Neural Network from Scratch in Go

🧠 Introduction

This package is written in Go (Golang) and implements a neural network from scratch — without using any external machine learning frameworks.
It’s designed to help you understand the mathematical foundations behind:

• Feed-forward neural networks
• Matrix operations
• Forward and backward propagation
• Gradient descent optimization

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⚙️ How a Multi-Layer Neural Network Works

A neural network consists of layers of neurons, each performing a mathematical transformation on the input data.

🔢 Inputs

Let X be a batch of input samples with shape (n × m):

• n → number of samples
• m → number of features per sample

⚖️ Biases and Weights

Each layer has:

• A weight matrix W of shape (k × m), where k is the number of neurons in the layer.
• A bias vector B of shape (k × 1), which shifts the activation values.

🔁 Forward Pass

For the first layer: output₁ = dot(X, W₁ᵀ) + B₁

For the second layer: output₂ = dot(output₁, W₂ᵀ) + B₂

This process continues for each layer, passing the output of one layer as the input to the next.
Finally, an activation function (such as ReLU or softmax) is applied to introduce non-linearity.

🔄 Backward Pass

During backpropagation:

• Gradients of the loss with respect to weights and biases are computed.
• Weights are updated using gradient descent:

W := W - learning_rate _ dW B := B - learning_rate _ dB

This allows the network to learn from errors.

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🧩 Example Architecture

Input (4 features) ↓ Dense Layer (3 neurons, ReLU) ↓ Dense Layer (3 neurons, ReLU) ↓ Output (Softmax)

Each layer performs a matrix multiplication, adds biases, and applies an activation function.

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📚 References

• NumPy Linear Algebra Documentation — for understanding matrix operations
• Matrix Multiplication — Wikipedia — mathematical foundation of forward pass
• Golang math Package Docs — Go’s standard math utilities
• Softmax Function — Wikipedia — for multi-class classification output
• Cross-Entropy Loss — Wikipedia — loss function used for classification

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🚀 Quick Start

# Clone this repository
git clone https://github.com/SobhanYasami/nn-go.git

cd nn-go

# Run the main example
go run ./cmd