🧠 Simple Neural Network with NumPy

This project demonstrates how to build basic feedforward neural networks from scratch using only NumPy — no machine learning libraries like TensorFlow or PyTorch involved.

It includes two parts:

1. A 2-layer neural network (input → hidden → output)
2. A 1-layer neural network (input → output)

These examples are perfect for educational purposes to understand how neural networks work under the hood.

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📦 Requirements

Only one dependency is required:

numpy

Install with:

pip install numpy

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📁 File Overview

import numpy as np

• 🔹 Part 1: Two-Layer Neural Network

X = np.array([[0, 0, 1],
              [1, 1, 1],
              [1, 0, 1],
              [0, 1, 1]])
y = np.array([[0, 1, 1, 0]]).T

• Input: 4 samples, each with 3 binary features
• Output: XOR-like pattern

The network architecture:

• Input layer: 3 neurons
• Hidden layer: 4 neurons
• Output layer: 1 neuron
• Activation Function: Sigmoid

Training loop runs for 6,000 iterations using basic forward and backward propagation.

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• 🔹 Part 2: One-Layer Neural Network

X = np.array([[0, 0, 1],
              [1, 1, 1],
              [1, 0, 1],
              [0, 1, 1]])
y = np.array([[0, 0, 1, 1]]).T

This version simplifies the network to just:

• Input layer: 3 neurons
• Output layer: 1 neuron
• Activation Function: Sigmoid

Training loop runs for 10,000 iterations.

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🧮 Concepts Covered

• Forward propagation
• Sigmoid activation function and its derivative
• Backpropagation (gradient descent)
• Weight updates using error deltas
• Manual weight initialization

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📤 Output

At the end of training, the model prints the output predictions for the dataset:

Output after training
[[0.00966449]
 [0.00786506]
 [0.99358911]
 [0.99337711]]

These values approach the target outputs [0, 0, 1, 1], showing the network has learned the task.

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🔧 How to Run

1. Save the script as neural_network.py
2. Run it with:

python neural_network.py

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📚 Learning Resource

This project is inspired by early neural network tutorials, particularly from:

• Andrew Trask’s blog: “A Neural Network in 11 Lines of Python”

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📝 License

MIT License — feel free to modify and use for your own learning or projects.