A lightweight neural network library built from scratch in modern C++.

Axion++ is a proof-of-concept educational neural network library that builds every major component from first principles starting with linear algebra and evolving incrementally into a complete deep learning engine. It relies on no external ML frameworks and is designed to be read, understood, and extended. Status: Under Construction

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Features (v0.1.0)

Matrix Library

Operation	Description
Matrix(rows, cols)	Zero-initialized matrix
Matrix(axion::matrix)	Construct from 2D vector
identity(n)	Convert to n×n identity matrix
fill(val)	Fill entire matrix with a value
A + B, A - B, A * B	Matrix–matrix arithmetic
A + x, A - x, A * x, A / x	Scalar arithmetic
transpose()	Returns the transposed matrix
A(i, j)	Element access
A == B, A != B	Equality comparison
rows_(), cols_()	Dimension accessors
cin >> A, cout << A	Stream I/O

Exceptions

All errors derive from axion::AxionError:

• MatrixDimensionError — incompatible shapes
• InvalidIndexError — out-of-bounds access
• InvalidShapeError — malformed construction
• DivisionByZeroError — scalar division by zero

Building

Requirements: CMake ≥ 3.20, C++20 compiler, Ninja (optional)

git clone https://github.com/vk22006/axion-plusplus.git
cd axion-plusplus

cmake -S . -B build -G Ninja
cmake --build build

Run Tests

ctest --test-dir build --output-on-failure

Generate Documentation

cmake --build build --target doc

Docs are generated into the docs/ directory using Doxygen.

Quick Start

#include <iostream>
#include <axion/matrix.hpp>

int main() {
    // Construct from a 2D initializer list
    axion::Matrix A({
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    });

    // Matrix arithmetic
    axion::Matrix B = A * 2;
    axion::Matrix C = A + B;

    // Transpose
    axion::Matrix T = A.transpose();

    // Element access
    std::cout << "A(1,1) = " << A(1, 1) << "\n";

    // Dimensions
    std::cout << "Rows: " << A.rows_() << ", Cols: " << A.cols_() << "\n";

    // Stream output
    std::cout << C;

    return 0;
}

More examples are in the examples/ directory.

Project Structure

axion-plusplus/
├── include/axion/     # Public headers
│   ├── config.hpp     # Core type aliases
│   ├── version.hpp    # Version constants
│   ├── exceptions.hpp # Exception hierarchy
│   └── matrix.hpp     # Matrix class
├── src/               # Implementation files
├── tests/             # CTest unit tests (9 suites)
├── benchmarks/        # Matrix performance benchmarks
├── examples/          # Standalone usage examples
├── docs/              # Doxygen-generated documentation
└── CMakeLists.txt

Roadmap

Axion++ grows incrementally. Planned milestones beyond v0.1.0:

• v0.2.0 — Dense (fully-connected) layer
• v0.3.0 — Activation functions (ReLU, Sigmoid, Tanh)
• v0.4.0 — Loss functions and optimizer (gradient descent)
• v0.5.0 — Backpropagation engine
• v1.0.0 — Model persistence, dataset utilities, full training pipeline

The project intentionally prioritizes clarity and maintainability over raw performance.

Technologies

Tool	Purpose
C++20	Core language
CMake	Build system
CTest	Unit testing
Doxygen	API documentation
GitHub Actions	Continuous integration

Contributing

Contributions, bug reports, and suggestions are welcome! Please read CONTRIBUTING.md before opening a pull request.

Changelog

See CHANGELOG.md for a full history of changes.

License

This project is licensed under the MIT License — © 2026 Kishore V.