oikan 0.0.2.1

OIKAN: Optimized Interpretable Kolmogorov-Arnold Networks

OIKAN: Optimized Interpretable Kolmogorov-Arnold Networks

Overview

OIKAN (Optimized Interpretable Kolmogorov-Arnold Networks) is a neuro-symbolic ML framework that combines modern neural networks with classical Kolmogorov-Arnold representation theory. It provides interpretable machine learning solutions through automatic extraction of symbolic mathematical formulas from trained models.

Key Features

• 🧠 Neuro-Symbolic ML: Combines neural network learning with symbolic mathematics
• 📊 Automatic Formula Extraction: Generates human-readable mathematical expressions
• 🎯 Scikit-learn Compatible: Familiar .fit() and .predict() interface
• 🚀 Production-Ready: Export symbolic formulas for lightweight deployment
• 📈 Multi-Task: Supports both regression and classification problems

Scientific Foundation

OIKAN is based on Kolmogorov's superposition theorem, which states that any multivariate continuous function can be represented as a composition of single-variable functions. We leverage this theory by:

1. Using neural networks to learn optimal basis functions
2. Employing SVD projection for dimensionality reduction
3. Applying symbolic regression to extract interpretable formulas

Quick Start

Installation

Method 1: Via PyPI (Recommended)

pip install -qU oikan

Method 2: Local Development

git clone https://github.com/silvermete0r/OIKAN.git
cd OIKAN
pip install -e .  # Install in development mode

Regression Example

from oikan.model import OIKANRegressor
from sklearn.model_selection import train_test_split

# Initialize model with optimal architecture
model = OIKANRegressor(
    hidden_dims=[16, 8],  # Network architecture
    num_basis=10,         # Number of basis functions
    degree=3,             # Polynomial degree
    dropout=0.1           # Regularization
)

# Fit model (sklearn-style)
model.fit(X_train, y_train, epochs=200, lr=0.01)

# Get predictions
y_pred = model.predict(X_test)

# Save interpretable formula to file with auto-generated guidelines
# The output file will contain:
# - Detailed symbolic formulas for each feature
# - Instructions for practical implementation
# - Recommendations for production deployment
model.save_symbolic_formula("regression_formula.txt")

Example of the saved symbolic formula instructions: outputs/regression_symbolic_formula.txt

Classification Example

from oikan.model import OIKANClassifier

# Similar sklearn-style interface for classification
model = OIKANClassifier(hidden_dims=[16, 8])
model.fit(X_train, y_train)
probas = model.predict_proba(X_test)

# Save classification formulas with implementation guidelines
# The output file will contain:
# - Decision boundary formulas for each class
# - Softmax application instructions
# - Production deployment recommendations
model.save_symbolic_formula("classification_formula.txt")

Example of the saved symbolic formula instructions: outputs/classification_symbolic_formula.txt

Architecture Details

OIKAN's architecture consists of three main components:

1. Basis Function Layer: Learns optimal single-variable transformations

   • B-spline bases for smooth function approximation
   • Trigonometric bases for periodic patterns
   • Polynomial bases for algebraic relationships

2. Neural Composition Layer: Combines transformed features

   • SVD projection for dimensionality reduction
   • Dropout for regularization
   • Skip connections for gradient flow

3. Symbolic Extraction Layer: Generates interpretable formulas

   • L1 regularization for sparse representations
   • Symbolic regression for formula extraction
   • LaTeX export for documentation

Contributing

We welcome contributions! Key areas of interest:

• Model architecture improvements
• Novel basis function implementations
• Improved symbolic extraction algorithms
• Real-world case studies and applications
• Performance optimizations

Please see CONTRIBUTING.md for guidelines.

Citation

If you use OIKAN in your research, please cite:

@software{oikan2025,
  title = {OIKAN: Optimized Interpretable Kolmogorov-Arnold Networks},
  author = {Zhalgasbayev, Arman},
  year = {2025},
  url = {https://github.com/silvermete0r/OIKAN}
}

License

This project is licensed under the MIT License - see the LICENSE file for details.