This is a Pytorch implementation of Reformer https://openreview.net/pdf?id=rkgNKkHtvB

It includes LSH attention, reversible network, and chunking. It has been validated with an auto-regressive task (enwik8).

81k tokens with half precision

```
$ pip install reformer_pytorch
```

A simple Reformer language model

```
# should fit in ~ 5gb - 8k tokens
import torch
from reformer_pytorch import ReformerLM
model = ReformerLM(
num_tokens= 20000,
dim = 1024,
depth = 12,
max_seq_len = 8192,
heads = 8,
lsh_dropout = 0.1,
ff_dropout = 0.1,
post_attn_dropout = 0.1,
layer_dropout = 0.1, # layer dropout from 'Reducing Transformer Depth on Demand' paper
causal = True, # auto-regressive or not
bucket_size = 64, # average size of qk per bucket, 64 was recommended in paper
n_hashes = 4, # 4 is permissible per author, 8 is the best but slower
emb_dim = 128, # embedding factorization for further memory savings
dim_head = 64, # be able to fix the dimension of each head, making it independent of the embedding dimension and the number of heads
ff_chunks = 200, # number of chunks for feedforward layer, make higher if there are memory issues
attn_chunks = 8, # process lsh attention in chunks, only way for memory to fit when scaling to 16k tokens
num_mem_kv = 128, # persistent learned memory key values, from all-attention paper
full_attn_thres = 1024, # use full attention if context length is less than set value
reverse_thres = 1024, # turn off reversibility for 2x speed for sequence lengths shorter or equal to the designated value
use_scale_norm = False, # use scale norm from 'Transformers without tears' paper
use_rezero = False, # remove normalization and use rezero from 'ReZero is All You Need'
one_value_head = False, # use one set of values for all heads from 'One Write-Head Is All You Need'
weight_tie = False, # tie parameters of each layer for no memory per additional depth
weight_tie_embedding = False, # use token embedding for projection of output, some papers report better results
n_local_attn_heads = 2, # many papers suggest mixing local attention heads aids specialization and improves on certain tasks
pkm_layers = (4,7), # specify layers to use product key memory. paper shows 1 or 2 modules near the middle of the transformer is best
pkm_num_keys = 128, # defaults to 128, but can be increased to 256 or 512 as memory allows
use_full_attn = False # only turn on this flag to override and turn on full attention for all sequence lengths. for comparison with LSH to show that it is working
).cuda()
x = torch.randint(0, 20000, (1, 8192)).long().cuda()
y = model(x) # (1, 8192, 20000)
```

The Reformer (just a stack of reversible LSH attention)

```
# should fit in ~ 5gb - 8k embeddings
import torch
from reformer_pytorch import Reformer
model = Reformer(
dim = 512,
depth = 12,
heads = 8,
lsh_dropout = 0.1,
causal = True
).cuda()
x = torch.randn(1, 8192, 512).cuda()
y = model(x) # (1, 8192, 512)
```

Self Attention with LSH

```
import torch
from reformer_pytorch import LSHSelfAttention
attn = LSHSelfAttention(
dim = 128,
heads = 8,
bucket_size = 64,
n_hashes = 8,
causal = False
)
x = torch.randn(10, 1024, 128)
y = attn(x) # (10, 1024, 128)
```

LSH (locality sensitive hashing) Attention

```
import torch
from reformer_pytorch import LSHAttention
attn = LSHAttention(
bucket_size = 64,
n_hashes = 16,
causal = True
)
qk = torch.randn(10, 1024, 128)
v = torch.randn(10, 1024, 128)
out, attn, buckets = attn(qk, v) # (10, 1024, 128)
# attn contains the unsorted attention weights, provided return_attn is set to True (costly otherwise)
# buckets will contain the bucket number (post-argmax) of each token of each batch
```

This repository supports masks on the input sequence `input_mask (b x i_seq)`

, the context sequence `context_mask (b x c_seq)`

, as well as the rarely used full attention matrix itself `input_attn_mask (b x i_seq x i_seq)`

, all made compatible with LSH attention. Masks are made of booleans where `False`

denotes masking out prior to the softmax.

The causal triangular mask is all taken care of for you if you set `causal = True`

.

```
import torch
from reformer_pytorch import ReformerLM
CONTEXT_LEN = 512
SEQ_LEN = 8192
model = ReformerLM(
num_tokens= 20000,
dim = 1024,
depth = 1,
max_seq_len = SEQ_LEN,
ff_chunks = 8,
causal = True
)
c = torch.randn(1, CONTEXT_LEN, 1024)
x = torch.randint(0, 20000, (1, SEQ_LEN)).long()
i_mask = torch.ones(1, SEQ_LEN).bool()
c_mask = torch.ones(1, CONTEXT_LEN).bool()
y = model(x, keys = c, input_mask = i_mask, context_mask = c_mask)
# masking done correctly in LSH attention
```

The default positional embedding uses rotary embeddings.

However, Aran has informed me that the Reformer team used axial position embeddings with great results on longer sequences.

You can turn on axial positional embedding and adjust the shape and dimension of the axial embeddings by following the instructions below.

```
import torch
from reformer_pytorch import ReformerLM
model = ReformerLM(
num_tokens= 20000,
dim = 1024,
depth = 12,
max_seq_len = 8192,
ff_chunks = 8,
attn_chunks = 2,
causal = True,
axial_position_emb = True, # set this to True
axial_position_shape = (128, 64), # the shape must multiply up to the max_seq_len (128 x 64 = 8192)
)
x = torch.randint(0, 20000, (1, 8192)).long()
y = model(x) # (1, 8192, 20000)
```

If you would rather use absolute positional embeddings, you can turn it on with `absolute_position_emb = True`

flag on initialization.

Since version `0.17.0`

, and some corrections to the reversible network, Reformer Pytorch is compatible with Microsoft's Deepspeed! If you have multiple local GPUs, you can follow the instructions / example here.

A full Reformer sequence → sequence, say translation

```
import torch
from reformer_pytorch import ReformerLM
DE_SEQ_LEN = 4096
EN_SEQ_LEN = 4096
encoder = ReformerLM(
num_tokens = 20000,
emb_dim = 128,
dim = 1024,
depth = 12,
heads = 8,
max_seq_len = DE_SEQ_LEN,
fixed_position_emb = True,
return_embeddings = True # return output of last attention layer
).cuda()
decoder = ReformerLM(
num_tokens = 20000,
emb_dim = 128,
dim = 1024,
depth = 12,
heads = 8,
max_seq_len = EN_SEQ_LEN,
fixed_position_emb = True,
causal = True
).cuda()
x = torch.randint(0, 20000, (1, DE_SEQ_LEN)).long().cuda()
yi = torch.randint(0, 20000, (1, EN_SEQ_LEN)).long().cuda()
enc_keys = encoder(x) # (1, 4096, 1024)
yo = decoder(yi, keys = enc_keys) # (1, 4096, 20000)
```

A full Reformer image → caption

```
import torch
from torch.nn import Sequential
from torchvision import models
from reformer_pytorch import Reformer, ReformerLM
resnet = models.resnet50(pretrained=True)
resnet = Sequential(*list(resnet.children())[:-4])
SEQ_LEN = 4096
encoder = Reformer(
dim = 512,
depth = 6,
heads = 8,
max_seq_len = 4096
)
decoder = ReformerLM(
num_tokens = 20000,
dim = 512,
depth = 6,
heads = 8,
max_seq_len = SEQ_LEN,
causal = True
)
x = torch.randn(1, 3, 512, 512)
yi = torch.randint(0, 20000, (1, SEQ_LEN)).long()
visual_emb = resnet(x)
b, c, h, w = visual_emb.shape
visual_emb = visual_emb.view(1, c, h * w).transpose(1, 2) # nchw to nte
enc_keys = encoder(visual_emb)
yo = decoder(yi, keys = enc_keys) # (1, 4096, 20000)
```

**There is a bug in versions < 0.21.0. Please upgrade to at least the version specified for the working encoder / decoder Reformer.**

By popular demand, I have coded up a wrapper that removes a lot of the manual work in writing up a generic Reformer encoder / decoder architecture. To use, you would import the `ReformerEncDec`

class. Encoder keyword arguments would be passed with a `enc_`

prefix and decoder keyword arguments with `dec_`

. The model dimension (`dim`

) must be prefix free and will be shared between encoder and decoder. The framework will also take care of passing the encoder input mask to the decoder context mask, unless explicitly overridden.

```
import torch
from reformer_pytorch import ReformerEncDec
DE_SEQ_LEN = 4096
EN_SEQ_LEN = 4096
enc_dec = ReformerEncDec(
dim = 512,
enc_num_tokens = 20000,
enc_depth = 6,
enc_max_seq_len = DE_SEQ_LEN,
dec_num_tokens = 20000,
dec_depth = 6,
dec_max_seq_len = EN_SEQ_LEN
).cuda()
train_seq_in = torch.randint(0, 20000, (1, DE_SEQ_LEN)).long().cuda()
train_seq_out = torch.randint(0, 20000, (1, EN_SEQ_LEN)).long().cuda()
input_mask = torch.ones(1, DE_SEQ_LEN).bool().cuda()
loss = enc_dec(train_seq_in, train_seq_out, return_loss = True, enc_input_mask = input_mask)
loss.backward()
# learn
# evaluate with the following
eval_seq_in = torch.randint(0, 20000, (1, DE_SEQ_LEN)).long().cuda()
eval_seq_out_start = torch.tensor([[0.]]).long().cuda() # assume 0 is id of start token
samples = enc_dec.generate(eval_seq_in, eval_seq_out_start, seq_len = EN_SEQ_LEN, eos_token = 1) # assume 1 is id of stop token
print(samples.shape) # (1, <= 1024) decode the tokens
```

To see the benefits of using PKM, the learning rate of the values must be set higher than the rest of the parameters. (Recommended to be `1e-2`

)

You can follow the instructions here to set it correctly https://awesomeopensource.com/project/lucidrains/product-key-memory#learning-rates

By default, the activation function is `GELU`

. If you would like an alternative activation function, you can pass in the class to the keyword `ff_activation`

.

```
import torch
from reformer_pytorch import ReformerLM
from torch import nn
model = ReformerLM(
num_tokens= 20000,
dim = 512,
depth = 6,
max_seq_len = 8192,
ff_chunks = 8,
ff_dropout = 0.1,
ff_mult = 6,
ff_activation = nn.LeakyReLU,
ff_glu = True # use GLU in feedforward, from paper 'GLU Variants Improve Transformer'
)
x = torch.randint(0, 20000, (1, 8192)).long()
y = model(x) # (1, 8192, 20000)
```

To access the attention weights and bucket distribution, simply wrap the instantiated model with the `Recorder`

wrapper class.

```
import torch
from reformer_pytorch import Reformer, Recorder
model = Reformer(
dim = 512,
depth = 12,
max_seq_len = 8192,
heads = 8,
lsh_dropout = 0.1,
causal = True
).cuda()
model = Recorder(model)
x = torch.randn(1, 8192, 512).cuda()
y = model(x)
model.recordings[0] # a list of attention weights and buckets for the first forward pass
model.turn_off() # stop recording
model.turn_on() # start recording
model.clear() # clear the recordings
model = model.eject() # recover the original model and remove all listeners
```

Reformer comes with a slight drawback that the sequence must be neatly divisible by the bucket size * 2. I have provided a small helper tool that can help you auto-round the sequence length to the next best multiple.

```
import torch
from reformer_pytorch import ReformerLM, Autopadder
model = ReformerLM(
num_tokens= 20000,
dim = 1024,
depth = 12,
max_seq_len = 8192,
heads = 8,
lsh_dropout = 0.1,
causal = True,
bucket_size = 63, # odd bucket size
num_mem_kv = 77 # odd memory key length
).cuda()
model = Autopadder(model)
SEQ_LEN = 7777 # odd sequence length
keys = torch.randn(1, 137, 1024) # odd keys length
x = torch.randint(0, 20000, (1, SEQ_LEN)).long().cuda()
y = model(x, keys = keys) # (1, 7777, 20000)
```

A lot of users are only interested in an auto-regressive language model (like GPT-2). Here is a training wrapper to make it easy to both train and evaluate on arbitrarily lengthed sequences of encoded tokens. You will have to take care of the encoding and decoding yourself.

```
import torch
from torch import randint
from reformer_pytorch import ReformerLM
from reformer_pytorch.generative_tools import TrainingWrapper
model = ReformerLM(
num_tokens= 20000,
dim = 1024,
depth = 12,
max_seq_len = 4096,
lsh_dropout = 0.1,
causal = True,
full_attn_thres = 1024
)
# 0 is used for padding and no loss to be calculated on it
model = TrainingWrapper(model, ignore_index = 0, pad_value = 0)
# the wrapper can handle evenly packed sequences
x_train = randint(0, 20000, (3, 357))
# or if you have a list of uneven sequences, it will be padded for you
x_train = [
randint(0, 20000, (120,)),
randint(0, 20000, (253,)),
randint(0, 20000, (846,))
]
# when training, set return_loss equal to True
model.train()
loss = model(x_train, return_loss = True)
loss.backward()
# when evaluating, just use the generate function, which will default to top_k sampling with temperature of 1.
initial = torch.tensor([[0]]).long() # assume 0 is start token
sample = model.generate(initial, 100, temperature=1., filter_thres = 0.9, eos_token = 1) # assume end token is 1, or omit and it will sample up to 100
print(sample.shape) # (1, <=100) token ids
```

Andrea has uncovered that using O2 optimization level when training with mixed precision can lead to instability. Please use O1 instead, which can be set with the `amp_level`

in Pytorch Lightning, or `opt_level`

in Nvidia's Apex library.

- Routing Transformer - https://awesomeopensource.com/project/lucidrains/routing-transformer
- Sinkhorn Transformer - https://awesomeopensource.com/project/lucidrains/sinkhorn-transformer
- Performer - https://awesomeopensource.com/project/lucidrains/performer-pytorch
- Linear Transformer - https://github.com/lucidrains/linear-attention-transformer/
- Compressive Transformer - https://awesomeopensource.com/project/lucidrains/compressive-transformer-pytorch

```
@inproceedings{kitaev2020reformer,
title = {Reformer: The Efficient Transformer},
author = {Nikita Kitaev and Lukasz Kaiser and Anselm Levskaya},
booktitle = {International Conference on Learning Representations},
year = {2020},
url = {https://openreview.net/forum?id=rkgNKkHtvB}
}
```

```
@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},
}
```

```
@inproceedings{fan2020reducing,
title = {Reducing Transformer Depth on Demand with Structured Dropout},
author = {Angela Fan and Edouard Grave and Armand Joulin},
booktitle = {International Conference on Learning Representations},
year = {2020},
url = {https://openreview.net/forum?id=SylO2yStDr}
}
```

```
@article{Shazeer2019FastTD,
title = {Fast Transformer Decoding: One Write-Head is All You Need},
author = {Noam Shazeer},
journal = {ArXiv},
year = {2019},
volume = {abs/1911.02150}
}
```

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

```
@misc{roy*2020efficient,
title = {Efficient Content-Based Sparse Attention with Routing Transformers},
author = {Aurko Roy* and Mohammad Taghi Saffar* and David Grangier and Ashish Vaswani},
year = {2020},
url = {https://openreview.net/forum?id=B1gjs6EtDr}
}
```

```
@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{lample2019large,
title = {Large Memory Layers with Product Keys},
author = {Guillaume Lample and Alexandre Sablayrolles and Marc'Aurelio Ranzato and Ludovic Denoyer and Hervé Jégou},
year = {2019},
eprint = {1907.05242},
archivePrefix = {arXiv}
}
```

```
@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{dong2021attention,
title = {Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth},
author = {Yihe Dong and Jean-Baptiste Cordonnier and Andreas Loukas},
year = {2021},
eprint = {2103.03404}
}
```

```
@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}
}
```

```
@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}
}
```

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