"""
---
title: Multi-Headed Attention (MHA)
summary: >
This implements the Multi-Headed Attention used in transformers
using PyTorch with explanations.
---
# Multi-Headed Attention (MHA)
[](https://colab.research.google.com/github/labmlai/annotated_deep_learning_paper_implementations/blob/master/labml_nn/transformers/basic/autoregressive_experiment.ipynb)
This is a tutorial/implementation of multi-headed attention
from paper [Attention Is All You Need](https://arxiv.org/abs/1706.03762)
in [PyTorch](https://pytorch.org/).
The implementation is inspired from [Annotated Transformer](https://nlp.seas.harvard.edu/2018/04/03/attention.html).
Here is the [training code](basic/autoregressive_experiment.html) that uses a basic transformer
with MHA for NLP auto-regression.
[Here is an experiment implementation](basic/autoregressive_experiment.html) that trains a simple transformer.
"""
import math
from typing import Optional, List
import torch
from torch import nn
from labml import tracker
class PrepareForMultiHeadAttention(nn.Module):
"""
## Prepare for multi-head attention
This module does a linear transformation and splits the vector into given
number of heads for multi-head attention.
This is used to transform **key**, **query**, and **value** vectors.
"""
def __init__(self, d_model: int, heads: int, d_k: int, bias: bool):
super().__init__()
# Linear layer for linear transform
self.linear = nn.Linear(d_model, heads * d_k, bias=bias)
# Number of heads
self.heads = heads
# Number of dimensions in vectors in each head
self.d_k = d_k
def forward(self, x: torch.Tensor):
# Input has shape `[seq_len, batch_size, d_model]` or `[batch_size, d_model]`.
# We apply the linear transformation to the last dimension and split that into
# the heads.
head_shape = x.shape[:-1]
# Linear transform
x = self.linear(x)
# Split last dimension into heads
x = x.view(*head_shape, self.heads, self.d_k)
# Output has shape `[seq_len, batch_size, heads, d_k]` or `[batch_size, heads, d_model]`
return x
class MultiHeadAttention(nn.Module):
r"""
## Multi-Head Attention Module
This computes scaled multi-headed attention for given `query`, `key` and `value` vectors.
$$\mathop{Attention}(Q, K, V) = \underset{seq}{\mathop{softmax}}\Bigg(\frac{Q K^\top}{\sqrt{d_k}}\Bigg)V$$
In simple terms, it finds keys that matches the query, and gets the values of
those keys.
It uses dot-product of query and key as the indicator of how matching they are.
Before taking the $softmax$ the dot-products are scaled by $\frac{1}{\sqrt{d_k}}$.
This is done to avoid large dot-product values causing softmax to
give very small gradients when $d_k$ is large.
Softmax is calculated along the axis of of the sequence (or time).
"""
def __init__(self, heads: int, d_model: int, dropout_prob: float = 0.1, bias: bool = True):
"""
* `heads` is the number of heads.
* `d_model` is the number of features in the `query`, `key` and `value` vectors.
"""
super().__init__()
# Number of features per head
self.d_k = d_model // heads
# Number of heads
self.heads = heads
# These transform the `query`, `key` and `value` vectors for multi-headed attention.
self.query = PrepareForMultiHeadAttention(d_model, heads, self.d_k, bias=bias)
self.key = PrepareForMultiHeadAttention(d_model, heads, self.d_k, bias=bias)
self.value = PrepareForMultiHeadAttention(d_model, heads, self.d_k, bias=True)
# Softmax for attention along the time dimension of `key`
self.softmax = nn.Softmax(dim=1)
# Output layer
self.output = nn.Linear(d_model, d_model)
# Dropout
self.dropout = nn.Dropout(dropout_prob)
# Scaling factor before the softmax
self.scale = 1 / math.sqrt(self.d_k)
# We store attentions so that it can be used for logging, or other computations if needed
self.attn = None
def get_scores(self, query: torch.Tensor, key: torch.Tensor):
"""
### Calculate scores between queries and keys
This method can be overridden for other variations like relative attention.
"""
# Calculate $Q K^\top$ or $S_{ijbh} = \sum_d Q_{ibhd} K_{jbhd}$
return torch.einsum('ibhd,jbhd->ijbh', query, key)
def prepare_mask(self, mask: torch.Tensor, query_shape: List[int], key_shape: List[int]):
"""
`mask` has shape `[seq_len_q, seq_len_k, batch_size]`, where first dimension is the query dimension.
If the query dimension is equal to $1$ it will be broadcasted.
"""
assert mask.shape[0] == 1 or mask.shape[0] == query_shape[0]
assert mask.shape[1] == key_shape[0]
assert mask.shape[2] == 1 or mask.shape[2] == query_shape[1]
# Same mask applied to all heads.
mask = mask.unsqueeze(-1)
# resulting mask has shape `[seq_len_q, seq_len_k, batch_size, heads]`
return mask
def forward(self, *,
query: torch.Tensor,
key: torch.Tensor,
value: torch.Tensor,
mask: Optional[torch.Tensor] = None):
"""
`query`, `key` and `value` are the tensors that store
collection of *query*, *key* and *value* vectors.
They have shape `[seq_len, batch_size, d_model]`.
`mask` has shape `[seq_len, seq_len, batch_size]` and
`mask[i, j, b]` indicates whether for batch `b`,
query at position `i` has access to key-value at position `j`.
"""
# `query`, `key` and `value` have shape `[seq_len, batch_size, d_model]`
seq_len, batch_size, _ = query.shape
if mask is not None:
mask = self.prepare_mask(mask, query.shape, key.shape)
# Prepare `query`, `key` and `value` for attention computation.
# These will then have shape `[seq_len, batch_size, heads, d_k]`.
query = self.query(query)
key = self.key(key)
value = self.value(value)
# Compute attention scores $Q K^\top$.
# This gives a tensor of shape `[seq_len, seq_len, batch_size, heads]`.
scores = self.get_scores(query, key)
# Scale scores $\frac{Q K^\top}{\sqrt{d_k}}$
scores *= self.scale
# Apply mask
if mask is not None:
scores = scores.masked_fill(mask == 0, float('-inf'))
# $softmax$ attention along the key sequence dimension
# $\underset{seq}{softmax}\Bigg(\frac{Q K^\top}{\sqrt{d_k}}\Bigg)$
attn = self.softmax(scores)
# Save attentions if debugging
tracker.debug('attn', attn)
# Apply dropout
attn = self.dropout(attn)
# Multiply by values
# $$\underset{seq}{softmax}\Bigg(\frac{Q K^\top}{\sqrt{d_k}}\Bigg)V$$
x = torch.einsum("ijbh,jbhd->ibhd", attn, value)
# Save attentions for any other calculations
self.attn = attn.detach()
# Concatenate multiple heads
x = x.reshape(seq_len, batch_size, -1)
# Output layer
return self.output(x)