Transformer模型及源代码

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import math, copy, time
from torch.autograd import Variable
import matplotlib.pyplot as plt
import seaborn
seaborn.set_context(context='talk')
%matplotlib inline

模型架构

通用的 编码器解码器 架构：

class EncoderDecoder(nn.Module):
    def __init__(self, encoder, decoder, src_embed, tgt_embed, generator):
        """
        编码器、解码器、输入嵌入层、目标嵌入层、输出层
        """
        super(EncoderDecoder, self).__init__()
        self.encoder = encoder
        self.decoder = decoder
        self.src_embed = src_embed
        self.tgt_embed = tgt_embed
        self.generator = generator

    def forward(self, src, tgt, src_mask, tgt_mask):
        """
        src --> memory
        memory + tgt --> output
        """
        memory = self.encode(src, src_mask)
        return self.decode(memory, src_mask, tgt, tgt_mask)

    def encode(self, src, src_mask):
        """
        src --> memory
        """
        return self.encoder(self.src_embed(src), src_mask)

    def decode(self, memory, src_mask, tgt, tgt_mask):
        """
        memory + tgt --> output
        """
        return self.decoder(self.tgt_embed(tgt), memory, src_mask, tgt_mask)

class Generator(nn.Module):
    "Define standard linear + softmax generation step."

    def __init__(self, d_model, vocab):
        super(Generator, self).__init__()
        self.proj = nn.Linear(d_model, vocab)

    def forward(self, x):
        return F.log_softmax(self.proj(x), dim=-1)

编码器

编码器由多层 N=6 完全相同的层堆叠而成 其层次结构如上图中所示：

1. Encoder
    2. EncoderLayer
        3. SublayerConnection
            4. sublayer --> self_attn
            
        3. SublayerConnection
            4. sublayer --> feed_forward
            
    2. EncoderLayer
    .
    .
    .
    .

def clone(module, N):
    return nn.ModuleList([copy.deepcopy(module) for _ in range(N)])

class Encoder(nn.Module):
    def __init__(self, layer, N):
        super(Encoder, self).__init__()
        self.layers = clone(layer, N)
        self.norm = LayerNorm(layer.size)

    def forward(self, x, mask):
        """
        需要自主生成 mask 
        """
        for layer in self.layers:
            x = layer(x, mask)
        return self.norm(x)

class LayerNorm(nn.Module):
    """
    inputs: batch, seq_len, features
    沿输入数据的特征维度归一化
    """
    def __init__(self, features, eps=1e-6):
        # 需要指定特征数量 features
        super(LayerNorm, self).__init__()
        self.a_2 = nn.Parameter(torch.ones(features))
        self.b_2 = nn.Parameter(torch.ones(features))
        self.eps = eps

    def forward(self, x):
        """
        x --> (x - x.mean) / x.std 
        """
        mean = x.mean(-1, keepdim=True)
        std = x.std(-1, keepdim=True)
        return self.a_2 * (x - mean) / (std + self.eps) + self.b_2

def test_layernorm():
    x = np.array([[[1, 2, 3], [2, 4, 5]],],
                 dtype=np.float)
    print("Before Norm: \n", x)
    x = torch.from_numpy(x)  # batch, seq_len, features
    norm = LayerNorm(x.shape[-1])
    x = norm(x)
    print("After Norm: \n", x.detach().numpy())


test_layernorm()

Before Norm: 
 [[[1. 2. 3.]
  [2. 4. 5.]]]
After Norm: 
 [[[ 9.99999000e-07  1.00000000e+00  1.99999900e+00]
  [-9.10887369e-02  1.21821775e+00  1.87287099e+00]]]

class SublayerConnection(nn.Module):
    def __init__(self, size, dropout):
        super(SublayerConnection, self).__init__()
        self.norm = LayerNorm(size)
        self.dropout = nn.Dropout(dropout)
        
    def forward(self, x, sublayer):
        """
        指定内部的结构 sublayer，是 attention 层，还是 feed_forward 层
        """
        return x + self.dropout(sublayer(self.norm(x)))

class EncoderLayer(nn.Module):
    """size: d_model"""
    def __init__(self, size, self_attn, feed_forward, dropout):
        super(EncoderLayer, self).__init__()
        self.self_attn = self_attn
        self.feed_forward = feed_forward
        self.sublayer = clone(SublayerConnection(size, dropout), 2)
        self.size = size

    def forward(self, x, mask):
        x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, mask))
        return self.sublayer[1](x, self.feed_forward)

解码器

class Decoder(nn.Module):
    def __init__(self, layer, N):
        super(Decoder, self).__init__()
        self.layers = clone(layer, N)
        self.norm = LayerNorm(layer.size)

    def forward(self, x, memory, src_mask, tgt_mask):
        for layer in self.layers:
            x = layer(x, memory, src_mask, tgt_mask)
        return self.norm(x)

class DecoderLayer(nn.Module):
    def __init__(self, size, self_attn, src_attn, feed_forward, dropout):
        super(DecoderLayer, self).__init__()
        self.size = size  # 作为参数用于 layernorm 层
        self.self_attn = self_attn
        self.src_attn = src_attn
        self.feed_forward = feed_forward
        self.sublayer = clone(SublayerConnection(size, dropout), 3)

    def forward(self, x, memory, src_mask, tgt_mask):
        m = memory
        x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, tgt_mask))
        x = self.sublayer[1](x, lambda x: self.src_attn(x, m, m, src_mask))
        return self.sublayer[2](x, self.feed_forward)

# 解码器一次输入序列中向量，当前步后面的序列需要被遮盖
# 需要被遮盖的单词被标记为 False 

def subsequent_mask(size):
    attn_shape = (1, size, size)
    subsequent_mask = np.triu(np.ones(attn_shape), k=1).astype('uint8')
    return torch.from_numpy(subsequent_mask) == 0


plt.figure(figsize=(5, 5))
plt.imshow(subsequent_mask(20)[0])

<matplotlib.image.AxesImage at 0x7f83a0e5ec90>

np.triu(m,k=0)：第 k 对角线以下的元素归零，中心对角线索引为 0 ，索引向右上角增加 1、2、3 ，向左下角-1、-2、-3

>>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 0,  8,  9],
       [ 0,  0, 12]])

注意力

点积注意力

\[\mathrm{Attention}(Q, K, V) = \mathrm{softmax}(\frac{QK^T}{\sqrt{d_k}})V\]

def attention(query, key, value, mask=None, dropout=None):
    """
    query : batch, target_len, feats
    key   : batch, seq_len,    feats
    value : batch, seq_len,    val_feats
    
    return: batch, target_len, val_feats
    """
    d_k = query.size(-1)
    scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt(d_k)

    if mask is not None:
        scores = scores.masked_fill(mask == 0, -1e9)
    p_attn = F.softmax(scores, dim=-1)

    if dropout is not None:
        p_attn = dropout(p_attn)
    return torch.matmul(p_attn, value), p_attn

def test_attention():
    query = torch.randn(3, 5, 4)  # batch, target_len, feats
    key = torch.randn(3, 6, 4)  # batch, seq_len, feats
    value = torch.randn(3, 6, 8)  # batch, seq_len, val_feats
    attn, _ = attention(query, key, value)
    print(attn.shape)
    assert attn.shape == (3, 5, 8)
    print("Test passed")


test_attention()

torch.Size([3, 5, 8])
Test passed

多头注意力

class MultiHeadedAttention(nn.Module):
    def __init__(self, h, d_model, dropout=0.1):
        """
        h, num_heads
        d_model, features
        """
        super(MultiHeadedAttention, self).__init__()
        assert d_model % h == 0
        self.d_k = d_model // h
        self.h = h
        self.linears = clone(nn.Linear(d_model, d_model), 4)
        self.attn = None
        self.dropout = nn.Dropout(dropout)

    def forward(self, query, key, value, mask=None):
        # query,key,value: batch,seq_len,d_model
        
        if mask is not None:
            mask = mask.unsqueeze(1)
        nbatches = query.size(0)

        query, key, value = [
            l(x).view(nbatches, -1, self.h, self.d_k).transpose(1, 2)
            for l, x in zip(self.linears, (query, key, value))
        ]

        x, self.attn = attention(
            query,  # batch,num_head,seq_len,feats
            key,
            value,
            mask=mask,
            dropout=self.dropout)

        x = x.transpose(1, 2).contiguous().view(nbatches, -1,
                                                self.h * self.d_k)
        # batch,seq_len,num_head*feats
        return self.linears[-1](x)

def test_multi_head():
    x = torch.randn(2, 4, 12)
    d_model = x.shape[-1]
    model = MultiHeadedAttention(2, d_model)
    attn = model(x, x, x)
    assert attn.shape == (2, 4, 12)
    print("Test passed!")

test_multi_head()

Test passed!

前向层

class PositionwiseFeedForward(nn.Module):
    def __init__(self, d_model, d_ff, dropout=0.1):
        super(PositionwiseFeedForward, self).__init__()
        self.w_1 = nn.Linear(d_model, d_ff)
        self.w_2 = nn.Linear(d_ff, d_model)
        self.dropout = nn.Dropout(dropout)

    def forward(self, x):
        return self.w_2(self.dropout(F.relu(self.w_1(x))))

嵌入层

class Embeddings(nn.Module):
    def __init__(self, d_model, vocab):
        super(Embeddings, self).__init__()
        self.lut = nn.Embedding(vocab, d_model)
        self.d_model = d_model

    def forward(self, x):
        return self.lut(x) * math.sqrt(self.d_model)

位置编码

\[ \text{PE}(i,\delta) = \begin{cases} \sin(\frac{i}{10000^{2\delta'/d}}) & \text{if } \delta = 2\delta'\\ \cos(\frac{i}{10000^{2\delta'/d}}) & \text{if } \delta = 2\delta' + 1\\ \end{cases} \]

class PositionalEncoding(nn.Module):
    "Implement the PE function."

    def __init__(self, d_model, dropout, max_len=5000):
        super(PositionalEncoding, self).__init__()
        self.dropout = nn.Dropout(p=dropout)

        # Compute the positional encodings once in log space.
        pe = torch.zeros(max_len, d_model)
        position = torch.arange(0, max_len).unsqueeze(1)
        div_term = torch.exp(
            torch.arange(0, d_model, 2) * -(math.log(10000.0) / d_model))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        pe = pe.unsqueeze(0)
        self.register_buffer('pe', pe)

    def forward(self, x):
        x = x + Variable(self.pe[:, :x.size(1)], requires_grad=False)
        return self.dropout(x)

plt.figure(figsize=(15, 5))
pe = PositionalEncoding(20, 0)
y = pe.forward(Variable(torch.zeros(1, 100, 20)))
plt.plot(np.arange(100), y[0, :, 4:8].data.numpy())
plt.legend(["dim %d"%p for p in [4,5,6,7]])

<matplotlib.legend.Legend at 0x7f83a03f5f10>

完整的模型

def make_model(src_vocab,
               tgt_vocab,
               N=6,
               d_model=512,
               d_ff=2048,
               h=8,
               dropout=0.1):
    "Helper: Construct a model from hyperparameters."
    c = copy.deepcopy
    attn = MultiHeadedAttention(h, d_model)
    ff = PositionwiseFeedForward(d_model, d_ff, dropout)
    position = PositionalEncoding(d_model, dropout)
    model = EncoderDecoder(
        Encoder(EncoderLayer(d_model, c(attn), c(ff), dropout), N),
        Decoder(DecoderLayer(d_model, c(attn), c(attn), c(ff), dropout), N),
        nn.Sequential(Embeddings(d_model, src_vocab), c(position)),
        nn.Sequential(Embeddings(d_model, tgt_vocab), c(position)),
        Generator(d_model, tgt_vocab),
    )

    # This was important from their code.
    # Initialize parameters with Glorot / fan_avg.
    for p in model.parameters():
        if p.dim() > 1:
            nn.init.xavier_uniform_(p)
    return model

tmp_model = make_model(10, 10, 2)
tmp_model

EncoderDecoder(
  (encoder): Encoder(
    (layers): ModuleList(
      (0): EncoderLayer(
        (self_attn): MultiHeadedAttention(
          (linears): ModuleList(
            (0): Linear(in_features=512, out_features=512, bias=True)
            (1): Linear(in_features=512, out_features=512, bias=True)
            (2): Linear(in_features=512, out_features=512, bias=True)
            (3): Linear(in_features=512, out_features=512, bias=True)
          )
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (feed_forward): PositionwiseFeedForward(
          (w_1): Linear(in_features=512, out_features=2048, bias=True)
          (w_2): Linear(in_features=2048, out_features=512, bias=True)
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (sublayer): ModuleList(
          (0): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
          (1): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
        )
      )
      (1): EncoderLayer(
        (self_attn): MultiHeadedAttention(
          (linears): ModuleList(
            (0): Linear(in_features=512, out_features=512, bias=True)
            (1): Linear(in_features=512, out_features=512, bias=True)
            (2): Linear(in_features=512, out_features=512, bias=True)
            (3): Linear(in_features=512, out_features=512, bias=True)
          )
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (feed_forward): PositionwiseFeedForward(
          (w_1): Linear(in_features=512, out_features=2048, bias=True)
          (w_2): Linear(in_features=2048, out_features=512, bias=True)
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (sublayer): ModuleList(
          (0): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
          (1): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
        )
      )
    )
    (norm): LayerNorm()
  )
  (decoder): Decoder(
    (layers): ModuleList(
      (0): DecoderLayer(
        (self_attn): MultiHeadedAttention(
          (linears): ModuleList(
            (0): Linear(in_features=512, out_features=512, bias=True)
            (1): Linear(in_features=512, out_features=512, bias=True)
            (2): Linear(in_features=512, out_features=512, bias=True)
            (3): Linear(in_features=512, out_features=512, bias=True)
          )
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (src_attn): MultiHeadedAttention(
          (linears): ModuleList(
            (0): Linear(in_features=512, out_features=512, bias=True)
            (1): Linear(in_features=512, out_features=512, bias=True)
            (2): Linear(in_features=512, out_features=512, bias=True)
            (3): Linear(in_features=512, out_features=512, bias=True)
          )
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (feed_forward): PositionwiseFeedForward(
          (w_1): Linear(in_features=512, out_features=2048, bias=True)
          (w_2): Linear(in_features=2048, out_features=512, bias=True)
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (sublayer): ModuleList(
          (0): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
          (1): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
          (2): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
        )
      )
      (1): DecoderLayer(
        (self_attn): MultiHeadedAttention(
          (linears): ModuleList(
            (0): Linear(in_features=512, out_features=512, bias=True)
            (1): Linear(in_features=512, out_features=512, bias=True)
            (2): Linear(in_features=512, out_features=512, bias=True)
            (3): Linear(in_features=512, out_features=512, bias=True)
          )
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (src_attn): MultiHeadedAttention(
          (linears): ModuleList(
            (0): Linear(in_features=512, out_features=512, bias=True)
            (1): Linear(in_features=512, out_features=512, bias=True)
            (2): Linear(in_features=512, out_features=512, bias=True)
            (3): Linear(in_features=512, out_features=512, bias=True)
          )
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (feed_forward): PositionwiseFeedForward(
          (w_1): Linear(in_features=512, out_features=2048, bias=True)
          (w_2): Linear(in_features=2048, out_features=512, bias=True)
          (dropout): Dropout(p=0.1, inplace=False)
        )
        (sublayer): ModuleList(
          (0): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
          (1): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
          (2): SublayerConnection(
            (norm): LayerNorm()
            (dropout): Dropout(p=0.1, inplace=False)
          )
        )
      )
    )
    (norm): LayerNorm()
  )
  (src_embed): Sequential(
    (0): Embeddings(
      (lut): Embedding(10, 512)
    )
    (1): PositionalEncoding(
      (dropout): Dropout(p=0.1, inplace=False)
    )
  )
  (tgt_embed): Sequential(
    (0): Embeddings(
      (lut): Embedding(10, 512)
    )
    (1): PositionalEncoding(
      (dropout): Dropout(p=0.1, inplace=False)
    )
  )
  (generator): Generator(
    (proj): Linear(in_features=512, out_features=10, bias=True)
  )
)

tmp_model.src_embed

Sequential(
  (0): Embeddings(
    (lut): Embedding(10, 512)
  )
  (1): PositionalEncoding(
    (dropout): Dropout(p=0.1, inplace=False)
  )
)

训练

数据批次，同时创建 mask

class Batch:
    def __init__(self, src, trg=None, pad=0):
        """
        src: 输入序列
        trg: 目标序列
        """
        self.src = src
        self.src_mask = (src != pad).unsqueeze(-2)
        if trg is not None:
            self.trg = trg[:, :-1]
            self.trg_y = trg[:, 1:]
            self.trg_mask = self.make_std_mask(self.trg, pad)
            self.ntokens = (self.trg_y != pad).data.sum()

    @staticmethod
    def make_std_mask(tgt, pad):
        """
        将 pad 产生的 mask，和序列一次预测下一个单词产生的 mask 结合起来
        """
        tgt_mask = (tgt != pad).unsqueeze(-2)
        tgt_mask = tgt_mask & Variable(
            subsequent_mask(tgt.size(-1)).type_as(tgt_mask.data))
        return tgt_mask

src = torch.tensor([[3, 5, 7, 0, 0], [2, 4, 6, 8, 0]])  # batch=2,seq_len=5
trg = torch.tensor([[2, 3, 4, 5, 0, 0], [3, 5, 6, 0, 0,
                                         0]])  # batch=2,seq_len=6

sample = Batch(src, trg)
sample.src_mask

tensor([[[ True,  True,  True, False, False]],

        [[ True,  True,  True,  True, False]]])

sample.trg_mask, sample.ntokens

(tensor([[[ True, False, False, False, False],
          [ True,  True, False, False, False],
          [ True,  True,  True, False, False],
          [ True,  True,  True,  True, False],
          [ True,  True,  True,  True, False]],
 
         [[ True, False, False, False, False],
          [ True,  True, False, False, False],
          [ True,  True,  True, False, False],
          [ True,  True,  True, False, False],
          [ True,  True,  True, False, False]]]),
 tensor(5))

训练过程

def run_epoch(data_iter, model, loss_compute):
    start = time.time()
    total_tokens = 0
    total_loss = 0
    tokens = 0
    for i, batch in enumerate(data_iter):
        out = model.forward(batch.src, batch.trg, batch.src_mask,
                            batch.trg_mask)
        loss = loss_compute(out, batch.trg_y, batch.ntokens)
        total_loss += loss
        total_tokens += batch.ntokens  # 总 tokens 数
        tokens += batch.ntokens  # 50 批训练时的总 tokens 数
        if i % 50 == 1:
            elapsed = time.time() - start
            print("Epoch Step: %d Loss: %f Tokens per Sec: %f" %
                  (i, loss / batch.ntokens, tokens / elapsed))
            start = time.time()
            tokens = 0
    return total_loss / total_tokens

训练数据

standard WMT 2014 English-German dataset consisting of about 4.5 million sentence pairs

global max_src_in_batch, max_tgt_in_batch
def batch_size_fn(mew, count, sofar):
    global max_src_in_batch, max_tgt_in_batch
    if count == 1:
        max_src_in_batch = 0
        max_tgt_in_batch = 0
    max_src_in_batch = max(max_src_in_batch,  len(new.src))
    max_tgt_in_batch = max(max_tgt_in_batch,  len(new.trg) + 2)
    src_elements = count * max_src_in_batch
    tgt_elements = count * max_tgt_in_batch
    return max(src_elements, tgt_elements)        

优化器

Adam 优化器，参数\(\beta_1=0.9\)，\(\beta_2=0.98\)，\(\epsilon=10^{-9}\)，变学习率：

\[lrate = d_{\text{model}}^{-0.5} \cdot \min({step\_num}^{-0.5}, {step\_num} \cdot {warmup\_steps}^{-1.5})\]

其中： \(warmup_{steps}=4000\)

class NoamOpt:
    def __init__(self, model_size, factor, warmup, optimizer):
        self.optimizer = optimizer
        self._step = 0
        self.warmup = warmup
        self.factor = factor
        self.model_size = model_size
        self._rate = 0

    def step(self):
        self._step += 1
        rate = self.rate()
        for p in self.optimizer.param_groups:
            p['lr'] = rate
        self._rate = rate
        self.optimizer.step()

    def rate(self, step=None):
        if step is None:
            step = self._step
        return self.factor * (self.model_size**(-0.5) *
                              min(step**(-0.5), step * self.warmup**(-1.5)))


def get_std_opt(model):
    return NoamOpt(
        model.src_embed[0].d_model, 2, 4000,
        torch.optim.Adam(model.parameters(), lr=0, betas=(0.9, 0.98),
                         eps=1e-9))

opts = [
    NoamOpt(512, 1, 4000, None),
    NoamOpt(512, 1, 8000, None),
    NoamOpt(256, 1, 4000, None),
]
plt.plot(np.arange(1, 20000),
         [[opt.rate(i) for opt in opts] for i in range(1, 20000)])
plt.legend(["512:4000", "512:8000", "256:4000"])

<matplotlib.legend.Legend at 0x7ffb17580990>

正则化

标签平滑Label Smoothing：\(\epsilon_{ls}=0.1\)，会降低 perplexity，因为模型将更不确定，但增加精度和BLEU分数

class LabelSmoothing(nn.Module):
    def __init__(self, size, padding_idx, smoothing=0.0):
        super(LabelSmoothing, self).__init__()
        self.criterion = nn.KLDivLoss(size_average=False)
        self.padding_idx = padding_idx
        self.confidence = 1.0 - smoothing
        self.smoothing = smoothing
        self.size = size
        self.true_dist = None

    def forward(self, x, target):
        assert x.size(1) == self.size
        true_dist = x.data.clone()

        true_dist.fill_(self.smoothing / (self.size - 2))
        
        true_dist.scatter_(1, target.data.unsqueeze(1), self.confidence)
        
        true_dist[:, self.padding_idx] = 0
        mask = torch.nonzero(target.data == self.padding_idx)
        if mask.dim() > 0:
            true_dist.index_fill_(0, mask.squeeze(), 0.0)
        self.true_dist = true_dist
        return self.criterion(x, Variable(true_dist, requires_grad=False))

nn.KLDivLoss: 输入为log概率分布，目标为概率分布；\(l(x,y) = L = \{ l_1,\dots,l_N \}, \quad l_n = y_n \cdot \left( \log y_n - x_n \right)\)
指定reduction参数时： \[ \ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';} \\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases}\]

Tensor.scatter_(dim, index, src)：

x = tensor([[0.1333, 0.1333, 0.1333, 0.1333, 0.1333],
            [0.1333, 0.1333, 0.1333, 0.1333, 0.1333],
            [0.1333, 0.1333, 0.1333, 0.1333, 0.1333]])       
index = tensor([[2],
                [1],
                [0]])
x.scatter(1, index, 0.6) -->
tensor([[0.1333, 0.1333, 0.6, 0.1333, 0.1333],
        [0.1333, 0.6, 0.1333, 0.1333, 0.1333],
        [0.6, 0.1333, 0.1333, 0.1333, 0.1333]]) 
    

例如上述的五分类中，目标序列 [2，1，0] 表示类别 2，1，0。将明确的类别转换成概率分布，使概率分布更均匀些，然后与预测概率分布求损失

crit = LabelSmoothing(size=5, padding_idx=0, smoothing=0.4)
predict = torch.FloatTensor([
    [0, 0.2, 0.7, 0.1, 0],
    [0, 0.2, 0.7, 0.1, 0],
    [0, 0.2, 0.7, 0.1, 0],
])
v = crit(Variable(predict.log()), Variable(torch.LongTensor([2, 1, 0])))
plt.imshow(crit.true_dist)
crit.true_dist

tensor([[0.0000, 0.1333, 0.6000, 0.1333, 0.1333],
        [0.0000, 0.6000, 0.1333, 0.1333, 0.1333],
        [0.0000, 0.0000, 0.0000, 0.0000, 0.0000]])

crit = LabelSmoothing(5, 0, 0.1)


def loss(x):
    d = x + 3 * 1
    predict = torch.FloatTensor([
        [0, x / d, 1 / d, 1 / d, 1 / d],  # 概率分布，x 的值越大，标签 1 的概率越大
    ])
    #print(predict)
    return crit(
        Variable(predict.log()),
        Variable(torch.LongTensor([1])),  # 真实标签为 1
    ).item()


plt.plot(np.arange(1, 100), [loss(x) for x in range(1, 100)])

[<matplotlib.lines.Line2D at 0x7ffb16742c90>]

测试模型

# 生成随机数据
def data_gen(V, batch, nbatches):
    for i in range(nbatches):
        data = torch.from_numpy(np.random.randint(1, V, size=(batch, 10)))
        data[:, 0] = 1
        src = Variable(data, requires_grad=False)
        tgt = Variable(data, requires_grad=False)
        yield Batch(src, tgt, 0)

class SimpleLossCompute:
    def __init__(self, generator, criterion, opt=None):
        self.generator = generator  # 模型最后的输出层
        self.criterion = criterion
        self.opt = opt

    def __call__(self, x, y, norm):
        x = self.generator(x)
        loss = self.criterion(x.contiguous().view(-1, x.size(-1)),
                              y.contiguous().view(-1)) / norm
        loss.backward()
        if self.opt is not None:
            self.opt.step()
            self.opt.optimizer.zero_grad()
        return loss.data.item() * norm

V = 11
criterion = LabelSmoothing(size=V, padding_idx=0, smoothing=0.0)
model = make_model(V, V, N=2)
model_opt = NoamOpt(
    model.src_embed[0].d_model, 1, 400,
    torch.optim.Adam(model.parameters(), lr=0, betas=(0.9, 0.98), eps=1e-9))

for epoch in range(10):
    model.train()
    run_epoch(data_gen(V, 30, 20), model,
              SimpleLossCompute(model.generator, criterion, model_opt))
    model.eval()
    print(
        run_epoch(data_gen(V, 30, 5), model,
                  SimpleLossCompute(model.generator, criterion, None)))

Epoch Step: 1 Loss: 3.041517 Tokens per Sec: 2320.010498
Epoch Step: 1 Loss: 2.116642 Tokens per Sec: 3337.003174
tensor(2.0963)
Epoch Step: 1 Loss: 2.251899 Tokens per Sec: 2198.680176
Epoch Step: 1 Loss: 1.861713 Tokens per Sec: 3322.143066
tensor(1.9056)
Epoch Step: 1 Loss: 2.097054 Tokens per Sec: 2199.775635
Epoch Step: 1 Loss: 1.919798 Tokens per Sec: 3104.268799
tensor(1.9386)
Epoch Step: 1 Loss: 1.955538 Tokens per Sec: 2096.228027
Epoch Step: 1 Loss: 1.854445 Tokens per Sec: 3121.148926
tensor(1.8574)
Epoch Step: 1 Loss: 2.210659 Tokens per Sec: 2088.976074
Epoch Step: 1 Loss: 1.806028 Tokens per Sec: 3116.300537
tensor(1.7957)
Epoch Step: 1 Loss: 2.442501 Tokens per Sec: 2085.300537
Epoch Step: 1 Loss: 1.931611 Tokens per Sec: 3112.506348
tensor(1.9629)
Epoch Step: 1 Loss: 1.962478 Tokens per Sec: 2092.424561
Epoch Step: 1 Loss: 1.450812 Tokens per Sec: 3114.582275
tensor(1.5110)
Epoch Step: 1 Loss: 1.954074 Tokens per Sec: 2087.149170
Epoch Step: 1 Loss: 1.519574 Tokens per Sec: 3094.708252
tensor(1.4481)
Epoch Step: 1 Loss: 1.859929 Tokens per Sec: 2039.030151
Epoch Step: 1 Loss: 1.412592 Tokens per Sec: 3088.327881
tensor(1.3660)
Epoch Step: 1 Loss: 1.943988 Tokens per Sec: 2065.341797
Epoch Step: 1 Loss: 1.302344 Tokens per Sec: 2979.704590
tensor(1.3880)

解码算法

def greedy_decode(model, src, src_mask, max_len, start_symbol):
    memory = model.encode(src, src_mask)
    ys = torch.ones(1, 1).fill_(start_symbol).type_as(src.data)
    for i in range(max_len - 1):
        out = model.decode(
            memory, src_mask, Variable(ys),
            Variable(subsequent_mask(ys.size(1)).type_as(src.data)))
        prob = model.generator(out[:, -1])
        _, next_word = torch.max(prob, dim=1)
        next_word = next_word.item()
        ys = torch.cat(
            [ys, torch.ones(1, 1).type_as(src.data).fill_(next_word)], dim=1)
    return ys


model.eval()
src = Variable(torch.LongTensor([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]))
src_mask = Variable(torch.ones(1, 1, 10))
print(greedy_decode(model, src, src_mask, max_len=10, start_symbol=1))

tensor([[ 1,  2,  4,  3,  7,  9, 10,  8,  9,  8]])

实战

from torchtext import data, datasets

if True:
    import spacy
    spacy_de = spacy.load("de_core_news_sm")
    spacy_en = spacy.load("en_core_web_sm")

    def tokenize_de(text):
        return [tok.text for tok in spacy_de.tokenizer(text)]

    def tokenize_en(text):
        return [tok.text for tok in spacy_en.tokenizer(text)]

    BOS_WORD = '<s>'
    EOS_WORD = '</s>'
    BLANK_WORD = "<blank>"
    SRC = data.Field(tokenize=tokenize_de,
                     pad_token=BLANK_WORD)  # 定义预处理流程，分词、填充、
    TGT = data.Field(tokenize=tokenize_en,
                     init_token=BOS_WORD,
                     eos_token=EOS_WORD,
                     pad_token=BLANK_WORD)

    MAX_LEN = 100

    # 数据集
    train, val, test = datasets.IWSLT.splits(
        exts=('.de', '.en'),
        fields=(SRC, TGT),
        filter_pred=lambda x: len(vars(x)['src']) <= MAX_LEN and len(
            vars(x)['trg']) <= MAX_LEN)
    MIN_FREQ = 2

    # 创建词汇表
    SRC.build_vocab(train.src, min_freq=MIN_FREQ)
    TGT.build_vocab(train.trg, min_freq=MIN_FREQ)

# 数据分批对训练速度很重要：需要拆分成均匀的批次，最小的填充

class MyIterator(data.Iterator):
    def create_batches(self):
        if self.train: # 训练模式，数据分批，然后打乱顺序

            def pool(d, random_shuffler):
                for p in data.batch(d, self.batch_size * 100):
                    p_batch = data.batch(sorted(p, key=self.sort_key),
                                         self.batch_size, self.batch_size_fn)
                    for b in random_shuffler(list(p_batch)):
                        yield b

            self.batches = pool(self.data(), self.random_shuffler)

        else:
            self.batches = []
            for b in data.batch(self.data(), self.batch_size,
                                self.batch_size_fn):
                self.batches.append(sorted(b, key=self.sort_key))


def rebatch(pad_idx, batch): # batch first --> True
    "Fix order in torchtext to match ours"
    src, trg = batch.src.transpose(0, 1), batch.trg.transpose(0, 1)
    return Batch(src, trg, pad_idx)

并行计算

# 使用 multi-gpu 加速训练速度：将单词生成拆分成块，便于并行处理


class MultiGPULossCompute:
    def __init__(self, generator, criterion, devices, opt=None, chunk_size=5):
        self.generator = generator
        self.criterion = nn.parallel.replicate(criterion, devices=devices)
        self.opt = opt
        self.devices = devices
        self.chunk_size = chunk_size

    def __call__(self, out, targets, normalize):
        
        total = 0.0
        
        # 将最终的线性输出层 并行 到多个 gpu中
        generator = nn.parallel.replicate(self.generator, devices=devices)
        
        # 将 transformer 的输出张量 并行 多个 gpu 中
        out_scatter = nn.parallel.scatter(out, target_gpus=self.devices)
        out_grad = [[] for _ in out_scatter]
        
        # 将目标 并行 到多个 gpu 中
        targets = nn.parallel.scatter(targets, target_gpus=self.devices)

        # 将生成拆分成块？？
        chunk_size = self.chunk_size
        for i in range(0, out_scatter[0].size(1), chunk_size):

            # 预测分布
            out_column = [[
                Variable(o[:, i:i + chunk_size].data,
                         requires_grad=self.opt is not None)
            ] for o in out_scatter]
            gen = nn.parallel.parallel_apply(generator, out_column)

            # 计算损失
            y = [(g.contiguous().view(-1, g.size(-1)),
                  t[:, i:i + chunk_size].contiguous().view(-1))
                 for g, t in zip(gen, targets)]
            loss = nn.parallel.parallel_apply(self.criterion, y)

            # 损失求和并归一化
            l = nn.parallel.gather(loss, target_device=self.devices[0])
            l = l.sum()[0] / normalize
            total += l.data[0]

            # 反向传播
            if self.opt is not None:
                l.backward()
                for j, l in enumerate(loss):
                    out_grad[j].append(out_column[j][0].grad.data.clone())

        # 反向传播整个模型
        if self.opt is not None:
            out_grad = [Variable(torch.cat(og, dim=1)) for og in out_grad]
            o1 = out
            o2 = nn.parallel.gather(out_grad, target_device=self.devices[0])
            o1.backward(gradient=o2)
            self.opt.step()
            self.opt.optimizer.zero_grad()
        return total * normalize

devices = [0, 1, 2, 3]
if True:
    pad_idx = TGT.vocab.stoi["<blank>"]
    model = make_model(len(SRC.vocab), len(TGT.vocab), N=6)
    model.cuda()
    criterion = LabelSmoothing(size=len(TGT.vocab),
                               padding_idx=pad_idx,
                               smoothing=0.1)
    criterion.cuda()
    BATCH_SIZE = 12000
    train_iter = MyIterator(train,
                            batch_size=BATCH_SIZE,
                            device=0,
                            repeat=False,
                            sort_key=lambda x: (len(x.src), len(x.trg)),
                            batch_size_fn=batch_size_fn,
                            train=True)
    valid_iter = MyIterator(val,
                            batch_size=BATCH_SIZE,
                            device=0,
                            repeat=False,
                            sort_key=lambda x: (len(x.src), len(x.trg)),
                            batch_size_fn=batch_size_fn,
                            train=False)
    model_par = nn.DataParallel(model, device_ids=devices)

if False:
    model_opt = NoamOpt(
        model.src_embed[0].d_model, 1, 2000,
        torch.optim.Adam(model.parameters(), lr=0, betas=(0.9, 0.98),
                         eps=1e-9))
    for epoch in range(10):
        model_par.train()
        run_epoch((rebatch(pad_idx, b) for b in train_iter), model_par,
                  MultiGPULossCompute(model.generator,
                                      criterion,
                                      devices=devices,
                                      opt=model_opt))
        model_par.eval()
        loss = run_epoch((rebatch(pad_idx, b) for b in valid_iter), model_par,
                         MultiGPULossCompute(model.generator,
                                             criterion,
                                             devices=devices,
                                             opt=None))
        print(loss)
else:
    model = torch.load("iwslt.pt")

for i, batch in enumerate(valid_iter):
    src = batch.src.transpose(0, 1)[:1]
    src_mask = (src != SRC.vocab.stoi["<blank>"]).unsqueeze(-2)
    out = greedy_decode(model,
                        src,
                        src_mask,
                        max_len=60,
                        start_symbol=TGT.vocab.stoi["<s>"])
    print("Translation:", end="\t")
    for i in range(1, out.size(1)):
        sym = TGT.vocab.itos[out[0, i]]
        if sym == "</s>": break
        print(sym, end=" ")
    print()
    print("Target:", end="\t")
    for i in range(1, batch.trg.size(0)):
        sym = TGT.vocab.itos[batch.trg.data[i, 0]]
        if sym == "</s>": break
        print(sym, end=" ")
    print()
    break

额外的组件

BPE/ Word-piece：将单词拆分成 子词

共享权重：输入与目标的嵌入矩阵相同

if False:
    model.src_embed[0].lut.weight = model.tgt_embeddings[0].lut.weight
    model.generator.lut.weight = model.tgt_embed[0].lut.weight

Beam Search

https://github.com/OpenNMT/OpenNMT-py/blob/master/onmt/translate/beam_search.py

Model Averaging：将最后 k 个 checkpoint 平均，创造组合模型

def average(model, models):
    "Average models into model"
    for ps in zip(*[m.params() for m in [model] + models]):
        p[0].copy_(torch.sum(*ps[1:]) / len(ps[1:]))

注意力可视化

tgt_sent = trans.split()


def draw(data, x, y, ax):
    seaborn.heatmap(data,
                    xticklabels=x,
                    square=True,
                    yticklabels=y,
                    vmin=0.0,
                    vmax=1.0,
                    cbar=False,
                    ax=ax)


for layer in range(1, 6, 2):
    fig, axs = plt.subplots(1, 4, figsize=(20, 10))
    print("Encoder Layer", layer + 1)
    for h in range(4):
        draw(model.encoder.layers[layer].self_attn.attn[0, h].data,
             sent,
             sent if h == 0 else [],
             ax=axs[h])
    plt.show()

for layer in range(1, 6, 2):
    fig, axs = plt.subplots(1, 4, figsize=(20, 10))
    print("Decoder Self Layer", layer + 1)
    for h in range(4):
        draw(model.decoder.layers[layer].self_attn.attn[0, h].
             data[:len(tgt_sent), :len(tgt_sent)],
             tgt_sent,
             tgt_sent if h == 0 else [],
             ax=axs[h])
    plt.show()
    print("Decoder Src Layer", layer + 1)
    fig, axs = plt.subplots(1, 4, figsize=(20, 10))
    for h in range(4):
        draw(model.decoder.layers[layer].self_attn.attn[0, h].
             data[:len(tgt_sent), :len(sent)],
             sent,
             tgt_sent if h == 0 else [],
             ax=axs[h])
    plt.show()