This project explores the underlying mathematics of neural networks by implementing a simple classifier for the Iris dataset with manually set weights and biases. See each calculation with Linear and ReLU to see the math behind the model.

A custom Neural network but instead of traning it i manually set the parameters to see the data flow through the model to see the underlying math.

Rather than allowing a neural network to learn weights through training, this project:

• Sets weights and biases manually
• Implements custom linear transformations and ReLU activation functions
• Visualizes decision boundaries in 3D space
• Demonstrates how each component affects the final classification results

The model has a simple architecture:

• Input Layer: 2 nodes (petal_width, sepal_width)
• Hidden Layer: 2 nodes with ReLU activation
• Output Layer: 3 nodes (one for each Iris species: Setosa, Versicolor, Virginica)

The neural network uses:

1. Manual Weight Initialization:

   # First layer weights and biases
   weights1 = [[-2.5, 0.6],
               [-1.5, 0.4]]
   bias1 = [1.6, 0.7]
   
   # Second layer weights and biases
   weights2 = [[-0.1, 1.5],
               [2.4, -5.2],
               [-2.2, 3.7]]
   bias2 = [0.0, 0.0, 1.0]

2. Custom Linear Transformation:

   • Matrix multiplication of inputs with weights
   • Addition of bias term

3. Custom ReLU Activation:

   • Element-wise function that returns max(0, x)
   • Implemented manually to show the computation

The project includes comprehensive 3D visualizations showing:

• Probability surfaces for each class
• Decision boundaries between the three species
• How the feature space is divided based on the manually selected weights

This implementation demonstrates:

• How matrix operations and activation functions transform data through the network
• The impact of specific weight values on classification boundaries
• How a simple network with just 2 inputs and 2 hidden neurons can effectively separate the Iris classes
• The mathematical operations underlying "black box" neural networks

MIT License

Copyright (c) 2025 Morris Simons

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