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))
tgt_mask = torch.ones_like(tgt).bool()
loss = model(src, tgt, src_mask = src_mask, tgt_mask = tgt_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

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)

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,
        attn_dropout = 0.1,    # dropout post-attention
        ff_dropout = 0.1       # feedforward dropout
    )
)
x = torch.randint(0, 20000, (1, 1024))
model(x)

Features

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.

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
    )
)

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
    )
)

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
    )
)

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
    )
)

Rezero Is All You Need

https://arxiv.org/abs/2003.04887

This paper proposes to do away with normalization altogether, and instead gate the output of each branch with a single learned scalar, initialized at zero. They demonstrate convergence for very deep networks, convolution or attention, all without normalization.

I have had good results on usual datasets, but had met trouble with convergence on large datasets (GPT3 sized datasets). However, enough researchers have told me they had positive experiences with this that I decided to include it. If you run into trouble, please use Scalenorm instead.

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,
        use_rezero = True # set to true to use for all layers
    )
)

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)
    )
)

Alternatively, if you would like to use

entmax15

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_use_entmax15 = True  # use entmax15 for attention step
    )
)

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_talking_heads = True  # turn on information exchange between attention heads
    )
)

Collaborative Attention

https://arxiv.org/abs/2006.16362

Share redundent learned key/query projections accross heads. Collaborative attention reduces the number of parameters but requires slightly more memory and computation. A good compression factor to match the performance of the vanilla multi-head attention is between 0.25 and 0.5.

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_collab_heads = True,
        attn_collab_compression = .3,
    )
)

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,
        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
    )
)

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
    )
)

Position Infused Attention

https://arxiv.org/abs/2005.12872

https://ofir.io/shortformer.pdf

In these two papers, the authors independently figured out a new technique where fixed sinusoidal positional embeddings are injected into the input prior to the queries and keys projection for all layers, leading to "position infused" attention, but leaving the actual tokens (values) uncolored by positional embedding. The Shortformer paper uses this property to cache the tokens for simplified recurrent type of transformer that bested Transformer-XL.

I have tested this, and found that it produces better results than plain absolute positional encoding, even in the absence of recurrence. However, I have found that the T5 relative positional bias (also injected into all layers and has the same properties as PIA) performs even better. So given the option, you should just go with T5's

rel_pos_bias

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,
        position_infused_attn = True  # turns on position infused attention
    )
)

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

1e-4

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

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

TransformerWrapper

Decoder

rel_pos_bias

True

Then, you can retrieve the memories at each step with the

return_mems

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)

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

> 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
    )
)
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
    )
)

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.

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

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_emb = 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

shift_tokens + 1

[0, shift_tokens]

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
    )
)

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)

One of the other two changes 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

Finally, I have tried the parameterized scaling of the residual branch in the feedforward pre-norm block, but noticed some slight instability, so I will hold off from adding that feature until I investigate it a bit more.

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)

Pass in continuous values

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)

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}    
}

@misc{bachlechner2020rezero,
    title   = {ReZero is All You Need: Fast Convergence at Large Depth},
    author  = {Thomas Bachlechner and Bodhisattwa Prasad Majumder and Huanru Henry Mao and Garrison W. Cottrell and Julian McAuley},
    year    = {2020},
    url     = {https://arxiv.org/abs/2003.04887}
}

@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{cordonnier2020multihead,
    title   = {Multi-Head Attention: Collaborate Instead of Concatenate},
    author  = {Jean-Baptiste Cordonnier and Andreas Loukas and Martin Jaggi},
    year    = {2020},
    eprint  = {2006.16362},
    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{press2020shortformer,
    title   = {Shortformer: Better Language Modeling using Shorter Inputs},
    author  = {Ofir Press and Noah A. Smith and Mike Lewis},
    year    = {2020}
}

@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 and Zhenzhong Lan and Yanqi Zhou and Wei Li and Nan Ding and Jake Marcus and Adam Roberts and Colin Raffel},
    year        = {2021},
    eprint      = {2102.11972},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{zhang2019root,
    title   = {Root Mean Square Layer Normalization},
    author  = {Biao Zhang and Rico Sennrich},
    year    = {2019},
    eprint  = {1910.07467},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{su2021roformer,
    title   = {RoFormer: Enhanced Transformer with Rotary Position Embedding},
    author  = {Jianlin Su and Yu Lu and Shengfeng Pan and Bo Wen and Yunfeng Liu},
    year    = {2021},
    eprint  = {2104.09864},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@Article{AlphaFold2021,
    author  = {Jumper, John and Evans, Richard and Pritzel, Alexander and Green, Tim and Figurnov, Michael and Ronneberger, Olaf and Tunyasuvunakool, Kathryn and Bates, Russ and {\v{Z}}{\'\i}dek, Augustin and Potapenko, Anna and Bridgland, Alex and Meyer, Clemens and Kohl, Simon A A and Ballard, Andrew J and Cowie, Andrew and Romera-Paredes, Bernardino and Nikolov, Stanislav and Jain, Rishub and Adler, Jonas and Back, Trevor and Petersen, Stig and Reiman, David and Clancy, Ellen and Zielinski, Michal and Steinegger, Martin and Pacholska, Michalina and Berghammer, Tamas and Bodenstein, Sebastian and Silver, David and Vinyals, Oriol and Senior, Andrew W and Kavukcuoglu, Koray and Kohli, Pushmeet and Hassabis, Demis},
    journal = {Nature},
    title   = {Highly accurate protein structure prediction with {AlphaFold}},
    year    = {2021},
    doi     = {10.1038/s41586-021-03819-2},
    note    = {(Accelerated article preview)},
}

@software{peng_bo_2021_5196578,
    author       = {PENG Bo},
    title        = {BlinkDL/RWKV-LM: 0.01},
    month        = {aug},
    year         = {2021},
    publisher    = {Zenodo},
    version      = {0.01},
    doi          = {10.5281/zenodo.5196578},
    url          = {https://doi.org/10.5281/zenodo.5196578}
}

@misc{csordás2021devil,
    title   = {The Devil is in the Detail: Simple Tricks Improve Systematic Generalization of Transformers},
    author  = {Róbert Csordás and Kazuki Irie and Jürgen Schmidhuber},
    year    = {2021},
    eprint  = {2108.12284},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{so2021primer,
    title   = {Primer: Searching for Efficient Transformers for Language Modeling}, 
    author  = {David R. So and Wojciech Mańke and Hanxiao Liu and Zihang Dai and Noam Shazeer and Quoc V. Le},
    year    = {2021},
    eprint  = {2109.08668},
    archivePrefix = {arXiv},
    primaryClass = {cs.LG}
}

@misc{ding2021erniedoc,
    title   = {ERNIE-Doc: A Retrospective Long-Document Modeling Transformer}, 
    author  = {Siyu Ding and Junyuan Shang and Shuohuan Wang and Yu Sun and Hao Tian and Hua Wu and Haifeng Wang},
    year    = {2021},
    eprint  = {2012.15688},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL}
}

@misc{ding2021cogview,
    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}
}

@inproceedings{anonymous2022normformer,
    title   = {NormFormer: Improved Transformer Pretraining with Extra Normalization},
    author  = {Anonymous},
    booktitle = {Submitted to The Tenth International Conference on Learning Representations },
    year    = {2022},
    url     = {https://openreview.net/forum?id=GMYWzWztDx5},
    note    = {under review}
}

solve intelligence... then use that to solve everything else. - Demis Hassabis