How can we compute number of weights considering a convolutional neural network that is used to classify images into two classes :

• INPUT: 100x100 gray-scale images.
• LAYER 1: Convolutional layer with 60 7x7 convolutional filters (stride=1, valid padding).
• LAYER 2: Convolutional layer with 100 5x5 convolutional filters (stride=1, valid padding).
• LAYER 3: A max pooling layer that down-samples Layer 2 by a factor of 4 (e.g., from 500x500 to 250x250)
• LAYER 4: Dense layer with 250 units
• LAYER 5: Dense layer with 200 units
• LAYER 6: Single output unit

Assume the existence of biases in each layer. Moreover, pooling layer has a weight (similar to AlexNet)

How many weights does this network have?

Some Keras code

import keras
from keras.models import Sequential
from keras.layers import Dense
from keras.layers import Conv2D, MaxPooling2D

model = Sequential()

# Layer 1
model.add(Conv2D(60, (7, 7), input_shape = (100, 100, 1), padding="same", activation="relu"))

# Layer 2
model.add(Conv2D(100, (5, 5), padding="same", activation="relu"))

# Layer 3
model.add(MaxPooling2D(pool_size=(2, 2)))

# Layer 4
model.add(Dense(250))

# Layer 5
model.add(Dense(200))

model.summary()

TL;DR - For TensorFlow + Keras

Use Sequential.summary - Link to documentation.

Example usage:

from tensorflow.keras.models import *

model = Sequential([
    # Your architecture here
]);

model.summary()

The output for your architecture is:

Model: "sequential"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d (Conv2D)              (None, 94, 94, 60)        3000      
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 90, 90, 100)       150100    
_________________________________________________________________
max_pooling2d (MaxPooling2D) (None, 45, 45, 100)       0         
_________________________________________________________________
flatten (Flatten)            (None, 202500)            0         
_________________________________________________________________
dense (Dense)                (None, 250)               50625250  
_________________________________________________________________
dense_1 (Dense)              (None, 200)               50200     
_________________________________________________________________
dense_2 (Dense)              (None, 1)                 201       
=================================================================
Total params: 50,828,751
Trainable params: 50,828,751
Non-trainable params: 0
_________________________________________________________________

That's 50,828,751 parameters.

Explanation

Number of weights in a 2D Convolutional layer

For a 2D Convolutional layer having

• num_filters filters,
• a filter size of filter_size * filter_size * num_channels,
• and a bias parameter per filter

The number of weights is: (num_filters * filter_size * filter_size * num_channels) + num_filters

E.g.: LAYER 1 in your neural network has

• 60 filters
• and a filter size of 7 * 7 * 1. (Notice that the number of channels (1) comes from the input image.)

The number of weights in it is: (60 * 7 * 7 * 1) + 60, which is 3000.

Number of weights in a Dense layer

For a Dense layer having

• num_units neurons,
• num_inputs neurons in the layer prior to it,
• and a bias parameter per neuron

The number of weights is: (num_units * num_inputs) + num_units

E.g. LAYER 5 in your neural network has

• 200 neurons
• and the layer prior to it - LAYER 4 - has 250 neurons.

The number of weights in it is 200 * 250 + 200, which is 50200.