I am trying to write the neural network as written in the book "Neural Networks and Deep Learning" by Michael Nielsen. I have finally gotten the code to run but every epoch results in the same output no matter where it starts it gets stuck at a similar, very inaccurate value. The code and results are below.
import random
import numpy as np
def sigmoid(z):
return 1/(1-np.exp(z))
def sigmoid_prime(z):
return sigmoid(z)*(1-sigmoid(z))
class Network(object):
def __init__(self, sizes):
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes [1:]]
self.weights = [np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:])]
def feedForward(self, a):
for b, w in zip(self.biases, self.weights):
a = sigmoid((np.dot(w, a)+b))
return a
def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying
gradient descent using backpropagation to a single mini batch.
The "mini_batch" is a list of tuples "(x, y)", and "eta"
is the learning rate."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
def SGD(self, training_data, epochs, mini_batch_size, eta,
test_data=None):
"""Train the neural network using mini-batch stochastic
gradient descent. The "training_data" is a list of tuples
"(x, y)" representing the training inputs and the desired
outputs. The other non-optional parameters are
self-explanatory. If "test_data" is provided then the
network will be evaluated against the test data after each
epoch, and partial progress printed out. This is useful for
tracking progress, but slows things down substantially."""
training_data = list(training_data)
n = len(training_data)
if test_data:
test_data = list(test_data)
n_test = len(test_data)
for j in range(epochs):
random.shuffle(training_data)
mini_batches = [training_data[k:k+mini_batch_size]
for k in range(0, n, mini_batch_size)]
for batch in mini_batches:
self.update_mini_batch(batch, eta)
if test_data:
print ("Epoch {}: {} / {}".format(j, self.evaluate(test_data), n_test))
else:
print ("Epoch {} complete".format(j))
def backprop(self, x, y):
"""Return a tuple ``(nabla_b, nabla_w)`` representing the
gradient for the cost function C_x. ``nabla_b`` and
``nabla_w`` are layer-by-layer lists of numpy arrays, similar
to ``self.biases`` and ``self.weights``."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable l in the loop below is used a little
# differently to the notation in Chapter 2 of the book. Here,
# l = 1 means the last layer of neurons, l = 2 is the
# second-last layer, and so on. It's a renumbering of the
# scheme in the book, used here to take advantage of the fact
# that Python can use negative indices in lists.
for l in range(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def evaluate(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
test_results = [(np.argmax(self.feedForward(x)), y)
for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
def cost_derivative(self, output_activations, y):
"""Return the vector of partial derivatives \partial C_x /
\partial a for the output activations."""
return (output_activations-y)
def sigmoid(z):
return 1.0/(1.0-np.exp(z))
def sigmoid_prime(z):
return sigmoid(z)*(1-sigmoid(z))
Output in Shell
net.SGD(training_data, 10, 10, 3.0, test_data=test_data)
Epoch 0: 1010 / 10000
Epoch 1: 1010 / 10000
Epoch 2: 1010 / 10000
Epoch 3: 1010 / 10000
Epoch 4: 1010 / 10000
Epoch 5: 1010 / 10000
Epoch 6: 1010 / 10000
Epoch 7: 1010 / 10000
Epoch 8: 1010 / 10000
Epoch 9: 1010 / 10000
