Does MaxPooling reduce overfitting?

Question

I have trained the following CNN model with a smaller data set, therefore it does overfitting:

model = Sequential()
model.add(Conv2D(32, kernel_size=(3,3), input_shape=(28,28,1), padding='same'))
model.add(BatchNormalization())
model.add(Activation('relu'))

model.add(Conv2D(32, kernel_size=(3,3), padding='same'))
model.add(BatchNormalization())
model.add(Activation('relu'))
model.add(MaxPooling2D(pool_size=(2,2)))
model.add(Dropout(0.4))

model.add(Flatten())
model.add(Dense(512))
model.add(BatchNormalization())
model.add(Activation('relu'))
model.add(Dropout(0.5))
model.add(Dense(10, activation='softmax'))
model.compile(loss="categorical_crossentropy", optimizer=Adam(), metrics=['accuracy'])

The model has a lot of trainable parameters (more than 3 million, that's why I wonder if I should reduce the number of parameters with additional MaxPooling like follows?

Conv - BN - Act - MaxPooling - Conv - BN - Act - MaxPooling - Dropout - Flatten

or with an additional MaxPooling and Dropout like follows?

Conv - BN - Act - MaxPooling - Dropout - Conv - BN - Act - MaxPooling - Dropout - Flatten

I am trying to understand the full sense of MaxPooling and whether it can help against overfitting.

Answer 1

Overfitting can happen when your dataset is not large enough to accomodate your number of features. Max pooling uses a max operation to pool sets of features, leaving you with a smaller number of them. Therefore, max-pooling should logically reduce overfit.

Drop-out reduces reliance on any single feature by ensuring that feature is not always available, forcing the model to look for different potential hints, rather than just sticking with one -- which would easily allow the model to overfit on any apparently good hint. Therefore, this also should help reduce overfit.