Keras model.summary() result - Understanding the # of Parameters
Solution 1
The number of parameters is 7850 because with every hidden unit you have 784 input weights and one weight of connection with bias. This means that every hidden unit gives you 785 parameters. You have 10 units so it sums up to 7850.
The role of this additional bias term is really important. It significantly increases the capacity of your model. You can read details e.g. here Role of Bias in Neural Networks.
Solution 2
I feed a 514 dimensional real-valued input to a Sequential
model in Keras.
My model is constructed in following way :
predictivemodel = Sequential()
predictivemodel.add(Dense(514, input_dim=514, W_regularizer=WeightRegularizer(l1=0.000001,l2=0.000001), init='normal'))
predictivemodel.add(Dense(257, W_regularizer=WeightRegularizer(l1=0.000001,l2=0.000001), init='normal'))
predictivemodel.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy'])
When I print model.summary()
I get following result:
Layer (type) Output Shape Param # Connected to
================================================================
dense_1 (Dense) (None, 514) 264710 dense_input_1[0][0]
________________________________________________________________
activation_1 (None, 514) 0 dense_1[0][0]
________________________________________________________________
dense_2 (Dense) (None, 257) 132355 activation_1[0][0]
================================================================
Total params: 397065
________________________________________________________________
For the dense_1 layer , number of params is 264710. This is obtained as : 514 (input values) * 514 (neurons in the first layer) + 514 (bias values)
For dense_2 layer, number of params is 132355. This is obtained as : 514 (input values) * 257 (neurons in the second layer) + 257 (bias values for neurons in the second layer)
Solution 3
For Dense Layers:
output_size * (input_size + 1) == number_parameters
For Conv Layers:
output_channels * (input_channels * window_size + 1) == number_parameters
Consider following example,
model = Sequential([
Conv2D(32, (3, 3), activation='relu', input_shape=input_shape),
Conv2D(64, (3, 3), activation='relu'),
Conv2D(128, (3, 3), activation='relu'),
Dense(num_classes, activation='softmax')
])
model.summary()
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
conv2d_1 (Conv2D) (None, 222, 222, 32) 896
_________________________________________________________________
conv2d_2 (Conv2D) (None, 220, 220, 64) 18496
_________________________________________________________________
conv2d_3 (Conv2D) (None, 218, 218, 128) 73856
_________________________________________________________________
dense_9 (Dense) (None, 218, 218, 10) 1290
=================================================================
Calculating params,
assert 32 * (3 * (3*3) + 1) == 896
assert 64 * (32 * (3*3) + 1) == 18496
assert 128 * (64 * (3*3) + 1) == 73856
assert num_classes * (128 + 1) == 1290
Solution 4
The "none" in the shape means it does not have a pre-defined number. For example, it can be the batch size you use during training, and you want to make it flexible by not assigning any value to it so that you can change your batch size. The model will infer the shape from the context of the layers.
To get nodes connected to each layer, you can do the following:
for layer in model.layers:
print(layer.name, layer.inbound_nodes, layer.outbound_nodes)
Solution 5
Number of parameters is the amount of numbers that can be changed in the model. Mathematically this means number of dimensions of your optimization problem. For you as a programmer, each of this parameters is a floating point number, which typically takes 4 bytes of memory, allowing you to predict the size of this model once saved.
This formula for this number is different for each neural network layer type, but for Dense layer it is simple: each neuron has one bias parameter and one weight per input:
N = n_neurons * ( n_inputs + 1)
.
user3501476
Updated on July 05, 2022Comments
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user3501476 almost 2 years
I have a simple NN model for detecting hand-written digits from a 28x28px image written in python using Keras (Theano backend):
model0 = Sequential() #number of epochs to train for nb_epoch = 12 #amount of data each iteration in an epoch sees batch_size = 128 model0.add(Flatten(input_shape=(1, img_rows, img_cols))) model0.add(Dense(nb_classes)) model0.add(Activation('softmax')) model0.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy']) model0.fit(X_train, Y_train, batch_size=batch_size, nb_epoch=nb_epoch, verbose=1, validation_data=(X_test, Y_test)) score = model0.evaluate(X_test, Y_test, verbose=0) print('Test score:', score[0]) print('Test accuracy:', score[1])
This runs well and I get ~90% accuracy. I then perform the following command to get a summary of my network's structure by doing
print(model0.summary())
. This outputs the following:Layer (type) Output Shape Param # Connected to ===================================================================== flatten_1 (Flatten) (None, 784) 0 flatten_input_1[0][0] dense_1 (Dense) (None, 10) 7850 flatten_1[0][0] activation_1 (None, 10) 0 dense_1[0][0] ====================================================================== Total params: 7850
I don't understand how they get to 7850 total params and what that actually means?
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user3282611 over 5 yearsA quick note on how we have 784. 784 = 28x28 because of the image size is 28*28.
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Andrew almost 5 yearsNote to anyone reading this answer: these layers were built on an input size of [28x28x3] (RGB input) rather than the OP who has a single input channel.
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Aashish Amber over 4 years@Andrew can you please explain the output shape value calculation here .