深度学习：Attention机制（Bahdanau attention & Luong Attention）

传统seq2seq模型中encoder将输入序列编码成一个context向量，decoder将context向量作为初始隐状态，生成目标序列。随着输入序列长度的增加，编码器难以将所有输入信息编码为单一context向量，编码信息缺失，难以完成高质量的解码。

注意力机制是在每个时刻解码时，基于当前时刻解码器的隐状态、输入或输出等信息，计算其对输入序列各位置隐状态的注意力（分数）并加权生成context向量用于当前时刻解码。引入注意力机制，使得不同时刻的解码能够关注不同位置的输入信息，提高预测准确性。

Bahdanau Attention Mechanism

Overall process for Bahdanau Attention seq2seq model

Bahdanau本质是一种 加性attention机制，将decoder的隐状态和encoder所有位置输出通过线性组合对齐，得到context向量，用于改善序列到序列的翻译模型

Bahdanau的特点为：

• 编码器隐状态 ：编码器对于每一个输入向量产生一个隐状态向量；
• 计算对齐分数：使用上一时刻的隐状态${\mathbf{s}}_{t-1}$和编码器每个位置输出${\mathbf{x}}_i$计算对齐分数（使用前馈神经网络计算），编码器最终时刻隐状态可作为解码器初始时刻隐状态；
• 概率化对齐分数：解码器上一时刻隐状态${\mathbf{s}}_{t-1}$在编码器每个位置输出的对齐分数，通过softmax转化为概率分布向量；
• 计算上下文向量：根据概率分布化的对齐分数，加权编码器各位置输出，得上下文向量${\mathbf{c}}_t$；
• 解码器输出：将上下文向量${\mathbf{c}}_t$和上一时刻编码器输出${\hat{y}}_{t-1}$对应的embedding拼接，作为当前时刻编码器输入，经RNN网络产生新的输出和隐状态，训练过程中有真实目标序列$\mathbf{y}=(y_1\cdots y_m)$，多使用$y_{t-1}$取代${\hat{y}}_{t-1}$作为解码器$t$时刻输入；

时刻$t$，解码器的隐状态表示为
$${\mathbf{s}}_t=f({\mathbf{s}}_{t-1},{\mathbf{c}}_t,y_{t-1})$$
时刻$t$的隐状态${\mathbf{s}}_{t-1}$对编码器各时刻输出$X$的注意力分数为：
$${\mathbf{\alpha }}_t({\mathbf{s}}_{t-1},X)=\text{softmax}(\tanh ({\mathbf{s}}_{t-1}{W}_{decoder}+X{W}_{encoder})W_{alignment}),{\mathbf{c}}_t=\sum _i{\alpha }_{ti}{\mathbf{x}}_i$$

使用Bahdanau注意力机制的解码过程：

Overall process for Bahdanau Attention seq2seq model

Tensorflow源码实现

def _bahdanau_score(processed_query, keys, attention_v):
    """Implements Bahdanau-style (additive) scoring function.
    Args:
      processed_query: Tensor, shape `[batch_size, num_units]` to compare to
        keys.
      keys: Processed memory, shape `[batch_size, max_time, num_units]`.
      attention_v: Tensor, shape `[num_units]`.

    Returns:
      A `[batch_size, max_time]` tensor of unnormalized score values.
    """
    # Reshape from [batch_size, ...] to [batch_size, 1, ...] for broadcasting.
    processed_query = tf.expand_dims(processed_query, 1)
    return tf.reduce_sum(attention_v * tf.tanh(keys + processed_query), [2])


def _calculate_attention(self, query, state):
    """Score the query based on the keys and values.

    Args:
      query: Tensor of dtype matching `self.values` and shape
        `[batch_size, query_depth]`.
      state: Tensor of dtype matching `self.values` and shape
        `[batch_size, alignments_size]`
        (`alignments_size` is memory's `max_time`).

    Returns:
      alignments: Tensor of dtype matching `self.values` and shape
        `[batch_size, alignments_size]` (`alignments_size` is memory's
        `max_time`).
      next_state: same as alignments.
    """
    processed_query = self.query_layer(query) if self.query_layer else query
    score = _bahdanau_score(
        processed_query,
        self.keys,
        self.attention_v,
    )
    alignments = self.probability_fn(score, state)
    next_state = alignments
    return alignments, next_state

Tensorflow自定义实现

# Bahdanau Attention
self.att_w1 = tf.keras.layers.Dense(self.dec_units)
self.att_w2 = tf.keras.layers.Dense(self.dec_units)
self.att_v = tf.keras.layers.Dense(1)

def bahdanau_attention(self, query, values):
    """Bahdanau Attention注意力机制
        query: shape=(batch_size, hidden_size), 解码器隐状态
        values: shape=(batch_size, seq_len, hidden_size)，编码器输出
        """
    query = tf.expand_dims(query, axis=1)
    # shape=(batch_size, seq_len, 1)
    score = self.att_v(tf.nn.tanh(self.att_w1(query) + self.att_w2(values)))
    weight = tf.nn.softmax(score, axis=1)
    # shape=(batch_size, hidden_size)
    context = tf.reduce_sum(weight * values, axis=1)
    return context, weight

Luong attention mechanism

Overall process for Luong Attention seq2seq model

Luong本质是一种 乘性attention机制，将解码器隐状态和编码器输出进行矩阵乘法，得到上下文向量。

Luong注意力机制是对Bahdanau注意力机制的改进，根据是否全部使用所有编码器输出分为两种：全局注意力和局部注意力，全局注意力适合用于短输入序列，局部注意力适合用于长输入序列（计算全局注意力代价高），以下内容仅介绍全局注意力。

Luong注意力机制与Bahdanau注意力机制的主要不同点：

• 对齐分数计算：使用当前时刻的隐状态${\mathbf{s}}_t$计算在编码器位置i输出的对齐分数；
• 解码器输出：解码器在$t$时刻，拼接上下文向量${\mathbf{c}}_t$和当前时刻隐状态${\mathbf{s}}_t$，经全连接层，产生当前时刻输出${\hat{y}}_{t+1}$，并作为下一时刻输入；
• 流程图当前时刻计算的context向量，会被应用到下一时刻的输入？？？

Luong注意力的三种计算方法：

Tensorflow源码实现

def _calculate_attention(self, query, state):
	"""Score the query based on the keys and values.

	Args:
	  query: Tensor of dtype matching `self.values` and shape
		`[batch_size, query_depth]`.
	  state: Tensor of dtype matching `self.values` and shape
		`[batch_size, alignments_size]`
		(`alignments_size` is memory's `max_time`).

	Returns:
	  alignments: Tensor of dtype matching `self.values` and shape
		`[batch_size, alignments_size]` (`alignments_size` is memory's
		`max_time`).
	  next_state: Same as the alignments.
	"""
	score = _luong_score(query, self.keys, self.scale_weight)
	alignments = self.probability_fn(score, state)
	next_state = alignments
	return alignments, next_state


def _luong_score(query, keys, scale):
    """Implements Luong-style (multiplicative) scoring function.

    To enable the second form, call this function with `scale=True`.

    Args:
      query: Tensor, shape `[batch_size, num_units]` to compare to keys.
      keys: Processed memory, shape `[batch_size, max_time, num_units]`.
      scale: the optional tensor to scale the attention score.

    Returns:
      A `[batch_size, max_time]` tensor of unnormalized score values.

    Raises:
      ValueError: If `key` and `query` depths do not match.
    """
    # Reshape from [batch_size, depth] to [batch_size, 1, depth]
    query = tf.expand_dims(query, 1)

    score = tf.matmul(query, keys, transpose_b=True)
    score = tf.squeeze(score, [1])
	
    if scale is not None:
        score = scale * score
    return score

Differences between Bahdanau and Luong attention mechanism

I. context的计算方式不同

解码器在第t步，Bahdanau注意力机制使用decoder第t-1步的隐状态${\mathbf{s}}_{t-1}$与encoder的各位置的输出${\overline{\mathbf{s}}}_i$加权得到${\mathbf{c}}_t$，而Luong注意力机制使用decoder当前时刻的隐状态${\mathbf{s}}_t$与encoder的每一个隐状态${\overline{\mathbf{s}}}_i$加权得到${\mathbf{c}}_t$。

II. decoder的输入输出不同

解码器在第t步，Bahdanau注意力机制将前一时刻隐状态${\mathbf{s}}_{t-1}$与${\mathbf{c}}_t$拼接作为decoder输入，经RNN运算得到${\mathbf{s}}_t$，并直接输出${\hat{y}}_{t+1}$；Luong注意力机制将当前时刻隐状态${\mathbf{s}}_t$与${\mathbf{c}}_t$拼接，并通过全连接网络输出${\hat{y}}_{t+1}$，Luong注意力机制只处理最顶层！！！

解码器t时刻输出是$o_t$，由于其是下一时刻输出，所以多记作${\hat{y}}_{t+1}$。

III. 总结

Bahdanau的计算流程为${\mathbf{s}}_{t-1}\to {\mathbf{a}}_t\to {\mathbf{c}}_t\to {\mathbf{s}}_t$，而Luong的计算流程为${\mathbf{s}}_t\to {\mathbf{a}}_t\to {\mathbf{c}}_t\to {\tilde{\mathbf{s}}}_t$。

Reference

1. Attention: Sequence 2 Sequence model with Attention Mechanism
2. NEURAL MACHINE TRANSLATION BY JOINTLY LEARNING TO ALIGN AND TRANSLATE
3. Effective Approaches to Attention-based Neural Machine Translation
4. Attention Mechanism