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the_annotated_transformer.py
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the_annotated_transformer.py
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# -*- coding: utf-8 -*-
# ---
# jupyter:
# jupytext:
# formats: ipynb,py:percent
# text_representation:
# extension: .py
# format_name: percent
# format_version: '1.3'
# jupytext_version: 1.13.0
# kernelspec:
# display_name: Python 3 (ipykernel)
# language: python
# name: python3
# ---
# %% [markdown] id="SX7UC-8jTsp7" tags=[]
#
# <center><h1>The Annotated Transformer</h1> </center>
#
#
# <center>
# <p><a href="https://arxiv.org/abs/1706.03762">Attention is All You Need
# </a></p>
# </center>
#
# <img src="images/aiayn.png" width="70%"/>
#
# * *v2022: Austin Huang, Suraj Subramanian, Jonathan Sum, Khalid Almubarak,
# and Stella Biderman.*
# * *[Original](https://nlp.seas.harvard.edu/2018/04/03/attention.html):
# [Sasha Rush](https://rush-nlp.com/).*
#
#
# The Transformer has been on a lot of
# people's minds over the last <s>year</s> five years.
# This post presents an annotated version of the paper in the
# form of a line-by-line implementation. It reorders and deletes
# some sections from the original paper and adds comments
# throughout. This document itself is a working notebook, and should
# be a completely usable implementation.
# Code is available
# [here](https://github.com/harvardnlp/annotated-transformer/).
#
# %% [markdown] id="RSntDwKhTsp-"
# <h3> Table of Contents </h3>
# <ul>
# <li><a href="#prelims">Prelims</a></li>
# <li><a href="#background">Background</a></li>
# <li><a href="#part-1-model-architecture">Part 1: Model Architecture</a></li>
# <li><a href="#model-architecture">Model Architecture</a><ul>
# <li><a href="#encoder-and-decoder-stacks">Encoder and Decoder Stacks</a></li>
# <li><a href="#position-wise-feed-forward-networks">Position-wise Feed-Forward
# Networks</a></li>
# <li><a href="#embeddings-and-softmax">Embeddings and Softmax</a></li>
# <li><a href="#positional-encoding">Positional Encoding</a></li>
# <li><a href="#full-model">Full Model</a></li>
# <li><a href="#inference">Inference:</a></li>
# </ul></li>
# <li><a href="#part-2-model-training">Part 2: Model Training</a></li>
# <li><a href="#training">Training</a><ul>
# <li><a href="#batches-and-masking">Batches and Masking</a></li>
# <li><a href="#training-loop">Training Loop</a></li>
# <li><a href="#training-data-and-batching">Training Data and Batching</a></li>
# <li><a href="#hardware-and-schedule">Hardware and Schedule</a></li>
# <li><a href="#optimizer">Optimizer</a></li>
# <li><a href="#regularization">Regularization</a></li>
# </ul></li>
# <li><a href="#a-first-example">A First Example</a><ul>
# <li><a href="#synthetic-data">Synthetic Data</a></li>
# <li><a href="#loss-computation">Loss Computation</a></li>
# <li><a href="#greedy-decoding">Greedy Decoding</a></li>
# </ul></li>
# <li><a href="#part-3-a-real-world-example">Part 3: A Real World Example</a>
# <ul>
# <li><a href="#data-loading">Data Loading</a></li>
# <li><a href="#iterators">Iterators</a></li>
# <li><a href="#training-the-system">Training the System</a></li>
# </ul></li>
# <li><a href="#additional-components-bpe-search-averaging">Additional
# Components: BPE, Search, Averaging</a></li>
# <li><a href="#results">Results</a><ul>
# <li><a href="#attention-visualization">Attention Visualization</a></li>
# <li><a href="#encoder-self-attention">Encoder Self Attention</a></li>
# <li><a href="#decoder-self-attention">Decoder Self Attention</a></li>
# <li><a href="#decoder-src-attention">Decoder Src Attention</a></li>
# </ul></li>
# <li><a href="#conclusion">Conclusion</a></li>
# </ul>
# %% [markdown] id="BhmOhn9lTsp8"
# # Prelims
#
# <a href="#background">Skip</a>
# %% id="NwClcbH6Tsp8"
# # !pip install -r requirements.txt
# %% id="NwClcbH6Tsp8"
# # Uncomment for colab
# #
# # !pip install -q torchdata==0.3.0 torchtext==0.12 spacy==3.2 altair GPUtil
# # !python -m spacy download de_core_news_sm
# # !python -m spacy download en_core_web_sm
# %% id="v1-1MX6oTsp9"
import os
from os.path import exists
import torch
import torch.nn as nn
from torch.nn.functional import log_softmax, pad
import math
import copy
import time
from torch.optim.lr_scheduler import LambdaLR
import pandas as pd
import altair as alt
from torchtext.data.functional import to_map_style_dataset
from torch.utils.data import DataLoader
from torchtext.vocab import build_vocab_from_iterator
import torchtext.datasets as datasets
import spacy
import GPUtil
import warnings
from torch.utils.data.distributed import DistributedSampler
import torch.distributed as dist
import torch.multiprocessing as mp
from torch.nn.parallel import DistributedDataParallel as DDP
# Set to False to skip notebook execution (e.g. for debugging)
warnings.filterwarnings("ignore")
RUN_EXAMPLES = True
# %%
# Some convenience helper functions used throughout the notebook
def is_interactive_notebook():
return __name__ == "__main__"
def show_example(fn, args=[]):
if __name__ == "__main__" and RUN_EXAMPLES:
return fn(*args)
def execute_example(fn, args=[]):
if __name__ == "__main__" and RUN_EXAMPLES:
fn(*args)
class DummyOptimizer(torch.optim.Optimizer):
def __init__(self):
self.param_groups = [{"lr": 0}]
None
def step(self):
None
def zero_grad(self, set_to_none=False):
None
class DummyScheduler:
def step(self):
None
# %% [markdown] id="jx49WRyfTsp-"
# > My comments are blockquoted. The main text is all from the paper itself.
# %% [markdown] id="7phVeWghTsp_"
# # Background
# %% [markdown] id="83ZDS91dTsqA"
#
# The goal of reducing sequential computation also forms the
# foundation of the Extended Neural GPU, ByteNet and ConvS2S, all of
# which use convolutional neural networks as basic building block,
# computing hidden representations in parallel for all input and
# output positions. In these models, the number of operations required
# to relate signals from two arbitrary input or output positions grows
# in the distance between positions, linearly for ConvS2S and
# logarithmically for ByteNet. This makes it more difficult to learn
# dependencies between distant positions. In the Transformer this is
# reduced to a constant number of operations, albeit at the cost of
# reduced effective resolution due to averaging attention-weighted
# positions, an effect we counteract with Multi-Head Attention.
#
# Self-attention, sometimes called intra-attention is an attention
# mechanism relating different positions of a single sequence in order
# to compute a representation of the sequence. Self-attention has been
# used successfully in a variety of tasks including reading
# comprehension, abstractive summarization, textual entailment and
# learning task-independent sentence representations. End-to-end
# memory networks are based on a recurrent attention mechanism instead
# of sequencealigned recurrence and have been shown to perform well on
# simple-language question answering and language modeling tasks.
#
# To the best of our knowledge, however, the Transformer is the first
# transduction model relying entirely on self-attention to compute
# representations of its input and output without using sequence
# aligned RNNs or convolution.
# %% [markdown]
# # Part 1: Model Architecture
# %% [markdown] id="pFrPajezTsqB"
# # Model Architecture
# %% [markdown] id="ReuU_h-fTsqB"
#
# Most competitive neural sequence transduction models have an
# encoder-decoder structure
# [(cite)](https://arxiv.org/abs/1409.0473). Here, the encoder maps an
# input sequence of symbol representations $(x_1, ..., x_n)$ to a
# sequence of continuous representations $\mathbf{z} = (z_1, ...,
# z_n)$. Given $\mathbf{z}$, the decoder then generates an output
# sequence $(y_1,...,y_m)$ of symbols one element at a time. At each
# step the model is auto-regressive
# [(cite)](https://arxiv.org/abs/1308.0850), consuming the previously
# generated symbols as additional input when generating the next.
# %% id="k0XGXhzRTsqB"
class EncoderDecoder(nn.Module):
"""
A standard Encoder-Decoder architecture. Base for this and many
other models.
"""
def __init__(self, encoder, decoder, src_embed, tgt_embed, generator):
super(EncoderDecoder, self).__init__()
self.encoder = encoder
self.decoder = decoder
self.src_embed = src_embed
self.tgt_embed = tgt_embed
self.generator = generator
def forward(self, src, tgt, src_mask, tgt_mask):
"Take in and process masked src and target sequences."
return self.decode(self.encode(src, src_mask), src_mask, tgt, tgt_mask)
def encode(self, src, src_mask):
return self.encoder(self.src_embed(src), src_mask)
def decode(self, memory, src_mask, tgt, tgt_mask):
return self.decoder(self.tgt_embed(tgt), memory, src_mask, tgt_mask)
# %% id="NKGoH2RsTsqC"
class Generator(nn.Module):
"Define standard linear + softmax generation step."
def __init__(self, d_model, vocab):
super(Generator, self).__init__()
self.proj = nn.Linear(d_model, vocab)
def forward(self, x):
return log_softmax(self.proj(x), dim=-1)
# %% [markdown] id="mOoEnF_jTsqC"
#
# The Transformer follows this overall architecture using stacked
# self-attention and point-wise, fully connected layers for both the
# encoder and decoder, shown in the left and right halves of Figure 1,
# respectively.
# %% [markdown] id="oredWloYTsqC"
# ![](images/ModalNet-21.png)
# %% [markdown] id="bh092NZBTsqD"
# ## Encoder and Decoder Stacks
#
# ### Encoder
#
# The encoder is composed of a stack of $N=6$ identical layers.
# %% id="2gxTApUYTsqD"
def clones(module, N):
"Produce N identical layers."
return nn.ModuleList([copy.deepcopy(module) for _ in range(N)])
# %% id="xqVTz9MkTsqD"
class Encoder(nn.Module):
"Core encoder is a stack of N layers"
def __init__(self, layer, N):
super(Encoder, self).__init__()
self.layers = clones(layer, N)
self.norm = LayerNorm(layer.size)
def forward(self, x, mask):
"Pass the input (and mask) through each layer in turn."
for layer in self.layers:
x = layer(x, mask)
return self.norm(x)
# %% [markdown] id="GjAKgjGwTsqD"
#
# We employ a residual connection
# [(cite)](https://arxiv.org/abs/1512.03385) around each of the two
# sub-layers, followed by layer normalization
# [(cite)](https://arxiv.org/abs/1607.06450).
# %% id="3jKa_prZTsqE"
class LayerNorm(nn.Module):
"Construct a layernorm module (See citation for details)."
def __init__(self, features, eps=1e-6):
super(LayerNorm, self).__init__()
self.a_2 = nn.Parameter(torch.ones(features))
self.b_2 = nn.Parameter(torch.zeros(features))
self.eps = eps
def forward(self, x):
mean = x.mean(-1, keepdim=True)
std = x.std(-1, keepdim=True)
return self.a_2 * (x - mean) / (std + self.eps) + self.b_2
# %% [markdown] id="nXSJ3QYmTsqE"
#
# That is, the output of each sub-layer is $\mathrm{LayerNorm}(x +
# \mathrm{Sublayer}(x))$, where $\mathrm{Sublayer}(x)$ is the function
# implemented by the sub-layer itself. We apply dropout
# [(cite)](https://jmlr.org/papers/v15/srivastava14a.html) to the
# output of each sub-layer, before it is added to the sub-layer input
# and normalized.
#
# To facilitate these residual connections, all sub-layers in the
# model, as well as the embedding layers, produce outputs of dimension
# $d_{\text{model}}=512$.
# %% id="U1P7zI0eTsqE"
class SublayerConnection(nn.Module):
"""
A residual connection followed by a layer norm.
Note for code simplicity the norm is first as opposed to last.
"""
def __init__(self, size, dropout):
super(SublayerConnection, self).__init__()
self.norm = LayerNorm(size)
self.dropout = nn.Dropout(dropout)
def forward(self, x, sublayer):
"Apply residual connection to any sublayer with the same size."
return x + self.dropout(sublayer(self.norm(x)))
# %% [markdown] id="ML6oDlEqTsqE"
#
# Each layer has two sub-layers. The first is a multi-head
# self-attention mechanism, and the second is a simple, position-wise
# fully connected feed-forward network.
# %% id="qYkUFr6GTsqE"
class EncoderLayer(nn.Module):
"Encoder is made up of self-attn and feed forward (defined below)"
def __init__(self, size, self_attn, feed_forward, dropout):
super(EncoderLayer, self).__init__()
self.self_attn = self_attn
self.feed_forward = feed_forward
self.sublayer = clones(SublayerConnection(size, dropout), 2)
self.size = size
def forward(self, x, mask):
"Follow Figure 1 (left) for connections."
x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, mask))
return self.sublayer[1](x, self.feed_forward)
# %% [markdown] id="7ecOQIhkTsqF"
# ### Decoder
#
# The decoder is also composed of a stack of $N=6$ identical layers.
#
# %%
class Decoder(nn.Module):
"Generic N layer decoder with masking."
def __init__(self, layer, N):
super(Decoder, self).__init__()
self.layers = clones(layer, N)
self.norm = LayerNorm(layer.size)
def forward(self, x, memory, src_mask, tgt_mask):
for layer in self.layers:
x = layer(x, memory, src_mask, tgt_mask)
return self.norm(x)
# %% [markdown] id="dXlCB12pTsqF"
#
# In addition to the two sub-layers in each encoder layer, the decoder
# inserts a third sub-layer, which performs multi-head attention over
# the output of the encoder stack. Similar to the encoder, we employ
# residual connections around each of the sub-layers, followed by
# layer normalization.
# %% id="M2hA1xFQTsqF"
class DecoderLayer(nn.Module):
"Decoder is made of self-attn, src-attn, and feed forward (defined below)"
def __init__(self, size, self_attn, src_attn, feed_forward, dropout):
super(DecoderLayer, self).__init__()
self.size = size
self.self_attn = self_attn
self.src_attn = src_attn
self.feed_forward = feed_forward
self.sublayer = clones(SublayerConnection(size, dropout), 3)
def forward(self, x, memory, src_mask, tgt_mask):
"Follow Figure 1 (right) for connections."
m = memory
x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, tgt_mask))
x = self.sublayer[1](x, lambda x: self.src_attn(x, m, m, src_mask))
return self.sublayer[2](x, self.feed_forward)
# %% [markdown] id="FZz5rLl4TsqF"
#
# We also modify the self-attention sub-layer in the decoder stack to
# prevent positions from attending to subsequent positions. This
# masking, combined with fact that the output embeddings are offset by
# one position, ensures that the predictions for position $i$ can
# depend only on the known outputs at positions less than $i$.
# %% id="QN98O2l3TsqF"
def subsequent_mask(size):
"Mask out subsequent positions."
attn_shape = (1, size, size)
subsequent_mask = torch.triu(torch.ones(attn_shape), diagonal=1).type(
torch.uint8
)
return subsequent_mask == 0
# %% [markdown] id="Vg_f_w-PTsqG"
#
# > Below the attention mask shows the position each tgt word (row) is
# > allowed to look at (column). Words are blocked for attending to
# > future words during training.
# %% id="ht_FtgYAokC4"
def example_mask():
LS_data = pd.concat(
[
pd.DataFrame(
{
"Subsequent Mask": subsequent_mask(20)[0][x, y].flatten(),
"Window": y,
"Masking": x,
}
)
for y in range(20)
for x in range(20)
]
)
return (
alt.Chart(LS_data)
.mark_rect()
.properties(height=250, width=250)
.encode(
alt.X("Window:O"),
alt.Y("Masking:O"),
alt.Color("Subsequent Mask:Q", scale=alt.Scale(scheme="viridis")),
)
.interactive()
)
show_example(example_mask)
# %% [markdown] id="Qto_yg7BTsqG"
# ### Attention
#
# An attention function can be described as mapping a query and a set
# of key-value pairs to an output, where the query, keys, values, and
# output are all vectors. The output is computed as a weighted sum of
# the values, where the weight assigned to each value is computed by a
# compatibility function of the query with the corresponding key.
#
# We call our particular attention "Scaled Dot-Product Attention".
# The input consists of queries and keys of dimension $d_k$, and
# values of dimension $d_v$. We compute the dot products of the query
# with all keys, divide each by $\sqrt{d_k}$, and apply a softmax
# function to obtain the weights on the values.
#
#
#
# ![](images/ModalNet-19.png)
# %% [markdown] id="EYJLWk6cTsqG"
#
# In practice, we compute the attention function on a set of queries
# simultaneously, packed together into a matrix $Q$. The keys and
# values are also packed together into matrices $K$ and $V$. We
# compute the matrix of outputs as:
#
# $$
# \mathrm{Attention}(Q, K, V) = \mathrm{softmax}(\frac{QK^T}{\sqrt{d_k}})V
# $$
# %% id="qsoVxS5yTsqG"
def attention(query, key, value, mask=None, dropout=None):
"Compute 'Scaled Dot Product Attention'"
d_k = query.size(-1)
scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt(d_k)
if mask is not None:
scores = scores.masked_fill(mask == 0, -1e9)
p_attn = scores.softmax(dim=-1)
if dropout is not None:
p_attn = dropout(p_attn)
return torch.matmul(p_attn, value), p_attn
# %% [markdown] id="jUkpwu8kTsqG"
#
# The two most commonly used attention functions are additive
# attention [(cite)](https://arxiv.org/abs/1409.0473), and dot-product
# (multiplicative) attention. Dot-product attention is identical to
# our algorithm, except for the scaling factor of
# $\frac{1}{\sqrt{d_k}}$. Additive attention computes the
# compatibility function using a feed-forward network with a single
# hidden layer. While the two are similar in theoretical complexity,
# dot-product attention is much faster and more space-efficient in
# practice, since it can be implemented using highly optimized matrix
# multiplication code.
#
#
# While for small values of $d_k$ the two mechanisms perform
# similarly, additive attention outperforms dot product attention
# without scaling for larger values of $d_k$
# [(cite)](https://arxiv.org/abs/1703.03906). We suspect that for
# large values of $d_k$, the dot products grow large in magnitude,
# pushing the softmax function into regions where it has extremely
# small gradients (To illustrate why the dot products get large,
# assume that the components of $q$ and $k$ are independent random
# variables with mean $0$ and variance $1$. Then their dot product,
# $q \cdot k = \sum_{i=1}^{d_k} q_ik_i$, has mean $0$ and variance
# $d_k$.). To counteract this effect, we scale the dot products by
# $\frac{1}{\sqrt{d_k}}$.
#
#
# %% [markdown] id="bS1FszhVTsqG"
# ![](images/ModalNet-20.png)
# %% [markdown] id="TNtVyZ-pTsqH"
#
# Multi-head attention allows the model to jointly attend to
# information from different representation subspaces at different
# positions. With a single attention head, averaging inhibits this.
#
# $$
# \mathrm{MultiHead}(Q, K, V) =
# \mathrm{Concat}(\mathrm{head_1}, ..., \mathrm{head_h})W^O \\
# \text{where}~\mathrm{head_i} = \mathrm{Attention}(QW^Q_i, KW^K_i, VW^V_i)
# $$
#
# Where the projections are parameter matrices $W^Q_i \in
# \mathbb{R}^{d_{\text{model}} \times d_k}$, $W^K_i \in
# \mathbb{R}^{d_{\text{model}} \times d_k}$, $W^V_i \in
# \mathbb{R}^{d_{\text{model}} \times d_v}$ and $W^O \in
# \mathbb{R}^{hd_v \times d_{\text{model}}}$.
#
# In this work we employ $h=8$ parallel attention layers, or
# heads. For each of these we use $d_k=d_v=d_{\text{model}}/h=64$. Due
# to the reduced dimension of each head, the total computational cost
# is similar to that of single-head attention with full
# dimensionality.
# %% id="D2LBMKCQTsqH"
class MultiHeadedAttention(nn.Module):
def __init__(self, h, d_model, dropout=0.1):
"Take in model size and number of heads."
super(MultiHeadedAttention, self).__init__()
assert d_model % h == 0
# We assume d_v always equals d_k
self.d_k = d_model // h
self.h = h
self.linears = clones(nn.Linear(d_model, d_model), 4)
self.attn = None
self.dropout = nn.Dropout(p=dropout)
def forward(self, query, key, value, mask=None):
"Implements Figure 2"
if mask is not None:
# Same mask applied to all h heads.
mask = mask.unsqueeze(1)
nbatches = query.size(0)
# 1) Do all the linear projections in batch from d_model => h x d_k
query, key, value = [
lin(x).view(nbatches, -1, self.h, self.d_k).transpose(1, 2)
for lin, x in zip(self.linears, (query, key, value))
]
# 2) Apply attention on all the projected vectors in batch.
x, self.attn = attention(
query, key, value, mask=mask, dropout=self.dropout
)
# 3) "Concat" using a view and apply a final linear.
x = (
x.transpose(1, 2)
.contiguous()
.view(nbatches, -1, self.h * self.d_k)
)
del query
del key
del value
return self.linears[-1](x)
# %% [markdown] id="EDRba3J3TsqH"
# ### Applications of Attention in our Model
#
# The Transformer uses multi-head attention in three different ways:
# 1) In "encoder-decoder attention" layers, the queries come from the
# previous decoder layer, and the memory keys and values come from the
# output of the encoder. This allows every position in the decoder to
# attend over all positions in the input sequence. This mimics the
# typical encoder-decoder attention mechanisms in sequence-to-sequence
# models such as [(cite)](https://arxiv.org/abs/1609.08144).
#
#
# 2) The encoder contains self-attention layers. In a self-attention
# layer all of the keys, values and queries come from the same place,
# in this case, the output of the previous layer in the encoder. Each
# position in the encoder can attend to all positions in the previous
# layer of the encoder.
#
#
# 3) Similarly, self-attention layers in the decoder allow each
# position in the decoder to attend to all positions in the decoder up
# to and including that position. We need to prevent leftward
# information flow in the decoder to preserve the auto-regressive
# property. We implement this inside of scaled dot-product attention
# by masking out (setting to $-\infty$) all values in the input of the
# softmax which correspond to illegal connections.
# %% [markdown] id="M-en97_GTsqH"
# ## Position-wise Feed-Forward Networks
#
# In addition to attention sub-layers, each of the layers in our
# encoder and decoder contains a fully connected feed-forward network,
# which is applied to each position separately and identically. This
# consists of two linear transformations with a ReLU activation in
# between.
#
# $$\mathrm{FFN}(x)=\max(0, xW_1 + b_1) W_2 + b_2$$
#
# While the linear transformations are the same across different
# positions, they use different parameters from layer to
# layer. Another way of describing this is as two convolutions with
# kernel size 1. The dimensionality of input and output is
# $d_{\text{model}}=512$, and the inner-layer has dimensionality
# $d_{ff}=2048$.
# %% id="6HHCemCxTsqH"
class PositionwiseFeedForward(nn.Module):
"Implements FFN equation."
def __init__(self, d_model, d_ff, dropout=0.1):
super(PositionwiseFeedForward, self).__init__()
self.w_1 = nn.Linear(d_model, d_ff)
self.w_2 = nn.Linear(d_ff, d_model)
self.dropout = nn.Dropout(dropout)
def forward(self, x):
return self.w_2(self.dropout(self.w_1(x).relu()))
# %% [markdown] id="dR1YM520TsqH"
# ## Embeddings and Softmax
#
# Similarly to other sequence transduction models, we use learned
# embeddings to convert the input tokens and output tokens to vectors
# of dimension $d_{\text{model}}$. We also use the usual learned
# linear transformation and softmax function to convert the decoder
# output to predicted next-token probabilities. In our model, we
# share the same weight matrix between the two embedding layers and
# the pre-softmax linear transformation, similar to
# [(cite)](https://arxiv.org/abs/1608.05859). In the embedding layers,
# we multiply those weights by $\sqrt{d_{\text{model}}}$.
# %% id="pyrChq9qTsqH"
class Embeddings(nn.Module):
def __init__(self, d_model, vocab):
super(Embeddings, self).__init__()
self.lut = nn.Embedding(vocab, d_model)
self.d_model = d_model
def forward(self, x):
return self.lut(x) * math.sqrt(self.d_model)
# %% [markdown] id="vOkdui-cTsqH"
# ## Positional Encoding
#
# Since our model contains no recurrence and no convolution, in order
# for the model to make use of the order of the sequence, we must
# inject some information about the relative or absolute position of
# the tokens in the sequence. To this end, we add "positional
# encodings" to the input embeddings at the bottoms of the encoder and
# decoder stacks. The positional encodings have the same dimension
# $d_{\text{model}}$ as the embeddings, so that the two can be summed.
# There are many choices of positional encodings, learned and fixed
# [(cite)](https://arxiv.org/pdf/1705.03122.pdf).
#
# In this work, we use sine and cosine functions of different frequencies:
#
# $$PE_{(pos,2i)} = \sin(pos / 10000^{2i/d_{\text{model}}})$$
#
# $$PE_{(pos,2i+1)} = \cos(pos / 10000^{2i/d_{\text{model}}})$$
#
# where $pos$ is the position and $i$ is the dimension. That is, each
# dimension of the positional encoding corresponds to a sinusoid. The
# wavelengths form a geometric progression from $2\pi$ to $10000 \cdot
# 2\pi$. We chose this function because we hypothesized it would
# allow the model to easily learn to attend by relative positions,
# since for any fixed offset $k$, $PE_{pos+k}$ can be represented as a
# linear function of $PE_{pos}$.
#
# In addition, we apply dropout to the sums of the embeddings and the
# positional encodings in both the encoder and decoder stacks. For
# the base model, we use a rate of $P_{drop}=0.1$.
#
#
# %% id="zaHGD4yJTsqH"
class PositionalEncoding(nn.Module):
"Implement the PE function."
def __init__(self, d_model, dropout, max_len=5000):
super(PositionalEncoding, self).__init__()
self.dropout = nn.Dropout(p=dropout)
# Compute the positional encodings once in log space.
pe = torch.zeros(max_len, d_model)
position = torch.arange(0, max_len).unsqueeze(1)
div_term = torch.exp(
torch.arange(0, d_model, 2) * -(math.log(10000.0) / d_model)
)
pe[:, 0::2] = torch.sin(position * div_term)
pe[:, 1::2] = torch.cos(position * div_term)
pe = pe.unsqueeze(0)
self.register_buffer("pe", pe)
def forward(self, x):
x = x + self.pe[:, : x.size(1)].requires_grad_(False)
return self.dropout(x)
# %% [markdown] id="EfHacTJLTsqH"
#
# > Below the positional encoding will add in a sine wave based on
# > position. The frequency and offset of the wave is different for
# > each dimension.
# %% id="rnvHk_1QokC6" type="example"
def example_positional():
pe = PositionalEncoding(20, 0)
y = pe.forward(torch.zeros(1, 100, 20))
data = pd.concat(
[
pd.DataFrame(
{
"embedding": y[0, :, dim],
"dimension": dim,
"position": list(range(100)),
}
)
for dim in [4, 5, 6, 7]
]
)
return (
alt.Chart(data)
.mark_line()
.properties(width=800)
.encode(x="position", y="embedding", color="dimension:N")
.interactive()
)
show_example(example_positional)
# %% [markdown] id="g8rZNCrzTsqI"
#
# We also experimented with using learned positional embeddings
# [(cite)](https://arxiv.org/pdf/1705.03122.pdf) instead, and found
# that the two versions produced nearly identical results. We chose
# the sinusoidal version because it may allow the model to extrapolate
# to sequence lengths longer than the ones encountered during
# training.
# %% [markdown] id="iwNKCzlyTsqI"
# ## Full Model
#
# > Here we define a function from hyperparameters to a full model.
# %% id="mPe1ES0UTsqI"
def make_model(
src_vocab, tgt_vocab, N=6, d_model=512, d_ff=2048, h=8, dropout=0.1
):
"Helper: Construct a model from hyperparameters."
c = copy.deepcopy
attn = MultiHeadedAttention(h, d_model)
ff = PositionwiseFeedForward(d_model, d_ff, dropout)
position = PositionalEncoding(d_model, dropout)
model = EncoderDecoder(
Encoder(EncoderLayer(d_model, c(attn), c(ff), dropout), N),
Decoder(DecoderLayer(d_model, c(attn), c(attn), c(ff), dropout), N),
nn.Sequential(Embeddings(d_model, src_vocab), c(position)),
nn.Sequential(Embeddings(d_model, tgt_vocab), c(position)),
Generator(d_model, tgt_vocab),
)
# This was important from their code.
# Initialize parameters with Glorot / fan_avg.
for p in model.parameters():
if p.dim() > 1:
nn.init.xavier_uniform_(p)
return model
# %% [markdown]
# ## Inference:
#
# > Here we make a forward step to generate a prediction of the
# model. We try to use our transformer to memorize the input. As you
# will see the output is randomly generated due to the fact that the
# model is not trained yet. In the next tutorial we will build the
# training function and try to train our model to memorize the numbers
# from 1 to 10.
# %%
def inference_test():
test_model = make_model(11, 11, 2)
test_model.eval()
src = torch.LongTensor([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])
src_mask = torch.ones(1, 1, 10)
memory = test_model.encode(src, src_mask)
ys = torch.zeros(1, 1).type_as(src)
for i in range(9):
out = test_model.decode(
memory, src_mask, ys, subsequent_mask(ys.size(1)).type_as(src.data)
)
prob = test_model.generator(out[:, -1])
_, next_word = torch.max(prob, dim=1)
next_word = next_word.data[0]
ys = torch.cat(
[ys, torch.empty(1, 1).type_as(src.data).fill_(next_word)], dim=1
)
print("Example Untrained Model Prediction:", ys)
def run_tests():
for _ in range(10):
inference_test()
show_example(run_tests)
# %% [markdown]
# # Part 2: Model Training
# %% [markdown] id="05s6oT9fTsqI"
# # Training
#
# This section describes the training regime for our models.
# %% [markdown] id="fTxlofs4TsqI"
#
# > We stop for a quick interlude to introduce some of the tools
# > needed to train a standard encoder decoder model. First we define a
# > batch object that holds the src and target sentences for training,
# > as well as constructing the masks.
# %% [markdown] id="G7SkCenXTsqI"
# ## Batches and Masking
# %%
class Batch:
"""Object for holding a batch of data with mask during training."""
def __init__(self, src, tgt=None, pad=2): # 2 = <blank>
self.src = src
self.src_mask = (src != pad).unsqueeze(-2)
if tgt is not None:
self.tgt = tgt[:, :-1]
self.tgt_y = tgt[:, 1:]
self.tgt_mask = self.make_std_mask(self.tgt, pad)
self.ntokens = (self.tgt_y != pad).data.sum()
@staticmethod
def make_std_mask(tgt, pad):
"Create a mask to hide padding and future words."
tgt_mask = (tgt != pad).unsqueeze(-2)
tgt_mask = tgt_mask & subsequent_mask(tgt.size(-1)).type_as(
tgt_mask.data
)
return tgt_mask
# %% [markdown] id="cKkw5GjLTsqI"
#
# > Next we create a generic training and scoring function to keep
# > track of loss. We pass in a generic loss compute function that
# > also handles parameter updates.
# %% [markdown] id="Q8zzeUc0TsqJ"
# ## Training Loop
# %%
class TrainState:
"""Track number of steps, examples, and tokens processed"""
step: int = 0 # Steps in the current epoch
accum_step: int = 0 # Number of gradient accumulation steps
samples: int = 0 # total # of examples used
tokens: int = 0 # total # of tokens processed
# %% id="2HAZD3hiTsqJ"
def run_epoch(
data_iter,
model,
loss_compute,
optimizer,
scheduler,
mode="train",
accum_iter=1,
train_state=TrainState(),
):
"""Train a single epoch"""
start = time.time()
total_tokens = 0
total_loss = 0
tokens = 0
n_accum = 0
for i, batch in enumerate(data_iter):
out = model.forward(
batch.src, batch.tgt, batch.src_mask, batch.tgt_mask
)
loss, loss_node = loss_compute(out, batch.tgt_y, batch.ntokens)
# loss_node = loss_node / accum_iter
if mode == "train" or mode == "train+log":
loss_node.backward()
train_state.step += 1
train_state.samples += batch.src.shape[0]
train_state.tokens += batch.ntokens
if i % accum_iter == 0:
optimizer.step()
optimizer.zero_grad(set_to_none=True)
n_accum += 1
train_state.accum_step += 1
scheduler.step()
total_loss += loss
total_tokens += batch.ntokens
tokens += batch.ntokens
if i % 40 == 1 and (mode == "train" or mode == "train+log"):
lr = optimizer.param_groups[0]["lr"]
elapsed = time.time() - start
print(
(
"Epoch Step: %6d | Accumulation Step: %3d | Loss: %6.2f "
+ "| Tokens / Sec: %7.1f | Learning Rate: %6.1e"
)
% (i, n_accum, loss / batch.ntokens, tokens / elapsed, lr)
)
start = time.time()
tokens = 0
del loss
del loss_node
return total_loss / total_tokens, train_state