深入理解推荐系统：微软xDeepFM原理与实践

import tensorflow as tf

B = 2
D = 3
m = 2
H = 2 ## 理解为 H_{k-1}
a = tf.reshape(tf.range(B * D * m, dtype=tf.float32),
              (B, m, D))
b = tf.split(a, D * [1], 2)
c = tf.matmul(b, b, transpose_b=True)

with tf.Session() as sess:
    print(sess.run(tf.shape(c))) ## shape 为 [D, B, m, H_{k-1}]

import tensorflow as tf

B = 2
D = 3
E = 4  ## 代表 m * H_{k-1}
F = 5  ## 代表 H_{k}
a = tf.reshape(tf.range(B * D * E, dtype=tf.float32),
              (B, D, E))
b = tf.reshape(tf.range(1 * E * F, dtype=tf.float32),
              (1, E, F))
curr_out = tf.nn.conv1d(
    a, filters=b, stride=1, padding='VALID')

with tf.Session() as sess:
    print(sess.run(tf.shape(curr_out))) ## 结果为 [B, D, H_{k}]

class CIN(Layer):
    """Compressed Interaction Network used in xDeepFM.This implemention is
    adapted from code that the author of the paper published on https://github.com/Leavingseason/xDeepFM.
      Input shape
        - 3D tensor with shape: ``(batch_size,field_size,embedding_size)``.
      Output shape
        - 2D tensor with shape: ``(batch_size, featuremap_num)`` ``featuremap_num =  sum(self.layer_size[:-1]) // 2 + self.layer_size[-1]`` if ``split_half=True``,else  ``sum(layer_size)`` .
      Arguments
        - **layer_size** : list of int.Feature maps in each layer.
        - **activation** : activation function used on feature maps.
        - **split_half** : bool.if set to False, half of the feature maps in each hidden will connect to output unit.
        - **seed** : A Python integer to use as random seed.
      References
        - [Lian J, Zhou X, Zhang F, et al. xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systems[J]. arXiv preprint arXiv:1803.05170, 2018.] (https://arxiv.org/pdf/1803.05170.pdf)
    """

    def __init__(self, layer_size=(128, 128), activation='relu', split_half=True, l2_reg=1e-5, seed=1024, **kwargs):
        if len(layer_size) == 0:
            raise ValueError(
                "layer_size must be a list(tuple) of length greater than 1")
        self.layer_size = layer_size
        self.split_half = split_half
        self.activation = activation
        self.l2_reg = l2_reg
        self.seed = seed
        super(CIN, self).__init__(**kwargs)

    def build(self, input_shape):
        if len(input_shape) != 3:
            raise ValueError(
                "Unexpected inputs dimensions %d, expect to be 3 dimensions" % (len(input_shape)))

        self.field_nums = [int(input_shape[1])]
        self.filters = []
        self.bias = []
        for i, size in enumerate(self.layer_size):
   
   ## layer_size 对应着论文中的 H_{k}, 表示 CIN 每层中 feature map 的个数
   ## self.filters[i] 的 shape 为 [1, m * H_{k-1}, H_{k}]
            self.filters.append(
             self.add_weight(name='filter' + str(i),
                                shape=[1, self.field_nums[-1] * self.field_nums[0], size],
        dtype=tf.float32, initializer=glorot_uniform(seed=self.seed + i),
                                regularizer=l2(self.l2_reg)))
   ## self.bias[i] 的 shape 为 [H_{k}]
            self.bias.append(
             self.add_weight(name='bias' + str(i), 
                 shape=[size], dtype=tf.float32,
                                initializer=tf.keras.initializers.Zeros()))

            if self.split_half:
                if i != len(self.layer_size) - 1 and size % 2 > 0:
                    raise ValueError(
                        "layer_size must be even number except for the last layer when split_half=True")

                self.field_nums.append(size // 2)
            else:
                self.field_nums.append(size)

        self.activation_layers = [activation_layer(
            self.activation) for _ in self.layer_size]

        super(CIN, self).build(input_shape)  # Be sure to call this somewhere!

    def call(self, inputs, **kwargs):
  ## inputs 的 shape 为 [B, m, D], 其中 m 为 Field 的数量,
  ## D 为 embedding size, 我注释的符号尽量和论文中的一样
        if K.ndim(inputs) != 3:
            raise ValueError(
                "Unexpected inputs dimensions %d, expect to be 3 dimensions" % (K.ndim(inputs)))

        dim = int(inputs.get_shape()[-1]) # D
        hidden_nn_layers = [inputs]
        final_result = []
  
  ## split_tensor0 表示 list: [x1, x2, ..., xD], 其中 xi 的 shape 为 [B, m, 1]
        split_tensor0 = tf.split(hidden_nn_layers[0], dim * [1], 2)
        for idx, layer_size in enumerate(self.layer_size):
         ## split_tensor 表示 list: [t1, t2, ..., tH_{k-1}], 即有 H_{k-1} 个向量;
         ## 其中 ti 的 shape 为 [B, H_{k-1}, 1]
            split_tensor = tf.split(hidden_nn_layers[-1], dim * [1], 2)
   
   ## dot_result_m 为一个 tensor, 其 shape 为 [D, B, m, H_{k-1}]
            dot_result_m = tf.matmul(
                split_tensor0, split_tensor, transpose_b=True)

   ## dot_result_o 的 shape 为 [D, B, m * H_{k-1}]
            dot_result_o = tf.reshape(
                dot_result_m, shape=[dim, -1, self.field_nums[0] * self.field_nums[idx]])
   
   ## dot_result 的 shape 为 [B, D, m * H_{k-1}]
            dot_result = tf.transpose(dot_result_o, perm=[1, 0, 2])
   
   ## 牛掰啊, 还可以这样写, 精彩!
   ## self.filters[idx] 的 shape 为 [1, m * H_{k-1}, H_{k}]
   ## 因此 curr_out 的 shape 为 [B, D, H_{k}]
            curr_out = tf.nn.conv1d(
                dot_result, filters=self.filters[idx], stride=1, padding='VALID')
   
   ## self.bias[idx] 的 shape 为 [H_{k}]
   ## 因此 curr_out 的 shape 为 [B, D, H_{k}]
            curr_out = tf.nn.bias_add(curr_out, self.bias[idx])
   
   ## curr_out 的 shape 为 [B, D, H_{k}]
            curr_out = self.activation_layers[idx](curr_out)
   
   ## curr_out 的 shape 为 [B, H_{k}, D]
            curr_out = tf.transpose(curr_out, perm=[0, 2, 1])
   
            if self.split_half:
                if idx != len(self.layer_size) - 1:
                    next_hidden, direct_connect = tf.split(
                        curr_out, 2 * [layer_size // 2], 1)
                else:
                    direct_connect = curr_out
                    next_hidden = 0
            else:
                direct_connect = curr_out
                next_hidden = curr_out

            final_result.append(direct_connect)
            hidden_nn_layers.append(next_hidden)
  
  ## 先假设不走 self.split_half 的逻辑, 此时 result 的
  ## shape 为 [B, sum(H_{k}), D] (k=1 -> T, T 为 CIN 的总层数)
        result = tf.concat(final_result, axis=1)
        ## result 最终的 shape 为 [B, sum(H_{k})]
        result = reduce_sum(result, -1, keep_dims=False)

        return result