keras.applications中的input_shape如何工作？

Question

I have been through the Keras documentation but I am still unable to figure how does the input_shape parameter works and why it does not change the number of parameters for my DenseNet model when I pass it my custom input shape. An example:

import keras
from keras import applications
from keras.layers import Conv3D, MaxPool3D, Flatten, Dense
from keras.layers import Dropout, Input, BatchNormalization
from keras import Model

# define model 1
INPUT_SHAPE = (224, 224, 1) # used to define the input size to the model
n_output_units = 2
activation_fn = 'sigmoid'
densenet_121_model = applications.densenet.DenseNet121(include_top=False, weights=None, input_shape=INPUT_SHAPE, pooling='avg')
inputs = Input(shape=INPUT_SHAPE, name='input')
model_base = densenet_121_model(inputs)
output = Dense(units=n_output_units, activation=activation_fn)(model_base)
model = Model(inputs=inputs, outputs=output)
model.summary()

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input (InputLayer)           (None, 224, 224, 1)       0         
_________________________________________________________________
densenet121 (Model)          (None, 1024)              7031232   
_________________________________________________________________
dense_1 (Dense)              (None, 2)                 2050      
=================================================================
Total params: 7,033,282
Trainable params: 6,949,634
Non-trainable params: 83,648
_________________________________________________________________



# define model 2
INPUT_SHAPE = (512, 512, 1) # used to define the input size to the model
n_output_units = 2
activation_fn = 'sigmoid'
densenet_121_model = applications.densenet.DenseNet121(include_top=False, weights=None, input_shape=INPUT_SHAPE, pooling='avg')
inputs = Input(shape=INPUT_SHAPE, name='input')
model_base = densenet_121_model(inputs)
output = Dense(units=n_output_units, activation=activation_fn)(model_base)
model = Model(inputs=inputs, outputs=output)
model.summary()
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input (InputLayer)           (None, 512, 512, 1)       0         
_________________________________________________________________
densenet121 (Model)          (None, 1024)              7031232   
_________________________________________________________________
dense_2 (Dense)              (None, 2)                 2050      
=================================================================
Total params: 7,033,282
Trainable params: 6,949,634
Non-trainable params: 83,648
_________________________________________________________________

Ideally with an increase in the input shape the number of parameters should increase, however as you can see they stay exactly the same. My questions are thus:

1. Why do the number of parameters not change with a change in the input_shape ?
2. I have only defined one channel in my input_shape , what would happen to my model training in this scenario? The documentation says the following:

input_shape: optional shape tuple, only to be specified if include_top is False (otherwise the input shape has to be (224, 224, 3) (with 'channels_last' data format) or (3, 224, 224) (with 'channels_first' data format). It should have exactly 3 inputs channels, and width and height should be no smaller than 32. Eg (200, 200, 3) would be one valid value.

However when I run the model with this configuration it runs without any problems. Could there be something that I am missing out?

Using Keras 2.2.4 with Tensorflow 1.12.0 as backend.

Answer 1

1. In the convolutional layers the input size does not influence the number of weights, because the number of weights is determined by the kernel matrix dimensions. A larger input size leads to a larger output size, but not to an increasing number of weights.

This means, that the output size of the convolutional layers of the second model will be larger than for the first model, which would increase the number of weights in the following dense layer. However if you take a look into the architecture of DenseNet you notice that there's a GlobalMaxPooling2D layer after all the convolutional layers, which averages all the values for each output channel. Thats why the output of DenseNet will be of size 1024, whatever the input shape.

2. Yes, the model will still work. I'm not entirely sure about that, but my guess is that the single channel will be broadcasted (dublicated) to fill all three channels. Thats at least how these things are usually handled (see for exaple tensorflow or numpy ).

Answer 2

The DenseNet is composed of two parts, the convolution part, and the global pooling part.

The number of the convolution part's trainable weights doesn't depend on the input shape.

Usually, a classification network should employ fully connected layers to infer the classification, however, in DenseNet , global pooling is used and doesn't bring any trainable weights.

Therefore, the input shape doesn't affect the number of weights of the entire network.