NeuralNet.notes

Matrices: 2 x 3, "two by three", two rows & 3 columns

# 1 x 2 = (1 x OUTPUT)
output_layer_errors = -(numpy.mat(result) - layer2_output)

# 1 x 2 = (1 x OUTPUT)
sigmoid_prime_layer2 = self.sigmoid_prime(layer2_net_input)
# 1 x 2 = (1 x OUTPUT)
adjusted_output_layer_errors = numpy.multiply(output_layer_errors, sigmoid_prime_layer2)
# (1 x 2) * (2 x 2) = (1 x OUTPUT) * (OUTPUT x HIDDEN) = 1 x 2 = (1 x HIDDEN)
hidden_layer_errors = numpy.dot(adjusted_output_layer_errors, self.matrix_weights2.T)

# Step 3: compute the weight changes for each layer
# (1 x HIDDEN).T = HIDDEN x 1 = 2 x 1
transposed_layer1_output = layer1_output.T
# (HIDDEN x 1) * (1 x OUTPUT) = HIDDEN x OUTPUT = 2 x 2
grad_weights2 = numpy.dot(transposed_layer1_output, output_layer_errors)
# multiply(HIDDEN x OUTPUT, OUTPUT) = 2 x 2
gradient_weights2 = numpy.multiply(grad_weights2, sigmoid_prime_layer2)

# Todo: check matrix sizes. Do example by hand. See how they should improve. Turn off screen while doing it.

grad_weights1 = numpy.dot(input_data.T, hidden_layer_errors)
sigmoid_prime_layer1 = self.sigmoid_prime(layer1_net_input)
gradient_weights1 = numpy.multiply(grad_weights1, sigmoid_prime_layer1)


---------- Bias --------
grad_bias2 = numpy.multiply(numpy.multiply(bias2, sigmoid_prime_layer2), transposed_layer_output)


Let's do an example: