### Weight Initialization Methods for Neural Networks

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Demonstrates two weight initialization strategies for a neural network: the default method, which scales weights based on input connections (recommended), and a large weight method for comparison. This allows for experimenting with different weight distributions.

```python
import network2

net = network2.Network([784, 100, 10])

# Default: weights ~ N(0, 1/sqrt(n_in)) - recommended
net.default_weight_initializer()

# Large weights: weights ~ N(0, 1) - for comparison with Chapter 1
net.large_weight_initializer()
```

--------------------------------

### Initialize Feedforward Network in Python

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Initializes a feedforward neural network with specified layer sizes. Weights and biases are randomly initialized from a Gaussian distribution. This code demonstrates creating a network and accessing its basic properties.

```python
import network
import mnist_loader

# Create a 3-layer network: 784 input, 30 hidden, 10 output neurons
net = network.Network([784, 30, 10])

# Network attributes:
print(net.num_layers)  # 3
print(net.sizes)       # [784, 30, 10]
print(len(net.biases)) # 2 (one per non-input layer)
print(len(net.weights))# 2 (connections between layers)
```

--------------------------------

### Load Data for GPU Training (Theano)

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Loads the MNIST dataset and converts it into Theano shared variables. This function is optimized for GPU computation, automatically transferring the data to the GPU if available, which significantly speeds up training for large datasets.

```python
import network3

# Load data as Theano shared variables
training_data, validation_data, test_data = network3.load_data_shared()
# Returns tuples of (shared_x, shared_y) for each dataset
# Data is automatically copied to GPU if available
```

--------------------------------

### Quadratic and Cross-Entropy Cost Functions

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Implements and demonstrates the use of `QuadraticCost` and `CrossEntropyCost` classes. These classes provide methods to calculate the cost and the delta error term required for backpropagation, supporting different loss functions for neural networks.

```python
import network2
import numpy as np

# Quadratic cost: C = 0.5 * ||a - y||^2
a = np.array([[0.8], [0.2]])  # Network output
y = np.array([[1.0], [0.0]])  # Target output
z = np.array([[1.0], [0.5]])  # Weighted input

cost = network2.QuadraticCost.fn(a, y)  # 0.02
delta = network2.QuadraticCost.delta(z, a, y)  # Error for backprop

# Cross-entropy cost: C = -sum(y*log(a) + (1-y)*log(1-a))
cost = network2.CrossEntropyCost.fn(a, y)  # ~0.223
delta = network2.CrossEntropyCost.delta(z, a, y)  # Simpler gradient: (a - y)
```

--------------------------------

### Train Neural Network with SGD in Python

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Trains a neural network using mini-batch stochastic gradient descent (SGD) with backpropagation. The function supports specifying training data, epochs, mini-batch size, learning rate, and optional testing data for evaluation after each epoch.

```python
import network
import mnist_loader

# Load data
training_data, validation_data, test_data = mnist_loader.load_data_wrapper()

# Create and train network
net = network.Network([784, 30, 10])
net.SGD(
    training_data=list(training_data),  # List of (x, y) tuples
    epochs=30,                           # Number of training epochs
    mini_batch_size=10,                  # Samples per mini-batch
    eta=3.0,                             # Learning rate
    test_data=list(test_data)            # Optional: evaluate each epoch
)
# Output:
# Epoch 0: 9129 / 10000
# Epoch 1: 9256 / 10000
# ...
# Epoch 29: 9487 / 10000
```

--------------------------------

### Describe Theano-based Activation Functions

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Lists and briefly describes common activation functions available in the network3 library, which utilizes Theano for computation. These include sigmoid, tanh, ReLU, and linear activation.

```python
# Theano-based activations (network3.py)
# sigmoid - standard logistic function
# tanh - hyperbolic tangent, outputs in [-1, 1]
# ReLU - rectified linear unit: max(0, z)
# linear - identity function: z
```

--------------------------------

### Implement Sigmoid and Sigmoid Prime Functions (NumPy)

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Provides NumPy-based implementations for the sigmoid activation function and its derivative (sigmoid prime). These are fundamental for neural network backpropagation.

```python
import numpy as np

# Using numpy-based sigmoid (network.py, network2.py)
def sigmoid_np(z):
    return 1.0 / (1.0 + np.exp(-z))

def sigmoid_prime(z):
    return sigmoid_np(z) * (1 - sigmoid_np(z))

z = np.array([-2.0, -1.0, 0.0, 1.0, 2.0])
print(sigmoid_np(z))       # [0.119, 0.269, 0.5, 0.731, 0.881]
print(sigmoid_prime(z))    # [0.105, 0.197, 0.25, 0.197, 0.105]
```

--------------------------------

### Save and Load Neural Network State

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Shows how to serialize a trained neural network to a JSON file and then load it back. This process preserves the network's architecture, weights, biases, and cost function, enabling continued training or inference without retraining from scratch.

```python
import network2

# Create and train network
net = network2.Network([784, 30, 10])
# ... training code ...

# Save to file
net.save("trained_network.json")

# Load from file
loaded_net = network2.load("trained_network.json")
# Network architecture, weights, biases, and cost function are restored
```

--------------------------------

### Train Convolutional Neural Network (Theano)

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Constructs and trains a complete Convolutional Neural Network (CNN) architecture using Theano for GPU acceleration. The network is defined as a list of layers, including convolutional, pooling, fully connected, and softmax layers, with support for activation functions and dropout.

```python
import network3
from network3 import Network, ConvPoolLayer, FullyConnectedLayer, SoftmaxLayer
from network3 import ReLU

# Load data
training_data, validation_data, test_data = network3.load_data_shared()

mini_batch_size = 10

# Define CNN architecture
net = Network([
    ConvPoolLayer(
        filter_shape=(20, 1, 5, 5),
        image_shape=(mini_batch_size, 1, 28, 28),
        activation_fn=ReLU
    ),
    ConvPoolLayer(
        filter_shape=(40, 20, 5, 5),
        image_shape=(mini_batch_size, 20, 12, 12),
        activation_fn=ReLU
    ),
    FullyConnectedLayer(
        n_in=40*4*4,
        n_out=100,
        activation_fn=ReLU,
        p_dropout=0.5
    ),
    SoftmaxLayer(n_in=100, n_out=10, p_dropout=0.5)
], mini_batch_size)
```

--------------------------------

### Load MNIST Data with Python

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Loads and preprocesses the MNIST handwritten digit dataset. It provides data in two formats: raw numpy arrays and tuples formatted for neural network training, including one-hot encoded labels.

```python
import mnist_loader

# Load raw data as numpy arrays
training_data, validation_data, test_data = mnist_loader.load_data()
# training_data[0].shape = (50000, 784) - images
# training_data[1].shape = (50000,) - labels (0-9)

# Load data formatted for neural network training
training_data, validation_data, test_data = mnist_loader.load_data_wrapper()
# training_data: list of 50,000 tuples (x, y)
#   x: (784, 1) numpy array - input image
#   y: (10, 1) numpy array - one-hot encoded label
# validation_data/test_data: list of 10,000 tuples (x, y)
#   x: (784, 1) numpy array - input image
#   y: integer 0-9 - digit label
```

--------------------------------

### Train Neural Network using SGD

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Trains a neural network using the Stochastic Gradient Descent (SGD) algorithm. It takes training, validation, and test data, along with parameters like epochs, mini-batch size, learning rate (eta), and L2 regularization (lmbda).

```python
net.SGD(
    training_data=training_data,
    epochs=60,
    mini_batch_size=mini_batch_size,
    eta=0.03,                       # Learning rate
    validation_data=validation_data,
    test_data=test_data,
    lmbda=0.1                       # L2 regularization
)
```

--------------------------------

### Train Network with L2 Regularization and Monitoring

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Trains a neural network using Stochastic Gradient Descent (SGD) with L2 regularization. It monitors evaluation and training accuracy and cost over a specified number of epochs. The function returns lists containing these metrics for each epoch.

```python
evaluation_cost, evaluation_accuracy, training_cost, training_accuracy = net.SGD(
    training_data=list(training_data),
    epochs=30,
    mini_batch_size=10,
    eta=0.5,                              # Learning rate
    lmbda=5.0,                            # L2 regularization parameter
    evaluation_data=list(validation_data),
    monitor_evaluation_accuracy=True,
    monitor_evaluation_cost=True,
    monitor_training_accuracy=True,
    monitor_training_cost=True
)
```

--------------------------------

### Expand MNIST Training Data with Image Shifting

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Expands the MNIST training dataset by creating translated versions of each image. Each original image is shifted one pixel up, down, left, and right, resulting in a larger dataset for potentially improved model training.

```python
import cPickle
import gzip
import numpy as np

# Load original data
f = gzip.open("../data/mnist.pkl.gz", 'rb')
training_data, validation_data, test_data = cPickle.load(f)
f.close()

# Expand by shifting images
expanded_pairs = []
for x, y in zip(training_data[0], training_data[1]):
    expanded_pairs.append((x, y))  # Original
    image = np.reshape(x, (-1, 28))

    # Create 4 shifted versions (up, down, left, right)
    for d, axis, idx_pos, idx in [(1, 0, "first", 0), (-1, 0, "first", 27),
                                   (1, 1, "last", 0), (-1, 1, "last", 27)]:
        new_img = np.roll(image, d, axis)
        if idx_pos == "first":
            new_img[idx, :] = np.zeros(28)
        else:
            new_img[:, idx] = np.zeros(28)
        expanded_pairs.append((np.reshape(new_img, 784), y))

# 50,000 * 5 = 250,000 training images
print(f"Expanded from 50,000 to {len(expanded_pairs)} training images")
```

--------------------------------

### Implement SVM Classifier for MNIST

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Implements a Support Vector Machine (SVM) classifier using scikit-learn for MNIST digit classification. It loads data, trains an SVC model, and predicts on test data, providing accuracy metrics.

```python
import mnist_loader
from sklearn import svm

# Load raw data
training_data, validation_data, test_data = mnist_loader.load_data()

# Train SVM classifier
clf = svm.SVC()
clf.fit(training_data[0], training_data[1])

# Test predictions
predictions = clf.predict(test_data[0])
num_correct = sum(int(a == y) for a, y in zip(predictions, test_data[1]))
print(f"SVM Baseline: {num_correct} / {len(test_data[1])} correct")
# Typical result: ~9435 / 10000 (94.35% accuracy)
```

--------------------------------

### Neural Network Feedforward and Evaluation in Python

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Performs a feedforward pass through the network to compute output activations for a given input. Also includes an evaluation method to count correct classifications on a dataset, useful for assessing network performance.

```python
import network
import numpy as np

net = network.Network([784, 30, 10])

# Single prediction
input_image = np.random.randn(784, 1)  # 28x28 image as column vector
output = net.feedforward(input_image)   # (10, 1) array of activations
predicted_digit = np.argmax(output)     # Index of highest activation

# Evaluate on test data
test_data = [(np.random.randn(784, 1), np.random.randint(10)) for _ in range(100)]
correct_count = net.evaluate(test_data)
print(f"Accuracy: {correct_count} / {len(test_data)}")
```

--------------------------------

### Network with Cost Functions and Regularization in Python

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Implements an improved neural network supporting multiple cost functions, such as cross-entropy and quadratic cost. It also incorporates L2 regularization to help prevent overfitting and improve generalization.

```python
import network2
import mnist_loader

# Load data
training_data, validation_data, test_data = mnist_loader.load_data_wrapper()

# Create network with cross-entropy cost (default)
net = network2.Network([784, 30, 10], cost=network2.CrossEntropyCost)

# Alternative: quadratic cost function
net_quadratic = network2.Network([784, 30, 10], cost=network2.QuadraticCost)
```

--------------------------------

### Define Convolutional Neural Network Layers (Theano)

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

Defines various layers commonly used in Convolutional Neural Networks (CNNs), including `ConvPoolLayer` for convolutional and pooling operations, `FullyConnectedLayer` for dense layers, and `SoftmaxLayer` for the output classification layer. Supports different activation functions and dropout for regularization.

```python
import network3
from network3 import ConvPoolLayer, FullyConnectedLayer, SoftmaxLayer
from network3 import sigmoid, tanh, ReLU

mini_batch_size = 10

# Convolutional + Max Pooling layer
conv_layer = ConvPoolLayer(
    filter_shape=(20, 1, 5, 5),     # 20 filters, 1 input map, 5x5 kernel
    image_shape=(mini_batch_size, 1, 28, 28),  # Batch, channels, height, width
    poolsize=(2, 2),                # 2x2 max pooling
    activation_fn=ReLU              # ReLU activation
)

# Fully connected layer with dropout
fc_layer = FullyConnectedLayer(
    n_in=20*12*12,                  # Flattened conv output
    n_out=100,                      # Hidden units
    activation_fn=sigmoid,          # Sigmoid activation
    p_dropout=0.5                   # 50% dropout during training
)

# Output layer with softmax
softmax_layer = SoftmaxLayer(
    n_in=100,                       # From hidden layer
    n_out=10,                       # 10 digit classes
    p_dropout=0.5
)
```

--------------------------------

### Implement Average Darkness Classifier

Source: https://context7.com/mnielsen/neural-networks-and-deep-learning/llms.txt

A naive baseline classifier that determines digit classification based on the average pixel intensity (darkness) of the training data for each digit. It calculates average darkness per class and then classifies test images by finding the nearest average darkness.

```python
import mnist_loader
from collections import defaultdict

training_data, validation_data, test_data = mnist_loader.load_data()

# Compute average darkness per digit class
digit_counts = defaultdict(int)
darknesses = defaultdict(float)
for image, digit in zip(training_data[0], training_data[1]):
    digit_counts[digit] += 1
    darknesses[digit] += sum(image)

avgs = {digit: darknesses[digit] / digit_counts[digit]
        for digit in digit_counts}

# Classify by nearest average darkness
def guess_digit(image, avgs):
    darkness = sum(image)
    distances = {k: abs(v - darkness) for k, v in avgs.items()}
    return min(distances, key=distances.get)

num_correct = sum(int(guess_digit(img, avgs) == digit)
                  for img, digit in zip(test_data[0], test_data[1]))
print(f"Average Darkness: {num_correct} / {len(test_data[1])} correct")
# Typical result: ~2225 / 10000 (22.25% accuracy)
```

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