参考链接
- https://www.bilibili.com/video/BV1JE411g7XF?p=54
- https://arxiv.org/abs/1706.03762
- https://blog.csdn.net/qq_36653505/article/details/83375160
简述自注意力机制（self-attention）
self-attention可以视为一个特征提取层，给定输入特征 a 1 , a 2 , ⋅ ⋅ ⋅ a n a^{1},a^{2},\cdot \cdot \cdot a^{n} a1,a2,⋅⋅⋅an，经过self-attention layer，融合每个输入特征，得到新的特征 b 1 , b 2 , ⋅ ⋅ ⋅ b n b^{1},b^{2},\cdot \cdot \cdot b^{n} b1,b2,⋅⋅⋅bn。具体如下：
设输入特征为
I
I
I，分别将其乘以三个矩阵
W
q
W^{q}
Wq、
W
k
W^{k}
Wk和
W
v
W^{v}
Wv得到
Q
Q
Q（query）、
K
K
K（key）和
V
V
V（value）三个矩阵；接下来使用矩阵
Q
Q
Q和
K
K
K的乘积得到注意力矩阵
A
A
A，归一化得到
A
^
\hat{A}
A^；最后，将归一化后的注意力矩阵
A
^
\hat{A}
A^乘上
V
V
V，得到最后的输出特征
O
O
O。
多头自注意力机制（multi-head self-attention）
上述的self-attention中，每个输入特征
a
i
a^{i}
ai乘上矩阵
W
q
W^{q}
Wq、
W
k
W^{k}
Wk和
W
v
W^{v}
Wv后，分别得到一个向量
q
i
q^{i}
qi、
k
i
k^{i}
ki和
v
i
v^{i}
vi，称为单头自注意力机制。如果将这些向量
q
i
q^{i}
qi、
k
i
k^{i}
ki和
v
i
v^{i}
vi分裂为
n
n
n个就得到
n
n
n头自注意力机制了。公认多头自注意力机制的效果好于单头的，因为前者可以捕获更多维度的信息。示意图如下：
代码实现
设超参数num_attention_heads为自注意力机制的头数，如此，计算出每个头的维度attention_head_size。
self.num_attention_heads = num_attention_heads
self.attention_head_size = int(hidden_size / num_attention_heads)
self.all_head_size = hidden_size
定义 W q W^{q} Wq、 W k W^{k} Wk和 W v W^{v} Wv三个矩阵。
self.query = nn.Linear(input_size, self.all_head_size)
self.key = nn.Linear(input_size, self.all_head_size)
self.value = nn.Linear(input_size, self.all_head_size)
下面开始逐步计算，需要主要的是计算过程中张量维度的变化。
将输入特征乘以三个矩阵
W
q
W^{q}
Wq、
W
k
W^{k}
Wk和
W
v
W^{v}
Wv，输出的张量此时还没有区分出多个头。维度变化为：input_tensor
(
b
a
t
c
h
,
n
,
i
n
p
u
t
_
s
i
z
e
)
\left ( batch,n,input\_size\right )
(batch,n,input_size)到mixed_query_layer
(
b
a
t
c
h
,
n
,
a
l
l
_
h
e
a
d
_
s
i
z
e
)
\left ( batch,n,all\_head\_size\right )
(batch,n,all_head_size)
mixed_query_layer = self.query(input_tensor)
mixed_key_layer = self.key(input_tensor)
mixed_value_layer = self.value(input_tensor)
切分为num_attention_heads个头，并变换维度。维度变化为：mixed_query_layer ( b a t c h , n , a l l _ h e a d _ s i z e ) \left ( batch,n,all\_head\_size\right ) (batch,n,all_head_size)到query_layer ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,num\_attention\_heads,n,attention\_head\_size\right ) (batch,num_attention_heads,n,attention_head_size)
def transpose_for_scores(self, x):
new_x_shape = x.size()[:-1] + (self.num_attention_heads, self.attention_head_size)
x = x.view(*new_x_shape)
return x.permute(0, 2, 1, 3)
query_layer = self.transpose_for_scores(mixed_query_layer)
key_layer = self.transpose_for_scores(mixed_key_layer)
value_layer = self.transpose_for_scores(mixed_value_layer)
矩阵 Q Q Q和 K K K相乘，得到注意力矩阵，并除以向量的维度的开方，防止注意力分数随维度增大而增大。维度变化为：query_layer ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,num\_attention\_heads,n,attention\_head\_size\right ) (batch,num_attention_heads,n,attention_head_size)到attention_scores ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , n ) \left ( batch,num\_attention\_heads,n,n\right ) (batch,num_attention_heads,n,n)
attention_scores = torch.matmul(query_layer, key_layer.transpose(-1, -2))
attention_scores = attention_scores / math.sqrt(self.attention_head_size)
注意力矩阵归一化。维度变化为：attention_scores ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , n ) \left ( batch,num\_attention\_heads,n,n\right ) (batch,num_attention_heads,n,n)到attention_probs ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , n ) \left ( batch,num\_attention\_heads,n,n\right ) (batch,num_attention_heads,n,n)
attention_probs = nn.Softmax(dim=-1)(attention_scores)
将注意力矩阵乘以矩阵 V V V。维度变化为：ttention_probs ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , n ) \left ( batch,num\_attention\_heads,n,n\right ) (batch,num_attention_heads,n,n)乘以value_layer ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,num\_attention\_heads,n,attention\_head\_size\right ) (batch,num_attention_heads,n,attention_head_size)到context_layer ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,num\_attention\_heads,n,attention\_head\_size\right ) (batch,num_attention_heads,n,attention_head_size)。
context_layer = torch.matmul(attention_probs, value_layer)
变换context_layer维度，为了后面将各头得到的结果拼接。这里的contiguous()是将tensor的内存变成连续的，为后面的view()做准备。维度变化为：context_layer ( b a t c h , n u m _ a t t e n t i o n _ h e a d s , n , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,num\_attention\_heads,n,attention\_head\_size\right ) (batch,num_attention_heads,n,attention_head_size)到context_layer ( b a t c h , n , n u m _ a t t e n t i o n _ h e a d s , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,n,num\_attention\_heads,attention\_head\_size\right ) (batch,n,num_attention_heads,attention_head_size)
context_layer = context_layer.permute(0, 2, 1, 3).contiguous()
将各头的结果拼接起来。维度变化为：context_layer ( b a t c h , n , n u m _ a t t e n t i o n _ h e a d s , a t t e n t i o n _ h e a d _ s i z e ) \left ( batch,n,num\_attention\_heads,attention\_head\_size\right ) (batch,n,num_attention_heads,attention_head_size)到context_layer ( b a t c h , n , a l l h e a d s i z e ) \left ( batch,n,all_head_size\right ) (batch,n,allheadsize)
new_context_layer_shape = context_layer.size()[:-2] + (self.all_head_size,)
context_layer = context_layer.view(*new_context_layer_shape)
完整代码
class LayerNorm(nn.Module):
def __init__(self, hidden_size, eps=1e-12):
"""Construct a layernorm module in the TF style (epsilon inside the square root).
"""
super(LayerNorm, self).__init__()
self.weight = nn.Parameter(torch.ones(hidden_size))
self.bias = nn.Parameter(torch.zeros(hidden_size))
self.variance_epsilon = eps
def forward(self, x):
u = x.mean(-1, keepdim=True)
s = (x - u).pow(2).mean(-1, keepdim=True)
x = (x - u) / torch.sqrt(s + self.variance_epsilon)
return self.weight * x + self.bias
class SelfAttention(nn.Module):
def __init__(self, num_attention_heads, input_size, hidden_size, hidden_dropout_prob):
super(SelfAttention, self).__init__()
if hidden_size % num_attention_heads != 0:
raise ValueError(
"The hidden size (%d) is not a multiple of the number of attention "
"heads (%d)" % (hidden_size, num_attention_heads))
self.num_attention_heads = num_attention_heads
self.attention_head_size = int(hidden_size / num_attention_heads)
self.all_head_size = hidden_size
self.query = nn.Linear(input_size, self.all_head_size)
self.key = nn.Linear(input_size, self.all_head_size)
self.value = nn.Linear(input_size, self.all_head_size)
self.attn_dropout = nn.Dropout(attention_probs_dropout_prob)
# 做完self-attention 做一个前馈全连接 LayerNorm 输出
self.dense = nn.Linear(hidden_size, hidden_size)
self.LayerNorm = LayerNorm(hidden_size, eps=1e-12)
self.out_dropout = nn.Dropout(hidden_dropout_prob)
def transpose_for_scores(self, x):
new_x_shape = x.size()[:-1] + (self.num_attention_heads, self.attention_head_size)
x = x.view(*new_x_shape)
return x.permute(0, 2, 1, 3)
def forward(self, input_tensor):
mixed_query_layer = self.query(input_tensor)
mixed_key_layer = self.key(input_tensor)
mixed_value_layer = self.value(input_tensor)
query_layer = self.transpose_for_scores(mixed_query_layer)
key_layer = self.transpose_for_scores(mixed_key_layer)
value_layer = self.transpose_for_scores(mixed_value_layer)
# Take the dot product between "query" and "key" to get the raw attention scores.
attention_scores = torch.matmul(query_layer, key_layer.transpose(-1, -2))
attention_scores = attention_scores / math.sqrt(self.attention_head_size)
# Apply the attention mask is (precomputed for all layers in BertModel forward() function)
# [batch_size heads seq_len seq_len] scores
# [batch_size 1 1 seq_len]
# attention_scores = attention_scores + attention_mask
# Normalize the attention scores to probabilities.
attention_probs = nn.Softmax(dim=-1)(attention_scores)
# This is actually dropping out entire tokens to attend to, which might
# seem a bit unusual, but is taken from the original Transformer paper.
# Fixme
attention_probs = self.attn_dropout(attention_probs)
context_layer = torch.matmul(attention_probs, value_layer)
context_layer = context_layer.permute(0, 2, 1, 3).contiguous()
new_context_layer_shape = context_layer.size()[:-2] + (self.all_head_size,)
context_layer = context_layer.view(*new_context_layer_shape)
hidden_states = self.dense(context_layer)
hidden_states = self.out_dropout(hidden_states)
hidden_states = self.LayerNorm(hidden_states + input_tensor)
return hidden_states