Implement NumPy neural network with MNIST training from scratch

[Copilot]

Adds a fully-connected neural network implemented entirely in NumPy, trained and evaluated on MNIST digit classification.

Core library (neural_network.py)

• NeuralNetwork class with configurable layer sizes, He-initialized weights, and mini-batch gradient descent
• Forward pass: ReLU hidden activations, numerically stable softmax output
• Backward pass: analytical backpropagation with combined softmax + cross-entropy gradient
• train() returns per-epoch loss/accuracy history; predict() / evaluate() for inference

Training script (train.py)

• Loads MNIST via TensorFlow/Keras with scikit-learn fetch_openml as fallback
• Default architecture: 784 → 128 → 64 → 10, 20 epochs, batch size 64, lr 0.1
• Prints per-epoch loss + training accuracy; reports final test accuracy

Tests (test_neural_network.py)

• 28 unit tests covering activations, loss, parameter init, forward/backward shapes
• Numerical gradient check validates backprop correctness against finite differences
• End-to-end training test on a toy dataset verifies loss decrease and accuracy above chance

Example

from neural_network import NeuralNetwork
import numpy as np

model = NeuralNetwork([784, 128, 64, 10], learning_rate=0.1)
model.train(X_train, Y_train, epochs=20, batch_size=64)
print(f"Test accuracy: {model.evaluate(X_test, Y_test):.4f}")

Original prompt

Implement a neural network from scratch in Python using NumPy, including forward propagation, backpropagation, and gradient descent. Train on MNIST dataset and evaluate accuracy.