Neural Network From Scratch (NumPy • XOR Classifier)

This project implements a simple feed-forward neural network from scratch using NumPy, without using any machine-learning frameworks. The network learns the XOR logic function, demonstrating forward propagation, loss computation, backpropagation, and gradient-descent weight updates.

It’s designed as an educational reference to understand how neural networks work internally.

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🔹 Features

• Fully manual neural-network implementation
• Single hidden-layer architecture
• Sigmoid activation function
• Mean Squared Error (MSE) loss
• Gradient Descent optimization
• Clean and minimal NumPy code

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🧠 Problem: XOR Logic

Input A	Input B	Output
0	0	0
0	1	1
1	0	1
1	1	0

The XOR problem cannot be solved by a linear model, so it’s a classic example for neural networks.

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📦 Requirements

• Python 3.8+
• NumPy

Install NumPy if needed:

pip install numpy

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▶️ How To Run

python main.py

You should see the loss decreasing during training and final predictions close to:

Input: [0 0] → 0
Input: [0 1] → 1
Input: [1 0] → 1
Input: [1 1] → 0

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🏗️ Network Architecture

• Input layer: 2 neurons
• Hidden layer: 4 neurons
• Output layer: 1 neuron
• Activation: Sigmoid
• Loss: Mean Squared Error
• Optimizer: Gradient Descent

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📘 How It Works (Summary)

1. Forward Pass

   • Inputs → Hidden Layer → Output Layer
   • Sigmoid squashes outputs between 0–1

2. Loss Calculation

   • Mean Squared Error compares predictions with expected outputs

3. Backpropagation

   • Gradients are computed using the chain rule
   • Each weight is updated based on its contribution to the error

4. Gradient Descent Update

   • Weights and biases are adjusted repeatedly to reduce loss

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🧪 Example Output

Epoch 0      Loss: 0.25
Epoch 2000   Loss: 0.12
Epoch 4000   Loss: 0.05
Epoch 6000   Loss: 0.02
Epoch 8000   Loss: 0.01

Predictions:
[[0.02]
 [0.97]
 [0.97]
 [0.03]]

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🎯 Learning Goals

This project helps you understand:

✔️ What forward propagation really does ✔️ How gradients are computed manually ✔️ How neural networks actually “learn” ✔️ Why activation functions matter

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📁 Project Structure

.
├── main.py     # Neural network implementation
└── README.md   # Documentation

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🤝 Contributing

Feel free to open issues or submit pull requests to improve or extend the project.

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📜 License

This project is open-source. Use it for learning, demos, or further development.