and Noam Shazeer and Niki Parmar and Jakob Uszkoreit and Llion Jones and Aidan N. Gomez and Lukasz Kaiser and Illia Polosukhin},
    year    = {2017},
    eprint  = {1706.03762},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@article{DBLP:journals/corr/abs-1907-01470,
    author    = {Sainbayar Sukhbaatar and Edouard Grave and Guillaume Lample and Herv{\'{e}} J{\'{e}}gou and Armand Joulin},
    title     = {Augmenting Self-attention with Persistent Memory},
    journal   = {CoRR},
    volume    = {abs/1907.01470},
    year      = {2019},
    url       = {http://arxiv.org/abs/1907.01470}
}

@article{1910.05895,
    author  = {Toan Q. Nguyen and Julian Salazar},
    title   = {Transformers without Tears: Improving the Normalization of Self-Attention},
    year    = {2019},
    eprint  = {arXiv:1910.05895},
    doi     = {10.5281/zenodo.3525484},
}

@misc{shazeer2020glu,
    title   = {GLU Variants Improve Transformer},
    author  = {Noam Shazeer},
    year    = {2020},
    url     = {https://arxiv.org/abs/2002.05202}
}

@inproceedings{Zoph2022STMoEDS,
    title   = {ST-MoE: Designing Stable and Transferable Sparse Expert Models},
    author  = {Barret Zoph and Irwan Bello and Sameer Kumar and Nan Du and Yanping Huang and Jeff Dean and Noam M. Shazeer and William Fedus},
    year    = {2022}
}

@misc{bhojanapalli2020lowrank,
    title   = {Low-Rank Bottleneck in Multi-head Attention Models},
    author  = {Srinadh Bhojanapalli and Chulhee Yun and Ankit Singh Rawat and Sashank J. Reddi and Sanjiv Kumar},
    year    = {2020},
    eprint  = {2002.07028}
}

@misc{burtsev2020memory,
    title   = {Memory Transformer},
    author  = {Mikhail S. Burtsev and Grigory V. Sapunov},
    year    = {2020},
    eprint  = {2006.11527},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@misc{zhao2019explicit,
    title   = {Explicit Sparse Transformer: Concentrated Attention Through Explicit Selection},
    author  = {Guangxiang Zhao and Junyang Lin and Zhiyuan Zhang and Xuancheng Ren and Qi Su and Xu Sun},
    year    = {2019},
    eprint  = {1912.11637},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@misc{correia2019adaptively,
    title   = {Adaptively Sparse Transformers},
    author  = {Gonçalo M. Correia and Vlad Niculae and André F. T. Martins},
    year    = {2019},
    eprint  = {1909.00015},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@misc{shazeer2020talkingheads,
    title   = {Talking-Heads Attention},
    author  = {Noam Shazeer and Zhenzhong Lan and Youlong Cheng and Nan Ding and Le Hou},
    year    = {2020},
    eprint  = {2003.02436},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{press2020improving,
    title   = {Improving Transformer Models by Reordering their Sublayers},
    author  = {Ofir Press and Noah A. Smith and Omer Levy},
    year    = {2020},
    eprint  = {1911.03864},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@misc{lu2019understanding,
    title   = {Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View},
    author  = {Yiping Lu and Zhuohan Li and Di He and Zhiqing Sun and Bin Dong and Tao Qin and Liwei Wang and Tie-Yan Liu},
    year    = {2019},
    eprint  = {1906.02762},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{ke2020rethinking,
    title     = {Rethinking Positional Encoding in Language Pre-training},
    author    = {Guolin Ke and Di He and Tie-Yan Liu},
    year      = {2020},
    eprint    = {2006.15595},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@misc{dosovitskiy2020image,
    title   = {An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale},
    author  = {Alexey Dosovitskiy and Lucas Beyer and Alexander Kolesnikov and Dirk Weissenborn and Xiaohua Zhai and Thomas Unterthiner and Mostafa Dehghani and Matthias Minderer and Georg Heigold and Sylvain Gelly and Jakob Uszkoreit and Neil Houlsby},
    year    = {2020},
    eprint  = {2010.11929},
    archivePrefix = {arXiv},
    primaryClass = {cs.CV}
}

@misc{huang2019attention,
    title   = {Attention on Attention for Image Captioning},
    author  = {Lun Huang and Wenmin Wang and Jie Chen and Xiao-Yong Wei},
    year    = {2019},
    eprint  = {1908.06954},
    archivePrefix = {arXiv},
    primaryClass = {cs.CV}
}

@misc{raffel2020exploring,
    title   = {Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer},
    author  = {Colin Raffel and Noam Shazeer and Adam Roberts and Katherine Lee and Sharan Narang and Michael Matena and Yanqi Zhou and Wei Li and Peter J. Liu},
    year    = {2020},
    eprint  = {1910.10683},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@inproceedings{martins-etal-2020-sparse,
    title   = "Sparse Text Generation",
    author  = "Martins, Pedro Henrique  and
        Marinho, Zita  and
        Martins, Andr{\'e} F. T.",
    booktitle = "Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)",
    month   = nov,
    year    = "2020",
    address = "Online",
    publisher = "Association for Computational Linguistics",
    url     = "https://www.aclweb.org/anthology/2020.emnlp-main.348"
}

@misc{he2020realformer,
    title   = {RealFormer: Transformer Likes Residual Attention},
    author  = {Ruining He and Anirudh Ravula and Bhargav Kanagal and Joshua Ainslie},
    year    = {2020},
    eprint  = {2012.11747},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{carion2020endtoend,
    title   = {End-to-End Object Detection with Transformers},
    author  = {Nicolas Carion and Francisco Massa and Gabriel Synnaeve and Nicolas Usunier and Alexander Kirillov and Sergey Zagoruyko},
    year    = {2020},
    eprint  = {2005.12872},
    archivePrefix = {arXiv},
    primaryClass = {cs.CV}
}

@misc{press2021ALiBi,
    title   = {Train Short, Test Long: Attention with Linear Biases Enable Input Length Extrapolation},
    author  = {Ofir Press and Noah A. Smith and Mike Lewis},
    year    = {2021},
    url     = {https://ofir.io/train_short_test_long.pdf}
}

@misc{parisotto2019stabilizing,
    title     = {Stabilizing Transformers for Reinforcement Learning},
    author    = {Emilio Parisotto and H. Francis Song and Jack W. Rae and Razvan Pascanu and Caglar Gulcehre and Siddhant M. Jayakumar and Max Jaderberg and Raphael Lopez Kaufman and Aidan Clark and Seb Noury and Matthew M. Botvinick and Nicolas Heess and Raia Hadsell},
    year      = {2019},
    eprint    = {1910.06764},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{narang2021transformer,
    title       = {Do Transformer Modifications Transfer Across Implementations and Applications?},
    author      = {Sharan Narang and Hyung Won Chung and Yi Tay and William Fedus and Thibault Fevry and Michael Matena and Karishma Malkan and Noah Fiedel and Noam Shazeer