注意力打分函数¶

In [1]:

import math
import torch
from torch import nn
from d2l import torch as d2l

遮蔽softmax操作

In [2]:

def masked_softmax(X, valid_lens):
    """通过在最后一个轴上遮蔽元素来执行 softmax 操作"""
    if valid_lens is None:
        return nn.functional.softmax(X, dim=-1)
    else:
        shape = X.shape
        if valid_lens.dim() == 1:
            valid_lens = torch.repeat_interleave(valid_lens, shape[1])
        else:
            valid_lens = valid_lens.reshape(-1)
        X = d2l.sequence_mask(X.reshape(-1, shape[-1]), valid_lens,
                              value=-1e6)
        return nn.functional.softmax(X.reshape(shape), dim=-1)

演示此函数是如何工作

In [3]:

masked_softmax(torch.rand(2, 2, 4), torch.tensor([2, 3]))

Out[3]:

tensor([[[0.5089, 0.4911, 0.0000, 0.0000],
         [0.5767, 0.4233, 0.0000, 0.0000]],

        [[0.2270, 0.4099, 0.3630, 0.0000],
         [0.2809, 0.3901, 0.3289, 0.0000]]])

In [4]:

masked_softmax(torch.rand(2, 2, 4), torch.tensor([[1, 3], [2, 4]]))

Out[4]:

tensor([[[1.0000, 0.0000, 0.0000, 0.0000],
         [0.2178, 0.4802, 0.3020, 0.0000]],

        [[0.3727, 0.6273, 0.0000, 0.0000],
         [0.2801, 0.2185, 0.2313, 0.2701]]])

加性注意力

In [5]:

class AdditiveAttention(nn.Module):
    """加性注意力"""
    def __init__(self, key_size, query_size, num_hiddens, dropout, **kwargs):
        super(AdditiveAttention, self).__init__(**kwargs)
        self.W_k = nn.Linear(key_size, num_hiddens, bias=False)
        self.W_q = nn.Linear(query_size, num_hiddens, bias=False)
        self.w_v = nn.Linear(num_hiddens, 1, bias=False)
        self.dropout = nn.Dropout(dropout)

    def forward(self, queries, keys, values, valid_lens):
        queries, keys = self.W_q(queries), self.W_k(keys)
        features = queries.unsqueeze(2) + keys.unsqueeze(1)
        features = torch.tanh(features)
        scores = self.w_v(features).squeeze(-1)
        self.attention_weights = masked_softmax(scores, valid_lens)
        return torch.bmm(self.dropout(self.attention_weights), values)

演示上面的AdditiveAttention类

In [6]:

queries, keys = torch.normal(0, 1, (2, 1, 20)), torch.ones((2, 10, 2))
values = torch.arange(40, dtype=torch.float32).reshape(1, 10,
                                                       4).repeat(2, 1, 1)
valid_lens = torch.tensor([2, 6])

attention = AdditiveAttention(key_size=2, query_size=20, num_hiddens=8,
                              dropout=0.1)
attention.eval()
attention(queries, keys, values, valid_lens)

Out[6]:

tensor([[[ 2.0000,  3.0000,  4.0000,  5.0000]],

        [[10.0000, 11.0000, 12.0000, 13.0000]]], grad_fn=<BmmBackward0>)

注意力权重

In [7]:

d2l.show_heatmaps(attention.attention_weights.reshape((1, 1, 2, 10)),
                  xlabel='Keys', ylabel='Queries')

缩放点积注意力

In [8]:

class DotProductAttention(nn.Module):
    """缩放点积注意力"""
    def __init__(self, dropout, **kwargs):
        super(DotProductAttention, self).__init__(**kwargs)
        self.dropout = nn.Dropout(dropout)

    def forward(self, queries, keys, values, valid_lens=None):
        d = queries.shape[-1]
        scores = torch.bmm(queries, keys.transpose(1, 2)) / math.sqrt(d)
        self.attention_weights = masked_softmax(scores, valid_lens)
        return torch.bmm(self.dropout(self.attention_weights), values)

演示上述的DotProductAttention类

In [9]:

queries = torch.normal(0, 1, (2, 1, 2))
attention = DotProductAttention(dropout=0.5)
attention.eval()
attention(queries, keys, values, valid_lens)

Out[9]:

tensor([[[ 2.0000,  3.0000,  4.0000,  5.0000]],

        [[10.0000, 11.0000, 12.0000, 13.0000]]])

均匀的注意力权重

In [10]:

d2l.show_heatmaps(attention.attention_weights.reshape((1, 1, 2, 10)),
                  xlabel='Keys', ylabel='Queries')