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Single-head causal self-attention.
Learns relationships between tokens in the input sequence.
Input Representation (X)
│
▼
Q = X @ Wq
K = X @ Wk
V = X @ Wv
│
▼
Scores = Q @ Kᵀ
│
▼
Scale by √d
│
▼
Apply Causal Mask
│
▼
Softmax
│
▼
Attention Weights
│
▼
Output = Attention Weights @ V
"""
from __future__ import annotations
import math
import torch
import torch.nn as nn
class Attention(nn.Module):
"""
Single-head causal self-attention.
Input:
(batch_size, context_length, d_model)
Output:
(batch_size, context_length, d_model)
"""
def __init__(self, d_model: int, context_length: int,):
super().__init__()
# --------------------------------------------------
# Learnable projection layers.
#
# Each nn.Linear layer contains a learnable weight
# matrix that projects the input representation into
# a different vector space.
#
# Transformer paper notation:
#
# Query Projection -> Wq
# Key Projection -> Wk
# Value Projection -> Wv
#
# During the forward pass:
#
# Q = X @ Wq
# K = X @ Wk
# V = X @ Wv
#
# In PyTorch, the multiplication is performed by
# calling the corresponding nn.Linear layer.
# --------------------------------------------------
self.query = nn.Linear(
in_features=d_model,
out_features=d_model,
bias=False,
)
self.key = nn.Linear(
in_features=d_model,
out_features=d_model,
bias=False,
)
self.value = nn.Linear(
in_features=d_model,
out_features=d_model,
bias=False,
)
# --------------------------------------------------
# Causal Mask
#
# Prevents tokens from attending to future tokens.
#
# The mask is created once during initialization
# and reused during every forward pass.
# --------------------------------------------------
self.register_buffer(
"mask",
torch.triu(
torch.ones(
context_length,
context_length,
dtype=torch.bool,
),
diagonal=1,
),
)
def forward(self,
x: torch.Tensor,
padding_mask: torch.Tensor | None = None,
) -> torch.Tensor:
"""
Parameters
----------
x
Input representation.
Shape:
(batch_size, context_length, d_model)
padding_mask
Optional mask indicating which positions contain
real tokens.
True -> real token
False -> padding
Shape:
(batch_size, context_length)
"""
# --------------------------------------------------
# Step 1
# Create Query (Q), Key (K) and Value (V)
#
# Mathematically:
#
# Q = X @ Wq
# K = X @ Wk
# V = X @ Wv
#
# where X is the input representation and Wq, Wk and
# Wv are the learnable weight matrices contained in
# the projection layers above.
# --------------------------------------------------
Q = self.query(x)
K = self.key(x)
V = self.value(x)
# --------------------------------------------------
# Step 2
# Compute Attention Scores
#
# Mathematically:
#
# Scores = Q @ Kᵀ
#
# Every Query vector is compared with every Key vector
# using the dot product, producing one attention score
# for every Query–Key pair.
#
# scores[i, j] answers:
#
# "How much should token i attend to token j?"
# --------------------------------------------------
scores = Q @ K.transpose(-2, -1)
# --------------------------------------------------
# Step 3
# Scale Attention Scores
#
# Mathematically:
#
# Q @ Kᵀ
# Scores = --------
# √d
#
# where d is the embedding dimension (d_model).
#
# Scaling keeps the magnitude of the attention
# scores relatively stable regardless of the
# embedding dimension.
# --------------------------------------------------
scores = scores / math.sqrt(Q.size(-1))
# --------------------------------------------------
# Step 4
# Apply Causal Mask
#
# Prevent each token from attending to future tokens.
#
# The masked positions are assigned negative infinity.
# After applying softmax, they will receive a
# probability of zero.
# --------------------------------------------------
context_length = scores.size(-1)
# --------------------------------------------------
# Step 4
# Apply Causal Mask
# "Don't look into the future."
# --------------------------------------------------
scores = scores.masked_fill(
self.mask[:context_length, :context_length],
float("-inf"),
)
# --------------------------------------------------
# Apply Padding Mask
#
# True -> real token
# False -> PAD
#
# We mask the KEY positions, meaning:
#
# "Do not allow any token to attend
# to a PAD token."
# --------------------------------------------------
if padding_mask is not None:
scores = scores.masked_fill(
~padding_mask[:, None, :],
float("-inf"),
)
# --------------------------------------------------
# Step 5
# Apply Softmax
#
# Convert the attention scores into probabilities.
#
# Softmax is applied independently to each row of
# the attention score matrix so that every row sums
# to one.
#
# Each probability represents how much attention a
# Query token pays to each Key token.
# --------------------------------------------------
attention = torch.softmax(
scores,
dim=-1,
)
# --------------------------------------------------
# Step 6
# Compute the Weighted Sum
#
# Mathematically:
#
# Output = Attention Weights @ V
#
# The attention weights determine how much
# information to retrieve from every Value vector.
#
# Each output vector is a weighted combination of
# all Value vectors visible to the current Query.
# --------------------------------------------------
output = attention @ V
return output
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