序

word embedding之后，经过连续的N次(如12or4）的BertLayer串联之后的之后的输出，即为Bert的输出。本篇文章，主要分析一次 BertLayer的过程。

所有的代码都在 pytorch_pretrained_bert/modeling.py 文件中。

BertLayer

首先，我们看下BertLayer前向时的处理过程，分别经过BertAttention层，BertIntermediate层，
BertOutput层，后续我们会依次分析这三层的实现。

image.png

图 1 一次 BertLayer的前向运算过程

class BertLayer(nn.Module):    
    def __init__(self, config):        
        super(BertLayer, self).__init__()        
        self.attention = BertAttention(config)        
        self.intermediate = BertIntermediate(config)        
        self.output = BertOutput(config)    
    def forward(self, hidden_states, attention_mask): 
        # BertAttention 层
        attention_output = self.attention(hidden_states, attention_mask) 
        # BertIntermediate 层
        intermediate_output = self.intermediate(attention_output)
        # BertOutput层 
        layer_output = self.output(intermediate_output, attention_output)       
        return layer_output

BertAttention

Bert中的SelfAttention主要是借鉴了<Attention is all you need>论文中提出的自注意力机制

如下图中，左图为selft-attention的过程。一组(Q,K,V)，可对输入进行一种处理。Mutli_head Attention是多组(h)(Q,K,V)同时存在时，对输入进行多种变换，提取多种特征的方法。多个Attention输出结果进行Contact。每个Attention可独立进行前向运算。他们之间在前向运行时，没有关联。所以可以组成矩阵的形式，利用GPU对矩阵并行计算的优势，加快运算速度。详细处理过程，请见下文代码分析。

image.png

图 2 Scaled Dot-Porduct Attention 和 Multi-Head Attention的图示

BertSelfAttention

class BertSelfAttention(nn.Module):
    def __init__(self, config):
         super(BertSelfAttention, self).__init__()
        if config.hidden_size % config.num_attention_heads != 0:
            raise ValueError(
                "The hidden size (%d) is not a multiple of the number of attention "
                "heads (%d)" % (config.hidden_size, config.num_attention_heads))
        self.num_attention_heads = config.num_attention_heads
        self.attention_head_size = int(config.hidden_size / config.num_attention_heads)
        self.all_head_size = self.num_attention_heads * self.attention_head_size
        # 此处可标红，哈哈，query,key,value都是对输入进行全连接层的变换得到的。 输入的节点数为config.hidden_size， 输出为self.all_head_size(也是config.hidden_size)，即权重矩阵为[config.hidden_size, config.hidden_size]
        self.query = nn.Linear(config.hidden_size, self.all_head_size)
        self.key = nn.Linear(config.hidden_size, self.all_head_size)
        self.value = nn.Linear(config.hidden_size, self.all_head_size)

        self.dropout = nn.Dropout(config.attention_probs_dropout_prob)
   
    def transpose_for_scores(self, x): 
        # 进行维度变换，如batch_size：32， seq_len：300， num_attention_heads：12，attention_head_size:26 (12 * 26 = 312即hidden_size为312)
        # new_x_shape 维度变换 [batch_size, seq_len, hidden_size]->[seq_len, seq_len, num_attention_heads, attention_head_size]即：[32, 300, 312] 转换为 [32, 300, 12, 26]
        new_x_shape = x.size()[:-1] + (self.num_attention_heads,            self.attention_head_size)
        # 重构涨量的维度
        x = x.view(*new_x_shape)
        # 维度换位：即[32, 300, 12, 26]经过换位之后的维度[32, 12, 300, 26]即[batch_size, num_attention_heads, seq_len, attention_head_size]
        return x.permute(0, 2, 1, 3)
   
    def forward(self, hidden_states, attention_mask):
        # 维度变换：[batch_size, seq_len, embedding_size]->[batch_size, seq_len, embedding_size]
        mixed_query_layer = self.query(hidden_states)
        mixed_key_layer = self.key(hidden_states)
        mixed_value_layer = self.value(hidden_states)
        
        # [batch_size, seq_len, embedding_size]-->[batch_size, num_attention_heads, seq_len, attention_head_size ]
        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.
        # query_layer[32, 12, 300, 26], key_layer.transpose(-1, -2):[32, 12, 26, 300],
        # attention_scores:[32, 12, 300, 300]
        attention_scores = torch.matmul(query_layer, key_layer.transpose(-1, -2))
        # 除以矩阵相乘时累加元素的格式 26，即左乘矩阵的列数 26,或是右乘矩阵的行数 26
        attention_scores = attention_scores / math.sqrt(self.attention_head_size)
        # Apply the attention mask is (precomputed for all layers in BertModel forward() function)
        # attention_mask，原句内容的位置值为0，补充到max_seq位置处的值为-1000.相加之后, 补充位置处的值会非常小。经过下面的softmax之后是一个接近于0的值。
        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.
        attention_probs = self.dropout(attention_probs)
        # 注意力矩阵attention_probs[32, 12, 300, 300] 和 value_layer[32, 12, 300, 26],
        # context_layer 维度为[32, 12, 300, 26]
        context_layer = torch.matmul(attention_probs, value_layer)
        # 维度换位 [32, 12, 300, 26]->[32, 300, 12, 26]
        context_layer = context_layer.permute(0, 2, 1, 3).contiguous()
        # 定义输出维度 [32, 300, 312]
        new_context_layer_shape = context_layer.size()[:-2] + (self.all_head_size,)
        # 维度变换
        context_layer = context_layer.view(*new_context_layer_shape)
        return context_layer
        

这里和上图2稍有不同，上图2的右图中，contact之后的linear处理，放在了BertSelfOutput层。即contact之后之后的输出，作为BertSelfOutput层的输入。BertSelfOutput依次做了(Linear->Add->BertLayerNorm )的处理。

class BertSelfOutput(nn.Module):    
    def __init__(self, config):        
        super(BertSelfOutput, self).__init__()        
        self.dense = nn.Linear(config.hidden_size, config.hidden_size)                           self.LayerNorm = BertLayerNorm(config.hidden_size, eps=1e-12)        
        self.dropout = nn.Dropout(config.hidden_dropout_prob)    
    def forward(self, hidden_states, input_tensor):
        # 全连接层处理
        hidden_states = self.dense(hidden_states)        
        hidden_states = self.dropout(hidden_states)  
        # ResNet结构 ：hidden_states（SelfAttention层之后再进行一次前向运算的输出） + input_tensor(SelfAttention层的输入)
        # 相加之后的和矩阵，进行LayerNorm运算。layerNorm的介绍，可参考前文。
        hidden_states = self.LayerNorm(hidden_states + input_tensor)        
        return hidden_states

BertAttention

class BertAttention(nn.Module):    
    def __init__(self, config):        
        super(BertAttention, self).__init__()       
        self.self = BertSelfAttention(config)        
        self.output = BertSelfOutput(config)    
    def forward(self, input_tensor, attention_mask):
        # 执行上文中的BertSelfAttention::forward函数，self_output维度为[batch_size, seq_len, embedding_size]
        self_output = self.self(input_tensor, attention_mask)
        # 执行上文中介绍的BertSelfOutput::forward函数函数，attention_output的维度为[batch_size, seq_len, embedding_size]
        attention_output = self.output(self_output, input_tensor)        
        return attention_output

BertIntermediate

对应图1中的FeedForword处理

class BertIntermediate(nn.Module):    
    def __init__(self, config):        
        super(BertIntermediate, self).__init__()   
        # 定义一个变换矩阵[config.hidden_size, config.intermediate_size], config.hidden_size即为embedding_size
        self.dense = nn.Linear(config.hidden_size, config.intermediate_size) 
        # 定义激活函数
        if isinstance(config.hidden_act, str) or (sys.version_info[0] == 2 and isinstance(config.hidden_act, unicode)):           
            self.intermediate_act_fn = ACT2FN[config.hidden_act]       
        else:            
            self.intermediate_act_fn = config.hidden_act    
   def forward(self, hidden_states):
        # 全连接层，矩阵维度变换[batch_size, seq_len, embedding_size]->[batch_size, seq_len, intermediate_size]
        hidden_states = self.dense(hidden_states)
        # 激活处理(gelu)
        hidden_states = self.intermediate_act_fn(hidden_states)        
        return hidden_states

BertOutput

图1中的Add&Norm处理放在了此层。BertOutput和BertSelfOutput是比较像的。 只有变换矩阵维度不同BertSelfOutput为[embedding_size, embedding_size], BertOutput为[intermediate_size, hidden_size]

class BertOutput(nn.Module):    
    def __init__(self, config):        
        super(BertOutput, self).__init__()        
        self.dense = nn.Linear(config.intermediate_size, config.hidden_size)                     self.LayerNorm = BertLayerNorm(config.hidden_size, eps=1e-12)        
        self.dropout = nn.Dropout(config.hidden_dropout_prob)    
    def forward(self, hidden_states, input_tensor):        
        hidden_states = self.dense(hidden_states)        
        hidden_states = self.dropout(hidden_states)  
        # Add & Norm
        hidden_states = self.LayerNorm(hidden_states + input_tensor)        
        return hidden_states

其他

初学pytorch,在看代码的时候有些函数的用法不是很明确，写下些小的测试例子，这里记录如下。

permute测试：

x = torch.randn(2, 3)
print(x)
'''
输入为:
tensor([[ 1.0246, -0.5259, -1.9292],
        [-0.4087, -0.0218,  0.5222]])
'''
x = x.permute(1, 0)
print(x)
'''
输出为：
tensor([[ 1.0246, -0.4087],
        [-0.5259, -0.0218],
        [-1.9292,  0.5222]])
'''

矩阵的加法，只要求两个矩阵的列数相等即可，

x = torch.randn(2, 2)
print(x)
'''
tensor([[ 0.0062,  0.5476],
        [-1.5412, -0.4478]])
'''
y = torch.randn(1, 2)
print(y)
'''
tensor([[-0.3993, -1.3920]])
'''
z = x + y
print(z)
'''
tensor([[-0.3930, -0.8444],
        [-1.9405, -1.8398]])
'''

view

和respahe的作用基本相同

contiguous: 没有修改底层一维数组，但是新建了一份Tensor元信息

t = torch.arange(12).reshape(3, 4)
print(t)
'''
tensor([[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11]])
'''
t2 = t.transpose(0, 1)
print(t2)
'''
tensor([[ 0,  4,  8],
        [ 1,  5,  9],
        [ 2,  6, 10],
        [ 3,  7, 11]])
'''
print(t.data_ptr() == t2.data_ptr())
'''
True
'''
t3 = t2.contiguous()
print(t3)
'''
tensor([[ 0,  4,  8],
        [ 1,  5,  9],
        [ 2,  6, 10],
        [ 3,  7, 11]])
'''
print(t3.data_ptr() == t2.data_ptr())
'''
False
'''
print(t.data_ptr() == t3.data_ptr())
'''
False
'''

dense

可以看到这里的dense,都是Linear类型。即进行的是线性变换。

class Linear(Module):
    __constants__ = ['in_features', 'out_features']
    in_features: int
    out_features: int
    weight: Tensor

    def __init__(self, in_features: int, out_features: int, bias: bool = True) -> None:
        super(Linear, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.weight = Parameter(torch.Tensor(out_features, in_features))
        if bias:
            self.bias = Parameter(torch.Tensor(out_features))
        else:
            self.register_parameter('bias', None)
        self.reset_parameters()

    def reset_parameters(self) -> None:
        init.kaiming_uniform_(self.weight, a=math.sqrt(5))
        if self.bias is not None:
            fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight)
            bound = 1 / math.sqrt(fan_in)
            init.uniform_(self.bias, -bound, bound)

    def forward(self, input: Tensor) -> Tensor:
        return F.linear(input, self.weight, self.bias)

    def extra_repr(self) -> str:
        return 'in_features={}, out_features={}, bias={}'.format(
            self.in_features, self.out_features, self.bias is not None
        )

tf版本的dense稍有不同, 其中有一参数activation，表示 使用什么激活函数（神经网络的非线性层），默认为None，不使用激活函数。

tf.layers.dense

tf.layers.dense(    inputs,    
    units,    
    activation=None,    
    use_bias=True,    
    kernel_initializer=None,    
    bias_initializer=tf.zeros_initializer(),    
    kernel_regularizer=None,    
    bias_regularizer=None,    
    activity_regularizer=None,    
    kernel_constraint=None,    
    bias_constraint=None,    
    trainable=True,    
    name=None,    
    reuse=None )