python - Keras 密集层输出形状

Question

我无法理解获取第一个隐藏层的输出形状背后的逻辑。我举了一些随意的例子如下；

示例 1:

model.add(Dense(units=4,activation='linear',input_shape=(784,)))  
model.add(Dense(units=10,activation='softmax'))
model.summary()

Model: "sequential_4"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_7 (Dense)              (None, 4)                 3140      
_________________________________________________________________
dense_8 (Dense)              (None, 10)                50        
=================================================================
Total params: 3,190
Trainable params: 3,190
Non-trainable params: 0

示例 2:

model.add(Dense(units=4,activation='linear',input_shape=(784,1)))   
model.add(Dense(units=10,activation='softmax'))
model.summary()
Model: "sequential_6"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_11 (Dense)             (None, 784, 4)            8         
_________________________________________________________________
dense_12 (Dense)             (None, 784, 10)           50        
=================================================================
Total params: 58
Trainable params: 58
Non-trainable params: 0

示例 3:

model.add(Dense(units=4,activation='linear',input_shape=(32,28)))    
model.add(Dense(units=10,activation='softmax'))
model.summary()
Model: "sequential_8"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_15 (Dense)             (None, 32, 4)             116       
_________________________________________________________________
dense_16 (Dense)             (None, 32, 10)            50        
=================================================================
Total params: 166
Trainable params: 166
Non-trainable params: 0

示例 4:

model.add(Dense(units=4,activation='linear',input_shape=(32,28,1)))    
model.add(Dense(units=10,activation='softmax'))
model.summary()
Model: "sequential_9"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_17 (Dense)             (None, 32, 28, 4)         8         
_________________________________________________________________
dense_18 (Dense)             (None, 32, 28, 10)        50        
=================================================================
Total params: 58
Trainable params: 58
Non-trainable params: 0

请帮助我理解逻辑。

另外，我认为排名 input_shape=(784,)和 input_shape=(784,1)是一样的那为什么他们的 Output Shape不同的？

Answer 1

根据 Keras 的官方文档，对于 Dense 层，当您输入为 input_shape=(input_units,) 时模态作为形状的输入数组 (*, input_units)并输出形状为 (*, output_units) 的数组[在你的情况下 input_shape=(784,)被视为 input shape=(*, 784)和输出是 output_shape=(*,4) ]

通常对于 (batch_size, ..., input_dim) 的输入维度，模态给出大小 (batch_size, ..., units) 的输出.

所以当你输入 input_shape=(784,)模态作为形状的输入数组 (*, 784) , 其中 *是批量大小和 784作为 input_dim，输出形状为 (*, 4) .

当输入为 (784,1) ，模态将其视为 (*, 784, 1)哪里*是批量大小，784是 ...和 1是 input_dim => (batch_size, ..., input_dim)并输出为 (*, 784, 4) => (batch_size, ..., units) .
input_shape=(32,28)=>(*,32,28) 也是如此, 给出输出 (*,32,4)和输入 input_shape=(32,28,1)=>(*,32,28,1)又在哪里*是批量大小，32,28是 ...和 1是 input_dim => (batch_size, ..., input_dim)
None 是什么意思，请查看 What is the meaning of the "None" in model.summary of KERAS?