x-transformers
A concise but fully-featured transformer, complete with a set of promising experimental features from various papers.
Install
$ pip install x-transformersUsage
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, you can also do so with one setting 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_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,
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
)
)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 above.
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 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 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)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
)
)
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-1Gated 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, so one can specify less heads for the ALiBi 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,
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 (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
)
)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.
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},
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}solve intelligence... then use that to solve everything else. - Demis Hassabis