通过公式结合文字通俗易懂的解释 BERT模型(Bidirectional Encoder Representations from Transformers)

Transformer Block

BERT中的点积注意力模型

公式：

代码：

class Attention(nn.Module):

"""

Scaled Dot Product Attention

"""

def forward(self, query, key, value, mask=None, dropout=None):

scores = torch.matmul(query, key.transpose(-2, -1)) \

/ math.sqrt(query.size(-1))

if mask is not None:

scores = scores.masked_fill(mask == 0, -1e9)

# softmax得到概率得分p_atten,

p_attn = F.softmax(scores, dim=-1)

# 如果有 dropout 就随机 dropout 比例参数

if dropout is not None:

p_attn = dropout(p_attn)

return torch.matmul(p_attn, value), p_attnt

头条代码编辑贼不方便，可以看我博客：https://www.shikanon.com/2019/机器学习/BERT代码实现及解读/

在 self-attention 的计算过程中, 通常使用 ? 来计算, 也就是一次计算多个句子，多句话得长度并不一致，因此，我们需要按照最大得长度对短句子进行补全，也就是padding零，但这样做得话，softmax计算就会被影响，e0=1也就是有值，这样就会影响结果，这并不是我们希望看到得，因此在计算得时候我们需要把他们mask起来，填充一个负无穷（-1e9这样得数值），这样计算就可以为0了，等于把计算遮挡住。

多头自注意力模型

公式：

Attention Mask

代码：

class MultiHeadedAttention(nn.Module):
 """
 Take in model size and number of heads.
 """
 def __init__(self, h, d_model, dropout=0.1):
 # h 表示模型个数
 super().__init__()
 assert d_model % h == 0
 # d_k 表示 key长度，d_model表示模型输出维度，需保证为h得正数倍
 self.d_k = d_model // h
 self.h = h
 self.linear_layers = nn.ModuleList([nn.Linear(d_model, d_model) for _ in range(3)])
 self.output_linear = nn.Linear(d_model, d_model)
 self.attention = Attention()
 self.dropout = nn.Dropout(p=dropout)
 def forward(self, query, key, value, mask=None):
 batch_size = query.size(0) 
 query, key, value = [l(x).view(batch_size, -1, self.h, self.d_k).transpose(1, 2)
 for l, x in zip(self.linear_layers, (query, key, value))]
 x, attn = self.attention(query, key, value, mask=mask, dropout=self.dropout)
 x = x.transpose(1, 2).contiguous().view(batch_size, -1, self.h * self.d_k)
 return self.output_linear(x)

Position-wise FFN

Position-wise FFN 是一个双层得神经网络，在论文中采用ReLU做激活层：

公式：

注：在 google github中的BERT的代码实现中用Gaussian Error Linear Unit代替了RelU作为激活函数

代码：

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)
 self.activation = GELU()
 def forward(self, x):
 return self.w_2(self.dropout(self.activation(self.w_1(x))))
class GELU(nn.Module):
 """
 Gaussian Error Linear Unit.
 This is a smoother version of the RELU.
 Original paper: https://arxiv.org/abs/1606.08415
 """
 def forward(self, x):
 return 0.5 * x * (1 + torch.tanh(math.sqrt(2 / math.pi) * (x + 0.044715 * torch.pow(x, 3))))

Layer Normalization

LayerNorm实际就是对隐含层做层归一化，即对某一层的所有神经元的输入进行归一化（沿着通道channel方向），使得其加快训练速度：

层归一化公式：

代码：

class LayerNorm(nn.Module):
 "Construct a layernorm module (See citation for details)."
 def __init__(self, features, eps=1e-6):
 super(LayerNorm, self).__init__()
 self.a_2 = nn.Parameter(torch.ones(features))
 self.b_2 = nn.Parameter(torch.zeros(features))
 self.eps = eps
 def forward(self, x):
 # mean(-1) 表示 mean(len(x)), 这里的-1就是最后一个维度，也就是最里面一层的维度
 mean = x.mean(-1, keepdim=True)
 std = x.std(-1, keepdim=True)
 return self.a_2 * (x - mean) / (std + self.eps) + self.b_2

残差连接

残差连接就是图中Add+Norm层。每经过一个模块的运算, 都要把运算之前的值和运算之后的值相加, 从而得到残差连接，残差可以使梯度直接走捷径反传到最初始层。

残差连接公式：

y=f(x)+x

X 表示输入的变量，实际就是跨层相加。

代码：

class SublayerConnection(nn.Module):
 """
 A residual connection followed by a layer norm.
 Note for code simplicity the norm is first as opposed to last.
 """
 def __init__(self, size, dropout):
 super(SublayerConnection, self).__init__()
 self.norm = LayerNorm(size)
 self.dropout = nn.Dropout(dropout)
 def forward(self, x, sublayer):
 "Apply residual connection to any sublayer with the same size."
 # Add and Norm
 return x + self.dropout(sublayer(self.norm(x)))

Transform Block

代码：

class TransformerBlock(nn.Module):
 """
 Bidirectional Encoder = Transformer (self-attention)
 Transformer = MultiHead_Attention + Feed_Forward with sublayer connection
 """
 def __init__(self, hidden, attn_heads, feed_forward_hidden, dropout):
 """
 :param hidden: hidden size of transformer
 :param attn_heads: head sizes of multi-head attention
 :param feed_forward_hidden: feed_forward_hidden, usually 4*hidden_size
 :param dropout: dropout rate
 """
 super().__init__()
 # 多头注意力模型
 self.attention = MultiHeadedAttention(h=attn_heads, d_model=hidden)
 # PFFN
 self.feed_forward = PositionwiseFeedForward(d_model=hidden, d_ff=feed_forward_hidden, dropout=dropout)
 # 输入层
 self.input_sublayer = SublayerConnection(size=hidden, dropout=dropout)
 # 输出层
 self.output_sublayer = SublayerConnection(size=hidden, dropout=dropout)
 self.dropout = nn.Dropout(p=dropout)
 def forward(self, x, mask):
 x = self.input_sublayer(x, lambda _x: self.attention.forward(_x, _x, _x, mask=mask))
 x = self.output_sublayer(x, self.feed_forward)
 return self.dropout(x)

Embedding嵌入层

Embedding采用三种相加的形式表示：

代码：

class BERTEmbedding(nn.Module):
 """
 BERT Embedding which is consisted with under features
 1. TokenEmbedding : normal embedding matrix
 2. PositionalEmbedding : adding positional information using sin, cos
 3. SegmentEmbedding : adding sentence segment info, (sent_A:1, sent_B:2)
 sum of all these features are output of BERTEmbedding
 """
 def __init__(self, vocab_size, embed_size, dropout=0.1):
 """
 :param vocab_size: total vocab size
 :param embed_size: embedding size of token embedding
 :param dropout: dropout rate
 """
 super().__init__()
 self.token = TokenEmbedding(vocab_size=vocab_size, embed_size=embed_size)
 self.position = PositionalEmbedding(d_model=self.token.embedding_dim)
 self.segment = SegmentEmbedding(embed_size=self.token.embedding_dim)
 self.dropout = nn.Dropout(p=dropout)
 self.embed_size = embed_size
 def forward(self, sequence, segment_label):
 x = self.token(sequence) + self.position(sequence) + self.segment(segment_label)
 return self.dropout(x)

位置编码(Positional Embedding)

位置嵌入的维度为 [ ?, ] , 嵌入的维度同词向量的维度, ? 属于超参数, 指的是限定的最大单个句长.

公式：

其所绘制的图形：

代码：

class PositionalEmbedding(nn.Module):
 def __init__(self, d_model, max_len=512):
 super().__init__()
 # Compute the positional encodings once in log space.
 pe = torch.zeros(max_len, d_model).float()
 pe.require_grad = False
 position = torch.arange(0, max_len).float().unsqueeze(1)
 div_term = (torch.arange(0, d_model, 2).float() * -(math.log(10000.0) / d_model)).exp()
 pe[:, 0::2] = torch.sin(position * div_term)
 pe[:, 1::2] = torch.cos(position * div_term)
 # 对数据维度进行扩充，扩展第0维
 pe = pe.unsqueeze(0)
 # 添加一个持久缓冲区pe,缓冲区可以使用给定的名称作为属性访问
 self.register_buffer('pe', pe)
 def forward(self, x):
 return self.pe[:, :x.size(1)]

Segment Embedding

主要用来做额外句子或段落划分新够词，

这里加入了三个维度，分别是句子

开头【CLS】,下一句【STEP】,遮盖词【MASK】

例如： [CLS] the man went to the store [SEP] he bought a gallon of milk [SEP]

代码：

class SegmentEmbedding(nn.Embedding):
 def __init__(self, embed_size=512):
 # 3个新词
 super().__init__(3, embed_size, padding_idx=0)

Token Embedding

代码：

class TokenEmbedding(nn.Embedding):
 def __init__(self, vocab_size, embed_size=512):
 super().__init__(vocab_size, embed_size, padding_idx=0)

BERT

class BERT(nn.Module):
 """
 BERT model : Bidirectional Encoder Representations from Transformers.
 """
 def __init__(self, vocab_size, hidden=768, n_layers=12, attn_heads=12, dropout=0.1):
 """
 :param vocab_size: 所有字的长度
 :param hidden: BERT模型隐藏层大小
 :param n_layers: Transformer blocks(layers)数量
 :param attn_heads: 多头注意力head数量
 :param dropout: dropout rate
 """
 super().__init__()
 self.hidden = hidden
 self.n_layers = n_layers
 self.attn_heads = attn_heads
 # paper noted they used 4*hidden_size for ff_network_hidden_size
 self.feed_forward_hidden = hidden * 4
 # 嵌入层, positional + segment + token
 self.embedding = BERTEmbedding(vocab_size=vocab_size, embed_size=hidden)
 # 多层transformer blocks
 self.transformer_blocks = nn.ModuleList(
 [TransformerBlock(hidden, attn_heads, hidden * 4, dropout) for _ in range(n_layers)])
 def forward(self, x, segment_info):
 # attention masking for padded token
 # torch.ByteTensor([batch_size, 1, seq_len, seq_len)
 mask = (x > 0).unsqueeze(1).repeat(1, x.size(1), 1).unsqueeze(1)
 # embedding the indexed sequence to sequence of vectors
 x = self.embedding(x, segment_info)
 # 多个transformer 堆叠
 for transformer in self.transformer_blocks:
 x = transformer.forward(x, mask)
 return x

语言模型训练的几点技巧

BERT如何做到自训练的，一下是几个小tip，让其做到自监督训练:

Mask

随机遮盖或替换一句话里面任意字或词, 然后让模型通过上下文的理解预测那一个被遮盖或替换的部分, 之后做的时候只计算被遮盖部分的。

随机把一句话中 15% 的 替换成以下内容:

• 1) 这些 有 80% 的几率被替换成 【】 ;
• 2) 有 10% 的几率被替换成任意一个其他的 ;
• 3) 有 10% 的几率原封不动.

让模型预测和还原被遮盖掉或替换掉的部分，损失函数只计算随机遮盖或替换部分的Loss。

代码：

class MaskedLanguageModel(nn.Module):
 """
 predicting origin token from masked input sequence
 n-class classification problem, n-class = vocab_size
 """
 def __init__(self, hidden, vocab_size):
 """
 :param hidden: output size of BERT model
 :param vocab_size: total vocab size
 """
 super().__init__()
 self.linear = nn.Linear(hidden, vocab_size)
 self.softmax = nn.LogSoftmax(dim=-1)
 def forward(self, x):
 return self.softmax(self.linear(x))

预测下一句

代码：

class NextSentencePrediction(nn.Module):
 """
 2-class classification model : is_next, is_not_next
 """
 def __init__(self, hidden):
 """
 :param hidden: BERT model output size
 """
 super().__init__()
 self.linear = nn.Linear(hidden, 2)
 # 这里采用了logsoftmax代替了softmax，
 # 当softmax值远离真实值的时候梯度也很小，logsoftmax的梯度会比
 self.softmax = nn.LogSoftmax(dim=-1)
 def forward(self, x):
 return self.softmax(self.linear(x[:, 0]))

损失函数

负对数最大似然损失(negative log likelihood)，也叫交叉熵(Cross-Entropy)公式：

代码：

# 在Pytorch中 CrossEntropyLoss()等于NLLLoss+ softmax，因此如果用CrossEntropyLoss最后一层就不用softmax了
criterion = nn.NLLLoss(ignore_index=0)
# 2-1. NLL(negative log likelihood) loss of is_next classification result
next_loss = criterion(next_sent_output, data["is_next"])
# 2-2. NLLLoss of predicting masked token word
mask_loss = criterion(mask_lm_output.transpose(1, 2), data["bert_label"])
# 2-3. Adding next_loss and mask_loss : 3.4 Pre-training Procedure
loss = next_loss + mask_loss

语言模型训练

代码：

class BERTLM(nn.Module):
 """
 BERT Language Model
 Next Sentence Prediction Model + Masked Language Model
 """
 def __init__(self, bert: BERT, vocab_size):
 """
 :param bert: BERT model which should be trained
 :param vocab_size: total vocab size for masked_lm
 """
 super().__init__()
 self.bert = bert
 self.next_sentence = NextSentencePrediction(self.bert.hidden)
 self.mask_lm = MaskedLanguageModel(self.bert.hidden, vocab_size)
 def forward(self, x, segment_label):
 x = self.bert(x, segment_label)
 return self.next_sentence(x), self.mask_lm(x)