Self-Attention

模型结构

上图架构以 batch_size 为 1，两个时间步的 X 为例子，计算过程如下：

位置编码

根据 self-attention 的模型结构，改变 X 的输入顺序，不影响 attention 的结果，所以还需要引入额外的位置信息，即位置编码。

$$\text{ 假设输入表示 }\mathbf{X}\in {\mathbb{R}}^{n\times d}\text{ 包含一个序列中 }n\text{ 个词元的 }d\text{ 维嵌入表示。位置编码使用相同形状的位置 }嵌入矩阵\mathbf{P}\in {\mathbb{R}}^{n\times d}输出\mathbf{X}+\mathbf{P}，矩阵第i行、第2j列和列2j+1上的元素为：$$

$$\begin{array}{rl}{p}_{i,2j}& =\sin \left(\frac{i}{10000^{2j/d}}\right)\\ p_{i,2j+1}& =\cos \left(\frac{i}{10000^{2j/d}}\right)\end{array}$$

图里计算机二进制编码的低位和位置编码矩阵的前面几列对应。
除了上面捕获绝对位置信息之外，上述的位置编码还允许模型学习得到输入序列中相对位置信息。 这是因为对于任何确定的位置偏移δ，位置 i+δ 处的位置编码可以线性投影位置 i 处的位置编码来表示。

$$\begin{array}{rl}& \left[\begin{array}{cc}\cos \left(\delta {\omega }_j\right)& \sin \left(\delta {\omega }_j\right)\\ -\sin \left(\delta {\omega }_j\right)& \cos \left(\delta {\omega }_j\right)\end{array}\right]\left[\begin{array}{c}{p}_{i,2j}\\ p_{i,2j+1}\end{array}\right]\\ =& \left[\begin{array}{c}\cos \left(\delta {\omega }_j\right)\sin \left(i{\omega }_j\right)+\sin \left(\delta {\omega }_j\right)\cos \left(i{\omega }_j\right)\\ -\sin \left(\delta {\omega }_j\right)\sin \left(i{\omega }_j\right)+\cos \left(\delta {\omega }_j\right)\cos \left(i{\omega }_j\right)\end{array}\right]\\ =& \left[\begin{array}{l}\sin \left((i+\delta ){\omega }_j\right)\\ \cos \left((i+\delta ){\omega }_j\right)\end{array}\right]\\ =& \left[\begin{array}{c}{p}_{i+\delta ,2j}\\ p_{i+\delta ,2j+1}\end{array}\right]\end{array}$$

代码

#@save
class PositionalEncoding(nn.Module):"""位置编码"""def __init__(self, num_hiddens, dropout, max_len=1000):super(PositionalEncoding, self).__init__()self.dropout = nn.Dropout(dropout)# 创建一个足够长的Pself.P = torch.zeros((1, max_len, num_hiddens))X = torch.arange(max_len, dtype=torch.float32).reshape(-1, 1) / torch.pow(10000, torch.arange(0, num_hiddens, 2, dtype=torch.float32) / num_hiddens)self.P[:, :, 0::2] = torch.sin(X)self.P[:, :, 1::2] = torch.cos(X)def forward(self, X):X = X + self.P[:, :X.shape[1], :].to(X.device)return self.dropout(X)

多头注意力

模型结构

两头注意力

七头注意力

七头注意力连接进行信息融合

掩码多头注意力
和多头注意力是一样的，只不过每个头的 self-attention 变成了 masked self-attention

代码

import math
import torch
from torch import nn
from d2l import torch as d2l#@save
def transpose_qkv(X, num_heads):"""为了多注意力头的并行计算而变换形状"""# 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)# 输出X的形状:(batch_size，查询或者“键－值”对的个数，num_heads，# num_hiddens/num_heads)X = X.reshape(X.shape[0], X.shape[1], num_heads, -1)# 输出X的形状:(batch_size，num_heads，查询或者“键－值”对的个数,# num_hiddens/num_heads)X = X.permute(0, 2, 1, 3)# 最终输出的形状:(batch_size*num_heads,查询或者“键－值”对的个数,# num_hiddens/num_heads)return X.reshape(-1, X.shape[2], X.shape[3])#@save
def transpose_output(X, num_heads):"""逆转transpose_qkv函数的操作"""X = X.reshape(-1, num_heads, X.shape[1], X.shape[2])X = X.permute(0, 2, 1, 3)return X.reshape(X.shape[0], X.shape[1], -1)#@save
class DotProductAttention(nn.Module):"""Scaled dot product attention.Defined in :numref:`subsec_additive-attention`"""def __init__(self, dropout, **kwargs):super(DotProductAttention, self).__init__(**kwargs)self.dropout = nn.Dropout(dropout)# Shape of `queries`: (`batch_size`, no. of queries, `d`)# Shape of `keys`: (`batch_size`, no. of key-value pairs, `d`)# Shape of `values`: (`batch_size`, no. of key-value pairs, value# dimension)# Shape of `valid_lens`: (`batch_size`,) or (`batch_size`, no. of queries)def forward(self, queries, keys, values, valid_lens=None):d = queries.shape[-1]# Set `transpose_b=True` to swap the last two dimensions of `keys`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)#@save
class MultiHeadAttention(nn.Module):"""多头注意力"""def __init__(self, key_size, query_size, value_size, num_hiddens,num_heads, dropout, bias=False, **kwargs):super(MultiHeadAttention, self).__init__(**kwargs)self.num_heads = num_headsself.attention = d2l.DotProductAttention(dropout)self.W_q = nn.Linear(query_size, num_hiddens, bias=bias)self.W_k = nn.Linear(key_size, num_hiddens, bias=bias)self.W_v = nn.Linear(value_size, num_hiddens, bias=bias)self.W_o = nn.Linear(num_hiddens, num_hiddens, bias=bias)def forward(self, queries, keys, values, valid_lens):# queries，keys，values的形状:# (batch_size，查询或者“键－值”对的个数，num_hiddens)# valid_lens　的形状:# (batch_size，)或(batch_size，查询的个数)# 经过变换后，输出的queries，keys，values　的形状:# (batch_size*num_heads，查询或者“键－值”对的个数，# num_hiddens/num_heads)queries = transpose_qkv(self.W_q(queries), self.num_heads)keys = transpose_qkv(self.W_k(keys), self.num_heads)values = transpose_qkv(self.W_v(values), self.num_heads)if valid_lens is not None:# 在轴0，将第一项（标量或者矢量）复制num_heads次，# 然后如此复制第二项，然后诸如此类。valid_lens = torch.repeat_interleave(valid_lens, repeats=self.num_heads, dim=0)# output的形状:(batch_size*num_heads，查询的个数，# num_hiddens/num_heads)output = self.attention(queries, keys, values, valid_lens)# output_concat的形状:(batch_size，查询的个数，num_hiddens)output_concat = transpose_output(output, self.num_heads)return self.W_o(output_concat)

Transformer

模型结构

具体的一个 encoder 块内部：

decoder:

代码

import math
import pandas as pd
import torch
from torch import nn
from d2l import torch as d2l#@save
class PositionWiseFFN(nn.Module):"""基于位置的前馈网络"""def __init__(self, ffn_num_input, ffn_num_hiddens, ffn_num_outputs,**kwargs):super(PositionWiseFFN, self).__init__(**kwargs)self.dense1 = nn.Linear(ffn_num_input, ffn_num_hiddens)self.relu = nn.ReLU()self.dense2 = nn.Linear(ffn_num_hiddens, ffn_num_outputs)def forward(self, X):return self.dense2(self.relu(self.dense1(X)))#@save
class AddNorm(nn.Module):"""残差连接后进行层规范化"""def __init__(self, normalized_shape, dropout, **kwargs):super(AddNorm, self).__init__(**kwargs)self.dropout = nn.Dropout(dropout)self.ln = nn.LayerNorm(normalized_shape)def forward(self, X, Y):return self.ln(self.dropout(Y) + X)#@save
class EncoderBlock(nn.Module):"""Transformer编码器块"""def __init__(self, key_size, query_size, value_size, num_hiddens,norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,dropout, use_bias=False, **kwargs):super(EncoderBlock, self).__init__(**kwargs)self.attention = d2l.MultiHeadAttention(key_size, query_size, value_size, num_hiddens, num_heads, dropout,use_bias)self.addnorm1 = AddNorm(norm_shape, dropout)self.ffn = PositionWiseFFN(ffn_num_input, ffn_num_hiddens, num_hiddens)self.addnorm2 = AddNorm(norm_shape, dropout)def forward(self, X, valid_lens):Y = self.addnorm1(X, self.attention(X, X, X, valid_lens))return self.addnorm2(Y, self.ffn(Y))#@save
class TransformerEncoder(d2l.Encoder):"""Transformer编码器"""def __init__(self, vocab_size, key_size, query_size, value_size,num_hiddens, norm_shape, ffn_num_input, ffn_num_hiddens,num_heads, num_layers, dropout, use_bias=False, **kwargs):super(TransformerEncoder, self).__init__(**kwargs)self.num_hiddens = num_hiddensself.embedding = nn.Embedding(vocab_size, num_hiddens)self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)self.blks = nn.Sequential()for i in range(num_layers):self.blks.add_module("block"+str(i),EncoderBlock(key_size, query_size, value_size, num_hiddens,norm_shape, ffn_num_input, ffn_num_hiddens,num_heads, dropout, use_bias))def forward(self, X, valid_lens, *args):# 因为位置编码值在-1和1之间，# 因此嵌入值乘以嵌入维度的平方根进行缩放，# 然后再与位置编码相加。X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))self.attention_weights = [None] * len(self.blks)for i, blk in enumerate(self.blks):X = blk(X, valid_lens)self.attention_weights[i] = blk.attention.attention.attention_weightsreturn Xclass DecoderBlock(nn.Module):"""解码器中第i个块"""def __init__(self, key_size, query_size, value_size, num_hiddens,norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,dropout, i, **kwargs):super(DecoderBlock, self).__init__(**kwargs)self.i = iself.attention1 = d2l.MultiHeadAttention(key_size, query_size, value_size, num_hiddens, num_heads, dropout)self.addnorm1 = AddNorm(norm_shape, dropout)self.attention2 = d2l.MultiHeadAttention(key_size, query_size, value_size, num_hiddens, num_heads, dropout)self.addnorm2 = AddNorm(norm_shape, dropout)self.ffn = PositionWiseFFN(ffn_num_input, ffn_num_hiddens,num_hiddens)self.addnorm3 = AddNorm(norm_shape, dropout)def forward(self, X, state):enc_outputs, enc_valid_lens = state[0], state[1]# 训练阶段，输出序列的所有词元都在同一时间处理，# 因此state[2][self.i]初始化为None。# 预测阶段，输出序列是通过词元一个接着一个解码的，# 因此state[2][self.i]包含着直到当前时间步第i个块解码的输出表示if state[2][self.i] is None:key_values = Xelse:key_values = torch.cat((state[2][self.i], X), axis=1)state[2][self.i] = key_valuesif self.training:batch_size, num_steps, _ = X.shape# dec_valid_lens的开头:(batch_size,num_steps),# 其中每一行是[1,2,...,num_steps]dec_valid_lens = torch.arange(1, num_steps + 1, device=X.device).repeat(batch_size, 1)else:dec_valid_lens = None# 自注意力X2 = self.attention1(X, key_values, key_values, dec_valid_lens)Y = self.addnorm1(X, X2)# 编码器－解码器注意力。# enc_outputs的开头:(batch_size,num_steps,num_hiddens)Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)Z = self.addnorm2(Y, Y2)return self.addnorm3(Z, self.ffn(Z)), stateclass TransformerDecoder(d2l.AttentionDecoder):def __init__(self, vocab_size, key_size, query_size, value_size,num_hiddens, norm_shape, ffn_num_input, ffn_num_hiddens,num_heads, num_layers, dropout, **kwargs):super(TransformerDecoder, self).__init__(**kwargs)self.num_hiddens = num_hiddensself.num_layers = num_layersself.embedding = nn.Embedding(vocab_size, num_hiddens)self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)self.blks = nn.Sequential()for i in range(num_layers):self.blks.add_module("block"+str(i),DecoderBlock(key_size, query_size, value_size, num_hiddens,norm_shape, ffn_num_input, ffn_num_hiddens,num_heads, dropout, i))self.dense = nn.Linear(num_hiddens, vocab_size)def init_state(self, enc_outputs, enc_valid_lens, *args):return [enc_outputs, enc_valid_lens, [None] * self.num_layers]def forward(self, X, state):X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))self._attention_weights = [[None] * len(self.blks) for _ in range (2)]for i, blk in enumerate(self.blks):X, state = blk(X, state)# 解码器自注意力权重self._attention_weights[0][i] = blk.attention1.attention.attention_weights# “编码器－解码器”自注意力权重self._attention_weights[1][i] = blk.attention2.attention.attention_weightsreturn self.dense(X), state@propertydef attention_weights(self):return self._attention_weightsnum_hiddens, num_layers, dropout, batch_size, num_steps = 32, 2, 0.1, 64, 10
lr, num_epochs, device = 0.005, 200, d2l.try_gpu()
ffn_num_input, ffn_num_hiddens, num_heads = 32, 64, 4
key_size, query_size, value_size = 32, 32, 32
norm_shape = [32]train_iter, src_vocab, tgt_vocab = d2l.load_data_nmt(batch_size, num_steps)encoder = TransformerEncoder(len(src_vocab), key_size, query_size, value_size, num_hiddens,norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,num_layers, dropout)
decoder = TransformerDecoder(len(tgt_vocab), key_size, query_size, value_size, num_hiddens,norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,num_layers, dropout)
net = d2l.EncoderDecoder(encoder, decoder)
d2l.train_seq2seq(net, train_iter, lr, num_epochs, tgt_vocab, device)

Bert

bert 开启了预训练模型的风潮，使用了带掩码的语言模型，具体就是通过大量的数据，模型获取了语言信息抽取的能力，从而可以通过 fine-tune 应用到各种 NLP 任务上。
3w 的词典，使用了 WordPiece。[cls] A [seq] B [seq]
位置嵌入换成了学习的矩阵。

模型结构

截取了 transformer 的 encoder（代码没有改动）
不同点：
输入

训练（类似完形填空，以及下一个句子预测）

尽管掩蔽语言建模能够编码双向上下文来表示单词，但它不能显式地建模文本对之间的逻辑关系。为了帮助理解两个文本序列之间的关系，BERT在预训练中考虑了一个二元分类任务——下一句预测。在为预训练生成句子对时，有一半的时间它们确实是标签为“真”的连续句子；在另一半的时间里，第二个句子是从语料库中随机抽取的，标记为“假”。

模型参数计算

BERT-base（H = 768，L = 12，A = 12）
Transformer encoder block 里面主要参数有：
嵌入层：H x 30000（vocab_size 约等于 30000）
2. 全连接层：H x 4H + 4H x H（一个 block 里面有两个全连接层）
3. 多头注意力机制层：H x H / head_num x 3（一个头的参数，3代表 Q，K，V 用不同矩阵做线性变换），所有头加起来 H x H x 3，再加上多头注意力机制层的线性变换 H x H，这里可以结合下图理解：

1，2，3 加起来就是 BERT-base 的参数数量。
计算公式： $L\ast 12H^2+30000\ast H\approx 110M(H=768,L=12)$
BERT-large 同理可以计算出参数数量约等于 340M。

GPT-3

截取了 transformer 的 decoder（代码没有改动）

参考

1. https://www.bilibili.com/list/1567748478?sid=358497&spm_id_from=333.999.0.0&desc=0&oid=974353636&bvid=BV1L44y1m768&p=2
2. 8.1. 序列模型 - 动手学深度学习 2.0.0 documentation
3. Visualizing A Neural Machine Translation Model (Mechanics of Seq2seq Models With Attention)
4. The Illustrated Transformer
5. https://www.coursera.org/learn/attention-models-in-nlp/lecture/AMz8y/masked-self-attention
6. BERT 论文逐段精读【论文精读】_哔哩哔哩_bilibili
7. GPT，GPT-2，GPT-3 论文精读【论文精读】_哔哩哔哩_bilibili