oikan 0.0.2.5

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.

Important Disclaimer: OIKAN is an experimental research project. It is not intended for production use or real-world applications. This framework is designed for research purposes, experimentation, and academic exploration of neuro-symbolic machine learning concepts.

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
• 🔬 Research-Focused: Designed for academic exploration and experimentation
• 📈 Multi-Task: Supports both regression and classification problems

Scientific Foundation

OIKAN implements the Kolmogorov-Arnold Representation Theorem through a novel neural architecture:

1. Theorem Background: Any continuous multivariate function f(x1,...,xn) can be represented as:

   f(x1,...,xn) = ∑(j=0 to 2n){ φj( ∑(i=1 to n) ψij(xi) ) }
   

   where φj and ψij are continuous single-variable functions.

2. Neural Implementation:

   # Pseudo-implementation of KAN architecture
   class KANLayer:
       def __init__(self, input_dim, output_dim):
           self.edges = [SymbolicEdge() for _ in range(input_dim * output_dim)]
           self.weights = initialize_weights(input_dim, output_dim)
   
       def forward(self, x):
           # Transform each input through basis functions
           edge_outputs = [edge(x_i) for x_i, edge in zip(x, self.edges)]
           # Combine using learned weights
           return combine_weighted_outputs(edge_outputs, self.weights)
   

3. Basis functions

# Edge activation contains interpretable basis functions
ADVANCED_LIB = {
      'x': (lambda x: x),          # Linear
      'x^2': (lambda x: x**2),     # Quadratic
      'sin(x)': np.sin,            # Periodic
      'tanh(x)': np.tanh          # Bounded
}

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 
model = OIKANRegressor()

# Fit model (sklearn-style)
model.fit(X_train, y_train, epochs=100, 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 testing and validation
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()
model.fit(X_train, y_train, epochs=100, lr=0.01)
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
# - Recommendations for testing and validation
model.save_symbolic_formula("classification_formula.txt")

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

Architecture Diagram

Key Design Principles

1. Interpretability First: All transformations maintain clear mathematical meaning
2. Scikit-learn Compatibility: Familiar .fit() and .predict() interface
3. Symbolic Formula Exporting: Export formulas as lightweight mathematical expressions
4. Automatic Simplification: Remove insignificant terms (|w| < 1e-4)

Key Model Components

1. EdgeActivation Layer:

   • Implements interpretable basis function transformations
   • Automatically prunes insignificant terms
   • Maintains mathematical transparency

2. Formula Extraction:

   • Combines edge transformations with learned weights
   • Applies symbolic simplification
   • Generates human-readable expressions

3. Training Process:

   • Gradient-based optimization of edge weights
   • Automatic feature importance detection
   • Complexity control through regularization

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.