non trainable parameters params in keras model is calculated

Question

I have following program taken from Internet

def my_model(input_shape):
    # Define the input placeholder as a tensor with shape input_shape. Think of this as your input image!
    X_input = Input(input_shape)

    # Zero-Padding: pads the border of X_input with zeroes
    X = ZeroPadding2D((3, 3))(X_input)

    # CONV -> BN -> RELU Block applied to X
    X = Conv2D(32, (7, 7), strides = (1, 1), name = 'conv0')(X)
    X = BatchNormalization(axis = 3, name = 'bn0')(X)
    X = Activation('relu')(X)

    # MAXPOOL
    X = MaxPooling2D((2, 2), name='max_pool')(X)

    # FLATTEN X (means convert it to a vector) + FULLYCONNECTED
    X = Flatten()(X)
    X = Dense(1, activation='sigmoid', name='fc')(X)

    # Create model. This creates your Keras model instance, you'll use this instance to train/test the model.
    model = Model(inputs = X_input, outputs = X, name='myModel')

    return model

mymodel = my_model((64,64,3))
mymodel.summary()

Here output of summary is shown as below

Layer (type)                 Output Shape              Param #   
=================================================================
input_3 (InputLayer)         (None, 64, 64, 3)         0         
_________________________________________________________________
zero_padding2d_3 (ZeroPaddin (None, 70, 70, 3)         0         
_________________________________________________________________
conv0 (Conv2D)               (None, 64, 64, 32)        4736      
_________________________________________________________________
bn0 (BatchNormalization)     (None, 64, 64, 32)        128       
_________________________________________________________________
activation_2 (Activation)    (None, 64, 64, 32)        0         
_________________________________________________________________
max_pool (MaxPooling2D)      (None, 32, 32, 32)        0         
_________________________________________________________________
flatten_2 (Flatten)          (None, 32768)             0         
_________________________________________________________________
fc (Dense)                   (None, 1)                 32769     
=================================================================
Total params: 37,633
Trainable params: 37,569
Non-trainable params: 64

---

My question is from which layer this non-trainable params are taken ie, 64. Another question is how batch normalization has parameters 128?

Request your help how above numbers we got from model defined above. Thanks for the time and help.

Answer 1

BatchNormalization layer is composed of [gamma weights, beta weights, moving_mean(non-trainable), moving_variance(non-trainable)] and for each parameter there is one value for each element in the last axis (by default in keras, but you can change the axis if you want to).

In your code you have a size 32 in the last dimension before the BatchNormalization layer, so 32*4=128 parameters and since there are 2 non-trainable parameters there are 32*2=64 non-trainable parameters