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Added sample code for quadratic cost for single neuron.
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Lines changed: 161 additions & 12 deletions

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‎digit_prediction.png‎

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‎guess_test.py‎

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import mnist_loader
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import network
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import numpy as np
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import matplotlib.pyplot as plt
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# Load data
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training_data, validation_data, test_data = mnist_loader.load_data_wrapper()
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# Ensure test_data is a list of (x, y) pairs
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test_data = list(test_data)
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# Pick one sample
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x, y = test_data[0]
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# Create and train a network
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net = network.Network([784, 30, 10])
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training_data = list(training_data)
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net.SGD(training_data, 1, 10, 3.0)
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# Call the guess function defined in network.py (it expects self, x)
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pred_by_guess = network.guess(net, x)
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# Reshape x from (784, 1) to (28, 28) and display as image
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x_image = x.reshape(28, 28)
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plt.figure(figsize=(6, 6))
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plt.imshow(x_image, cmap='gray')
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plt.title(f"Actual: {y}, Predicted: {int(pred_by_guess)}")
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plt.axis('off')
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plt.tight_layout()
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plt.savefig('digit_prediction.png')
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plt.show()
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print(f"Image saved as digit_prediction.png")
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print("Actual label:", y)
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print("network.guess predicted:", int(pred_by_guess))

‎network.py‎

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@@ -84,7 +84,7 @@ def update_mini_batch(self, mini_batch, eta):
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for x, y in mini_batch:
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delta_nabla_b, delta_nabla_w = self.backprop(x, y)
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nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
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nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
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nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
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self.weights = [w-(eta/len(mini_batch))*nw
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for w, nw in zip(self.weights, nabla_w)]
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self.biases = [b-(eta/len(mini_batch))*nb
@@ -95,6 +95,7 @@ def backprop(self, x, y):
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gradient for the cost function C_x. ``nabla_b`` and
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``nabla_w`` are layer-by-layer lists of numpy arrays, similar
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to ``self.biases`` and ``self.weights``."""
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# print("weights first row: {}".format(self.weights[0]))
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nabla_b = [np.zeros(b.shape) for b in self.biases]
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nabla_w = [np.zeros(w.shape) for w in self.weights]
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# feedforward
@@ -139,6 +140,14 @@ def cost_derivative(self, output_activations, y):
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\partial a for the output activations."""
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return (output_activations-y)
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def guess(self, x):
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"""Return the index of the highest activation neuron."""
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activation = x
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for b, w in zip(self.biases, self.weights):
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activation = sigmoid(np.dot(w, activation)+b)
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return np.argmax(activation)
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#### Miscellaneous functions
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def sigmoid(z):
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"""The sigmoid function."""

‎practice.py‎

Whitespace-only changes.

‎quadratic_cost_demo.py‎

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"""quadratic_cost_demo.py
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~~~~~~~~~~~~~~~~~~~~~~~~
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Demonstration of quadratic cost function during gradient descent training.
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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def sigmoid(z):
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"""The sigmoid function."""
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return 1.0/(1.0+np.exp(-z))
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def sigmoid_prime(z):
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"""Derivative of the sigmoid function."""
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return sigmoid(z)*(1-sigmoid(z))
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def quadraticCostDemo(epochs):
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"""Demonstrate quadratic cost function over epochs."""
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w = 0.6
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b = 0.9
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x = 1
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y = 0 # desired output
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cost_history = {} # dictionary to store cost values
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# Enable interactive mode for real-time plotting
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plt.ion()
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fig, ax = plt.subplots(figsize=(10, 6))
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for i in range(1, epochs):
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z = w * x + b
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a = sigmoid(z)
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cost = 0.5 * (a - y) ** 2
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cost_history[i] = cost
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# Calculate gradients
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nabla_cW = (a - y) * sigmoid_prime(z) * x
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nabla_cB = (a - y) * sigmoid_prime(z)
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# Update weights and bias
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w = w - nabla_cW
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b = b - nabla_cB
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# Update plot in real-time
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if i % 5 == 0 or i == 1: # Update every 5 epochs for better visualization
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ax.clear()
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epoch_list = sorted(cost_history.keys())
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cost_list = [cost_history[e] for e in epoch_list]
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ax.plot(epoch_list, cost_list, 'b-', linewidth=2)
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ax.set_xlabel('Epoch', fontsize=12)
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ax.set_ylabel('Quadratic Cost', fontsize=12)
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ax.set_title('Quadratic Cost Function Over Training Epochs', fontsize=14)
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ax.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.pause(0.01) # Small pause to see the update
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# Turn off interactive mode
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plt.ioff()
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return cost_history
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def plot_cost_history(cost_history):
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"""Plot the cost function over epochs."""
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epochs = sorted(cost_history.keys())
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costs = [cost_history[epoch] for epoch in epochs]
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plt.figure(figsize=(10, 6))
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plt.plot(epochs, costs, 'b-', linewidth=2)
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plt.xlabel('Epoch', fontsize=12)
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plt.ylabel('Quadratic Cost', fontsize=12)
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plt.title('Quadratic Cost Function Over Training Epochs', fontsize=14)
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plt.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('quadratic_cost_plot.png', dpi=150, bbox_inches='tight')
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print("Plot saved to quadratic_cost_plot.png")
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plt.show()
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if __name__ == "__main__":
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# Run the demo with 100 epochs
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epochs = 300
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cost_history = quadraticCostDemo(epochs)
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# Save final plot
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plt.figure(figsize=(10, 6))
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epoch_list = sorted(cost_history.keys())
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cost_list = [cost_history[e] for e in epoch_list]
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plt.plot(epoch_list, cost_list, 'b-', linewidth=2)
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plt.xlabel('Epoch', fontsize=12)
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plt.ylabel('Quadratic Cost', fontsize=12)
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plt.title('Quadratic Cost Function Over Training Epochs', fontsize=14)
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plt.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('quadratic_cost_plot.png', dpi=150, bbox_inches='tight')
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print("Plot saved to quadratic_cost_plot.png")
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plt.show()

‎quadratic_cost_plot.png‎

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‎test.py‎

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# ----------------------
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# - read the input data:
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'''
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import mnist_loader
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training_data, validation_data, test_data = mnist_loader.load_data_wrapper()
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training_data = list(training_data)
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'''
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# ---------------------
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# - network.py example:
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#import network
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import network
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'''
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net = network.Network([784, 30, 10])
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net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
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'''
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net.SGD(training_data, 1, 10, 3.0, test_data=test_data)
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# ----------------------
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# - network2.py example:
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"""
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'''
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def testTheano():
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from theano import function, config, shared, sandbox
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import theano.tensor as T
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print('Used the gpu')
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# Perform check:
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#testTheano()
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'''
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# ----------------------
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# - network3.py example:
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import network3
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from network3 import Network, ConvPoolLayer, FullyConnectedLayer, SoftmaxLayer # softmax plus log-likelihood cost is more common in modern image classification networks.
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# import network3
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# from network3 import Network, ConvPoolLayer, FullyConnectedLayer, SoftmaxLayer # softmax plus log-likelihood cost is more common in modern image classification networks.
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# read data:
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training_data, validation_data, test_data = network3.load_data_shared()
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# mini-batch size:
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mini_batch_size = 10
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# training_data, validation_data, test_data = network3.load_data_shared()
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# # mini-batch size:
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# mini_batch_size = 10
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# chapter 6 - shallow architecture using just a single hidden layer, containing 100 hidden neurons.
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'''
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'''
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# chapter 6 - rectified linear units and some l2 regularization (lmbda=0.1) => even better accuracy
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'''
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from network3 import ReLU
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net = Network([
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ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
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FullyConnectedLayer(n_in=40*4*4, n_out=100, activation_fn=ReLU),
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SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
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net.SGD(training_data, 60, mini_batch_size, 0.03, validation_data, test_data, lmbda=0.1)
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'''

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