与BatchNormalization层关联的参数数量是多少？

Question

我有以下代码。

x = keras.layers.Input(batch_shape = (None, 4096))
hidden = keras.layers.Dense(512, activation = 'relu')(x)
hidden = keras.layers.BatchNormalization()(hidden)
hidden = keras.layers.Dropout(0.5)(hidden)
predictions = keras.layers.Dense(80, activation = 'sigmoid')(hidden)
mlp_model = keras.models.Model(input = [x], output = [predictions])
mlp_model.summary()

这是模型摘要：

____________________________________________________________________________________________________
Layer (type)                     Output Shape          Param #     Connected to                     
====================================================================================================
input_3 (InputLayer)             (None, 4096)          0                                            
____________________________________________________________________________________________________
dense_1 (Dense)                  (None, 512)           2097664     input_3[0][0]                    
____________________________________________________________________________________________________
batchnormalization_1 (BatchNorma (None, 512)           2048        dense_1[0][0]                    
____________________________________________________________________________________________________
dropout_1 (Dropout)              (None, 512)           0           batchnormalization_1[0][0]       
____________________________________________________________________________________________________
dense_2 (Dense)                  (None, 80)            41040       dropout_1[0][0]                  
====================================================================================================
Total params: 2,140,752
Trainable params: 2,139,728
Non-trainable params: 1,024
____________________________________________________________________________________________________

BatchNormalization（BN）层的输入大小为512.根据Keras documentation，BN层的输出形状与512的输入相同。

那么与BN层相关的参数数量是多少是2048？

Answer 1

Keras中的批量规范化实现了this paper。

正如您可以在那里阅读的那样，为了在训练期间使批量标准化工作，他们需要跟踪每个标准化维度的分布。为此，由于您默认位于mode=0，因此它们会在前一层上为每个要素计算4个参数。这些参数确保您正确传播和反向传播信息。

所以4*512 = 2048，这应该回答你的问题。

Answer 2

这些2048参数实际上是[gamma weights, beta weights, moving_mean(non-trainable), moving_variance(non-trainable)]，每个参数都有512个元素（输入图层的大小）。