在多变量时序预测任务中，如何利用多头注意力机制计算各变量之间的相关系

在多变量时序预测任务中，如何利用多头注意力机制求得各变量之间的相关系？
例如输入为：（100,4,12）其中12为多个变量，我想计算变量之间的相关性，下面代码好像是计算时间步之间的相关性，求各位指点指点哇

class MultiHeadSelfAttention(Layer):
    def __init__(self, embed_dim, num_heads):
        super(MultiHeadSelfAttention, self).__init__()

        self.embed_dim = embed_dim
        self.num_heads = num_heads
        if embed_dim % num_heads != 0:
            raise ValueError(
                f"embedding dimension = {embed_dim} should be divisible by number of heads = {num_heads}"
            )

        self.projection_dim = embed_dim // num_heads
        self.query_dense = Dense(embed_dim)
        self.key_dense = Dense(embed_dim)
        self.value_dense = Dense(embed_dim)
        self.output_dense = Dense(embed_dim)
        # self.attention=MultiHeadAttention()

    def attention(self, query, key, value):
        score = tf.matmul(query, key, transpose_b=True)
        dim_key = tf.cast(tf.shape(key)[-1], tf.float32)
        scaled_score = score / tf.math.sqrt(dim_key)
        weights = tf.nn.softmax(scaled_score, axis=-1)
        out = tf.matmul(weights, value)
        return out, weights

    def separate_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.projection_dim))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def call(self, inputs):
        # x.shape = [batch_size, seq_len, embedding_dim]
        batch_size = tf.shape(inputs)[0]

        # Query
        # Dense layer to project and split embed_dim to num_heads*projection_dim
        query = self.query_dense(inputs)  # (batch_size, seq_len, embed_dim)
        query = self.separate_heads(
            query, batch_size
        )  # (batch_size, num_heads, seq_len, projection_dim)

        # Key
        # Dense layer to project and split embed_dim to num_heads*projection_dim
        key = self.key_dense(inputs)  # (batch_size, seq_len, embed_dim)
        key = self.separate_heads(
            key, batch_size
        )  # (batch_size, num_heads, seq_len, projection_dim)

        # Value
        # Dense layer to project and split embed_dim to num_heads*projection_dim
        value = self.value_dense(inputs)  # (batch_size, seq_len, embed_dim)
        value = self.separate_heads(
            value, batch_size
        )  # (batch_size, num_heads, seq_len, projection_dim)

        # Attention
        attention, weigths = self.attention(query, key, value)
        attention = tf.transpose(
            attention, perm=[0, 2, 1, 3]
        )  # (batch_size, seq_len, num_heads, projection_dim)

        # Combine back to num_heads*projection_dim
        concat_attention = tf.reshape(
            attention, (batch_size, -1, self.embed_dim)
        )  # (batch_size, seq_len, embed_dim)

        # Apply a final Dense layer
        out = self.output_dense(
            concat_attention
        )  # (batch_size, seq_len, embed_dim)
        return out

引用new bing作答：
在多变量时序预测任务中，利用多头注意力机制求得各变量之间的相关系数，需要对输入的数据进行一些处理和调整。假设输入数据的维度为(batch_size, seq_len, num_variables)，其中num_variables为变量的数量。具体的步骤如下：

1 将输入的数据进行转置，使得变量的数量成为第二个维度，即新的维度为(batch_size, num_variables, seq_len)。

2 将转置后的数据输入到多头注意力机制中，通过query, key和value的计算，可以得到注意力矩阵，注意力矩阵的维度为(batch_size, num_heads, seq_len, seq_len)，其中seq_len为序列的长度，num_heads为注意力头的数量。

3 将注意力矩阵进行汇总，得到每个时间步与其他时间步的相关系数，具体的计算方法为将每个头的注意力矩阵相加并除以num_heads，得到的维度为(batch_size, seq_len, seq_len)。

4 最后，将相关系数矩阵进行转置，使得变量的数量成为第一个维度，即新的维度为(batch_size, num_variables, num_variables)，即可得到各变量之间的相关系数矩阵。

下面是代码实现：

class MultiHeadAttention(Layer):
    def __init__(self, embed_dim, num_heads):
        super(MultiHeadAttention, self).__init__()
        self.embed_dim = embed_dim
        self.num_heads = num_heads
        if embed_dim % num_heads != 0:
            raise ValueError(
                f"embedding dimension = {embed_dim} should be divisible by number of heads = {num_heads}"
            )

        self.projection_dim = embed_dim // num_heads
        self.query_dense = Dense(embed_dim)
        self.key_dense = Dense(embed_dim)
        self.value_dense = Dense(embed_dim)
        self.output_dense = Dense(embed_dim)

    def attention(self, query, key, value):
        score = tf.matmul(query, key, transpose_b=True)
        dim_key = tf.cast(tf.shape(key)[-1], tf.float32)
        scaled_score = score / tf.math.sqrt(dim_key)
        weights = tf.nn.softmax(scaled_score, axis=-1)
        out = tf.matmul(weights, value)
        return out, weights

    def separate_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.projection_dim))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def call(self, inputs):
        # x.shape = [batch_size, seq_len, num_variables]
        batch_size = tf.shape(inputs)[0]

        # Transpose inputs to (batch_size, num_variables, seq_len)
        inputs = tf.transpose(inputs, perm=[0, 2, 1])

        # Query
        query = self.query_dense(inputs)
        query = self.separate_heads(query, batch_size)

        # Key
        key = self.key_dense(inputs)
        key = self.separate_heads(key, batch_size)

        # Value
        value = self.value_dense(inputs)
        value = self.separate_heads(value, batch_size)

        # Attention
        query_attention, weights = self.attention(query, key, value)

        # Concatenate heads
        query_attention = tf.transpose(query_attention, perm=[0, 2, 1, 3])
        concat_attention = tf.reshape(query_attention, (batch_size, -1, self.embed_dim))

        # Output
        output = self.output_dense(concat_attention)

        return output

最后输出的张量形状为 [batch_size, seq_len, embed_dim]，其中 embed_dim 是指输入张量中每个时间步的特征维度。如果需要对时间步进行汇总，可以对第二维进行相应的汇聚操作。

该回答引用于ChatGPT：
对于多变量时序预测任务中，可以使用多头注意力机制来计算不同变量之间的相关性。下面介绍一种利用多头注意力机制求得各变量之间的相关系数的方法：

首先，对于输入的数据，将每个时间步的变量按照最后一个维度进行拆分，得到 shape 为 (batch_size, num_vars, seq_len) 的张量。

然后，将该张量通过一个全连接层，得到 shape 为 (batch_size, num_vars, embed_dim) 的张量。

接着，将这个张量传入一个多头注意力机制层，注意力头数可以自己设置。多头注意力机制层的输出为 shape 为 (batch_size, num_vars, embed_dim) 的张量。

最后，对于每个时间步，分别计算不同变量之间的相关系数，可以通过计算对应时间步的多头注意力机制层输出的张量和该张量的转置的乘积。得到 shape 为 (batch_size, num_vars, num_vars) 的相关系数矩阵。

下面是相应的 Python 代码实现：

class MultiHeadAttention(Layer):
    def __init__(self, embed_dim, num_heads):
        super(MultiHeadAttention, self).__init__()

        self.embed_dim = embed_dim
        self.num_heads = num_heads
        if embed_dim % num_heads != 0:
            raise ValueError(
                f"embedding dimension = {embed_dim} should be divisible by number of heads = {num_heads}"
            )

        self.projection_dim = embed_dim // num_heads
        self.query_dense = Dense(embed_dim)
        self.key_dense = Dense(embed_dim)
        self.value_dense = Dense(embed_dim)
        self.output_dense = Dense(embed_dim)

    def call(self, inputs):
        # inputs.shape = [batch_size, num_vars, seq_len]
        batch_size = tf.shape(inputs)[0]

        # Project to embedding space
        x = self.query_dense(inputs)  # (batch_size, num_vars, seq_len, embed_dim)
        y = self.key_dense(inputs)  # (batch_size, num_vars, seq_len, embed_dim)
        z = self.value_dense(inputs)  # (batch_size, num_vars, seq_len, embed_dim)

        # Split embedding space to multiple heads
        x = tf.reshape(x, [batch_size, -1, self.num_heads, self.projection_dim])
        y = tf.reshape(y, [batch_size, -1, self.num_heads, self.projection_dim])
        z = tf.reshape(z, [batch_size, -1, self.num_heads, self.projection_dim])

        # Transpose for attention dot product
        x = tf.transpose(x, [0, 2, 1, 3])
        y = tf.transpose(y, [0, 2, 1, 3])
        z = tf.transpose(z, [0, 2, 1, 3])

        # Attention weights calculation
        query_key_dot_product = tf.matmul(x, y, transpose_b=True)
        scaled_query_key_dot_product = query_key_dot_product / (self.embed_dim ** 0.5)
        attention_weights = tf.nn.softmax(scaled_query_key_dot_product, axis=-1)

        # Attention output calculation
        attention_output = tf.matmul(attention_weights, z)

        # Reshape to original shape
        attention_output = tf.transpose(attention_output, [0, 2, 1, 3])
        attention_output = tf.reshape(attention_output, [batch_size, -1, self.embed_dim])

        # Project to output embedding space
        attention_output = self.output_dense(attention_output)

        return attention_output


class MultiHeadAttentionWithCorrelation(Layer):
    def __init__(self, embed_dim, num_heads):
        super(MultiHeadAttentionWithCorrelation, self).__init__()

        self.multi_head_attention = MultiHeadAttention(embed_dim, num_heads)

    def correlation(self, x, y):
        # x.shape = y.shape = (batch_size, num_vars, embed_dim)
        mean_x = tf.reduce_mean(x, axis=1, keepdims=True)  # (batch_size, 1, embed_dim)
        mean_y = tf.reduce_mean(y, axis=1, keepdims=True)  # (batch_size, 1, embed_dim)
        diff_x = x - mean_x  # (batch_size, num_vars, embed_dim)
        diff_y = y - mean_y  # (batch_size, num_vars, embed_dim)
        corr = tf.matmul(diff_x, diff_y, transpose_a=True) / (tf.norm(diff_x, axis=-1) * tf.norm(diff_y, axis=-1))
        return corr

    def call(self, inputs):
        # inputs.shape = [batch_size, num_vars, seq_len]
        batch_size = tf.shape(inputs)[0]

        # Multi-head attention
        attn_output = self.multi_head_attention(inputs)  # (batch_size, num_vars, embed_dim)

        # Correlation between variables
        attn_output_transpose = tf.transpose(attn_output, [0, 2, 1])  # (batch_size, embed_dim, num_vars)
        attn_output_corr = tf.map_fn(lambda x: self.correlation(x, x), attn_output_transpose)  # (batch_size, num_vars, num_vars)

        return attn_output_corr

该代码实现了一个 MultiHeadAttentionWithCorrelation 类，该类包含了一个多头注意力机制层和一个计算变量相关系数的方法，输入为 shape 为 (batch_size, num_vars, seq_len) 的张量，输出为 shape 为 (batch_size, num_vars, num_vars) 的相关系数矩阵。可以根据实际需要修改超参数 embed_dim 和 num_heads。

该回答引用ChatGPT
在多变量时序预测任务中，可以采用Multi-Head Attention机制来计算各变量之间的相关性。Multi-Head Attention是一种Attention机制的变体，通过将输入表示线性映射到多个子空间来计算多组注意力，每组注意力关注不同的上下文信息，并将这些注意力结果拼接起来形成最终的输出表示。具体实现如下：

python
class MultiHeadAttention(Layer):
    def __init__(self, num_heads, d_model, dropout=0.1):
        super(MultiHeadAttention, self).__init__()
        self.num_heads = num_heads
        self.d_model = d_model
        self.depth = d_model // num_heads

        self.query_dense = Dense(d_model)
        self.key_dense = Dense(d_model)
        self.value_dense = Dense(d_model)

        self.dropout = Dropout(dropout)
        self.final_dense = Dense(d_model)

    def split_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.depth))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def call(self, inputs):
        query, key, value, mask = inputs['query'], inputs['key'], inputs['value'], inputs['mask']
        batch_size = tf.shape(query)[0]

        query = self.query_dense(query)  # (batch_size, seq_len, d_model)
        key = self.key_dense(key)  # (batch_size, seq_len, d_model)
        value = self.value_dense(value)  # (batch_size, seq_len, d_model)

        query = self.split_heads(query, batch_size)  # (batch_size, num_heads, seq_len, depth)
        key = self.split_heads(key, batch_size)  # (batch_size, num_heads, seq_len, depth)
        value = self.split_heads(value, batch_size)  # (batch_size, num_heads, seq_len, depth)

        scaled_attention, attention_weights = self.scaled_dot_product_attention(query, key, value, mask)
        scaled_attention = tf.transpose(scaled_attention, perm=[0, 2, 1, 3])  # (batch_size, seq_len, num_heads, depth)

        concat_attention = tf.reshape(scaled_attention, (batch_size, -1, self.d_model))  # (batch_size, seq_len, d_model)

        output = self.final_dense(concat_attention)  # (batch_size, seq_len, d_model)
        return output

    def scaled_dot_product_attention(self, query, key, value, mask):
        matmul_qk = tf.matmul(query, key, transpose_b=True)
        depth = tf.cast(tf.shape(key)[-1], tf.float32)
        logits = matmul_qk / tf.math.sqrt(depth)

        if mask is not None:
            logits += (mask * -1e9)

        attention_weights = tf.nn.softmax(logits, axis=-1)

        if self.dropout is not None:
            attention_weights = self.dropout(attention_weights)

        output = tf.matmul(attention_weights, value)
        return output, attention_weights

其中，`query`、`key`和`value`分别是输入的查询、键和值向量，`num_heads`表示头的数量，`d_model`表示模型的维度。在实现中，首先将`query`、`key`和`value`分别进行线性映射，然后将结果分别在最后一维分割成`num_heads`份，并分别进行转置，形成`(batch_size, num_heads, seq_len, depth)`的张量。接着，利用缩放点积注意力机制求出每份注意力，将它们进行拼接，最后再次进行线性映射得到最终输出。在具体应用中，需要针对多变量时序数据进行适当调整，具体实现可参考以下代码：

python
class MultiVarMultiHeadAttention(Layer):
    def __init__(self, num_heads, d_model, num_vars, dropout=0.1):
        super(MultiVarMultiHeadAttention, self).__init__()
        self.num_heads = num_heads
        self.d_model = d_model
        self.depth = d_model // num_heads
        self.num_vars = num_vars

        self.query_dense = Dense(d_model * num_vars)
        self.key_dense = Dense(d_model * num_vars)
        self.value_dense = Dense(d_model * num_vars)

        self.dropout = Dropout(dropout)
        self.final_dense = Dense(d_model)

    def split_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, self.num_vars, -1, self.num_heads, self.depth))
        return tf.transpose(x, perm=[0, 1, 3, 2, 4])

    def call(self, inputs):
        query, key, value, mask = inputs['query'], inputs['key'], inputs['value'], inputs['mask']
        batch_size = tf.shape(query)[0]

        query = self.query_dense(query)  # (batch_size, num_vars*seq_len, d_model)
        key = self.key_dense(key)  # (batch_size, num_vars*seq_len, d_model)
        value = self.value_dense(value)  # (batch_size, num_vars*seq_len, d_model)

        query = self.split_heads(query, batch_size)  # (batch_size, num_vars, num_heads, seq_len, depth)
        key = self.split_heads(key, batch_size)  # (batch_size, num_vars, num_heads, seq_len, depth)
        value = self.split_heads(value, batch_size)  # (batch_size, num_vars, num_heads, seq_len, depth)

        scaled_attention, attention_weights = self.scaled_dot_product_attention(query, key, value, mask)
        scaled_attention = tf.transpose(scaled_attention, perm=[0, 1, 3, 2, 4])  # (batch_size, num_vars, seq_len, num_heads, depth)

        concat_attention = tf.reshape(scaled_attention, (batch_size, -1, self.d_model * self.num_vars))  # (batch_size, seq_len*num_vars, d_model)

        output = self.final_dense(concat_attention)  # (batch_size, num_vars, seq_len, d_model)
        return output

    def scaled_dot_product_attention(self, query, key, value, mask):
        matmul_qk = tf.matmul(query, key, transpose_b=True)
        depth = tf.cast(tf.shape(key)[-1], tf.float32)
        logits = matmul_qk / tf.math.sqrt(depth)

        if mask is not None:
            logits += (mask * -1e9)

        attention_weights = tf.nn.softmax(logits, axis=-1)

        if self.dropout is not None:
            attention_weights = self.dropout(attention_weights)

        output = tf.matmul(attention_weights, value)
        return output, attention_weights

该实现中，`num_vars`表示数据中有多少个变量。在计算注意力时，先将`query`、`key`和`value`分别进行线性映射，然后将它们在第一维（即变量维）分割成`num_vars`份，再在最后一维分割成`num_heads`份，并分别进行转置，形成`(batch_size, num_vars, num_heads, seq_len, depth)`的张量。接着，利用缩放点积注意力机制求出每份注意力，将它们进行拼接，最后再次进行线性映射得到最终输出。注意，本实现中没有计算时间步之间的相关性。如果需要计算时间步之间的相关性，可以使用下面这段代码：

python
class TemporalAttention(Layer):
    def __init__(self, d_model, num_heads, dropout=0.1):
        super(TemporalAttention, self).__init__()
        self.num_heads = num_heads
        self.d_model = d_model
        self.depth = d_model // num_heads

        self.query_dense = Dense(d_model)
        self.key_dense = Dense(d_model)
        self.value_dense = Dense(d_model)

        self.dropout = Dropout(dropout)
        self.final_dense = Dense(d_model)

    def split_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.depth))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def call(self, x):
        query = key = value = x
        batch_size, seq_len, d_model = tf.shape(x)[0], tf.shape(x)[1], tf.shape(x)[2]

        query = self.query_dense(query)  # (batch_size, seq_len, d_model)
        key = self.key_dense(key)  # (batch_size, seq_len, d_model)
        value = self.value_dense(value)  # (batch_size, seq_len, d_model)

        query = self.split_heads(query, batch_size)  # (batch_size, num_heads, seq_len, depth)
        key = self.split_heads(key, batch_size)  # (batch_size, num_heads, seq_len, depth)
        value = self.split_heads(value, batch_size)  # (batch_size, num_heads, seq_len, depth)

        scaled_attention, attention_weights = self.scaled_dot_product_attention(query, key, value, None)
        scaled_attention = tf.transpose(scaled_attention, perm=[0, 2, 1, 3])  # (batch_size, seq_len, num_heads, depth)

        concat_attention = tf.reshape(scaled_attention, (batch_size, seq_len, -1))  # (batch_size, seq_len, num_heads * depth)

        output = self.final_dense(concat_attention)  # (batch_size, seq_len, d_model)
        return output

    def scaled_dot_product_attention(self, query, key, value, mask):
        matmul_qk = tf.matmul(query, key, transpose_b=True)
        depth = tf.cast(tf.shape(key)[-1], tf.float32)
        logits = matmul_qk / tf.math.sqrt(depth)

        if mask is not None:
            logits += (mask * -1e9)

        attention_weights = tf.nn.softmax(logits, axis=-1)

        if self.dropout is not None:
            attention_weights = self.dropout(attention_weights)

        output = tf.matmul(attention_weights, value)
        return output, attention_weights

该实现中，直接将输入`x`分别作为`query`、`key`和`value`的输入，形成`(batch_size, seq_len, d_model)`的张量。然后将它们在最后一维分割成`num_heads`份，并分别进行转置，形成`(batch_size, num_heads, seq_len, depth)`的张量。接着，利用缩放点积注意力机制求出每份注意力，将它们进行拼接，最后再次进行线性映射得到最终输出。该回答引用ChatGPT
在多变量时序预测任务中，可以利用多头注意力机制计算各变量之间的相关系数。例如，我们可以输入一个形状为(batch_size, seq_len, num_vars)的张量，其中num_vars是各变量的数量，seq_len是时间步数，batch_size是批处理大小。

首先，我们可以通过查询、键和值的全连接层将输入张量从embed_dim维变换到num_heads x projection_dim维，其中projection_dim是embed_dim除以num_heads。我们可以将这三个张量变形成形状为(batch_size, num_heads, seq_len, projection_dim)的张量，并沿着num_heads轴进行提取和重组。

对于每个时间步和每对变量，我们可以计算一个分数。这个分数可以通过对查询张量和键张量执行矩阵乘积获得。将得分除以sqrt(projection_dim)，以控制梯度大小，然后在最后一个轴上进行softmax。最后，我们通过对值张量执行加权平均来获得该时间步的输出向量。

将每个时间步的输出张量组合成形状为(batch_size, seq_len, num_heads x projection_dim)的张量。通过另一个全连接层，我们将输出张量从num_heads x projection_dim维变换回embed_dim维，从而生成最终的输出张量。

下面是一个多头自注意力层的示例代码，它能够计算一个形状为(batch_size, seq_len, num_vars)的张量中各变量之间的相关性：

python
class MultiHeadAttention(Layer):
    def __init__(self, embed_dim, num_heads):
        super(MultiHeadAttention, self).__init__()

        self.embed_dim = embed_dim
        self.num_heads = num_heads
        if embed_dim % num_heads != 0:
            raise ValueError(
                f"embedding dimension = {embed_dim} should be divisible by number of heads = {num_heads}"
            )

        self.projection_dim = embed_dim // num_heads
        self.query_dense = Dense(embed_dim)
        self.key_dense = Dense(embed_dim)
        self.value_dense = Dense(embed_dim)
        self.output_dense = Dense(embed_dim)

    def call(self, inputs):
        # split the input tensor into num_vars tensors along last axis
        input_list = tf.unstack(inputs, axis=-1)

        # build a list of outputs from each input variable 
        output_list = []
        for i, input_var in enumerate(input_list):
            # Query
            query = self.query_dense(input_var)  # (batch_size, seq_len, embed_dim)
            query = self.separate_heads(query, batch_size)  # (batch_size, num_heads, seq_len, projection_dim)

            # Key
            key = self.key_dense(inputs)  # (batch_size, seq_len, embed_dim)
            key = self.separate_heads(key, batch_size)  # (batch_size, num_heads, seq_len, projection_dim)

            # Value
            value = self.value_dense(inputs)  # (batch_size, seq_len, embed_dim)
            value = self.separate_heads(value, batch_size)  # (batch_size, num_heads, seq_len, projection_dim)

            # Attention
            attention, weights = self.attention(query, key, value)
            attention = tf.transpose(
                attention, perm=[0, 2, 1, 3]
            )  # (batch_size, seq_len, num_heads, projection_dim)

            # Combine back to num_heads*projection_dim
            concat_attention = tf.reshape(
                attention, (batch_size, -1, self.embed_dim)
            )  # (batch_size, seq_len, embed_dim)

            # Apply a final Dense layer
            out = self.output_dense(
                concat_attention
            )  # (batch_size, seq_len, embed_dim)
            output_list.append(out)

        # combine output for each variable back into a single tensor
        outputs = tf.stack(output_list, axis=-1)       

        return outputs

    def separate_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.projection_dim))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def attention(self, query, key, value):
        score = tf.matmul(query, key, transpose_b=True)
        dim_key = tf.cast(tf.shape(key)[-1], tf.float32)
        scaled_score = score / tf.math.sqrt(dim_key)
        weights = tf.nn.softmax(scaled_score, axis=-1)
        out = tf.matmul(weights, value)
        return out, weights

请注意，我们需要先将输入张量拆分成num_vars个张量，然后分别计算每个变量的输出。最后，我们将分别计算出的所有输出张量组合成一个形状为(batch_size, seq_len, num_vars)的输出张量，其中最后一维是所有变量的相关性。

以下答案由GPT-3.5大模型与博主波罗歌共同编写：
在多变量时序预测任务中，可以利用多头注意力机制计算各变量之间的相关性。具体做法是将各个输入变量拆分成多个头，在这些头上计算注意力，然后将不同头的输出拼接起来。例如，在输入为（100，4，12）的情况下，可以将每个时间步上的每个变量拆分为多个头，进行注意力计算，最终将不同头的输出拼接起来。这样可以得到一个维度为（100，4，12）的输出张量，其中每个时间步上的每个变量都能够包含其他变量的信息。

以下是基于TensorFlow2的代码实现：

import tensorflow as tf
from tensorflow.keras.layers import Dense, Layer

class MultiHeadAttention(Layer):
    def __init__(self, embed_dim, num_heads):
        super(MultiHeadAttention, self).__init__()

        self.embed_dim = embed_dim
        self.num_heads = num_heads
        if embed_dim % num_heads != 0:
            raise ValueError(
                f"embedding dimension = {embed_dim} should be divisible by number of heads = {num_heads}"已黑化的小白             )

        self.projection_dim = embed_dim // num_heads
        self.query_dense = Dense(embed_dim)
        self.key_dense = Dense(embed_dim)
        self.value_dense = Dense(embed_dim)
        self.output_dense = Dense(embed_dim)

    def attention(self, query, key, value):
        score = tf.matmul(query, key, transpose_b=True)
        dim_key = tf.cast(tf.shape(key)[-1], tf.float32)
        scaled_score = score / tf.math.sqrt(dim_key)
        weights = tf.nn.softmax(scaled_score, axis=-1)
        out = tf.matmul(weights, value)
        return out, weights

    def separate_heads(self, x, batch_size):
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.projection_dim))
        return tf.transpose(x, perm=[0, 2, 1, 3])

    def call(self, inputs):
        batch_size = tf.shape(inputs)[0]

        # Split inputs into different heads
        inputs = tf.reshape(inputs, (batch_size, -1, self.num_heads, self.embed_dim//self.num_heads))

        # Query
        query = self.query_dense(inputs)
        query = self.separate_heads(query, batch_size)

        # Key
        key = self.key_dense(inputs)
        key = self.separate_heads(key, batch_size)

        # Value
        value = self.value_dense(inputs)
        value = self.separate_heads(value, batch_size)

        # Attention
        attention, weights = self.attention(query, key, value)

        # Merge attention outputs
        attention = tf.transpose(attention, perm=[0, 2, 1, 3])
        concat_attention = tf.reshape(attention, (batch_size, -1, self.embed_dim))

        # Apply final dense layer
        out = self.output_dense(concat_attention)

        return out

其中，输入张量inputs的维度为（batch_size，time_steps，features），其中features指输入变量的数量，time_steps为时间步。在MultiHeadAttention类中，通过将输入拆分为多个头来计算注意力，注意力计算的具体实现在attention函数中。最终，所有头的输出通过拼接来得到最终输出张量out。
如果我的回答解决了您的问题，请采纳！