MonoKAN: Certified monotonic Kolmogorov-Arnold network

Area of Science:

• Artificial Intelligence
• Machine Learning
• Explainable AI (XAI)

Background:

• Artificial Neural Networks (ANNs) excel at pattern recognition but lack interpretability.
• Explainable AI (XAI) methods improve transparency, but interpretability alone is often insufficient for critical applications.
• Partial monotonicity constraints are crucial in some domains, but traditional ANNs struggle to meet these requirements while maintaining interpretability.

Purpose of the Study:

• To introduce a novel ANN architecture, MonoKAN, that enhances interpretability and achieves certified partial monotonicity.
• To address the limitations of existing monotonic approaches in ANNs.
• To provide a more transparent and reliable AI model for applications requiring expert-imposed constraints.

Main Methods:

• Developed the MonoKAN architecture based on the Kolmogorov-Arnold Network (KAN) framework.
• Utilized cubic Hermite splines with conditions ensuring monotonicity.
• Employed positive weights in spline linear combinations to preserve monotonic relationships.

Main Results:

• MonoKAN demonstrates enhanced interpretability compared to traditional ANNs and existing monotonic models.
• The architecture achieves certified partial monotonicity.
• Experimental results show improved predictive performance on benchmarks, outperforming state-of-the-art monotonic Multi-layer Perceptrons (MLPs).

Conclusions:

• MonoKAN offers a promising solution for developing interpretable and reliably monotonic ANNs.
• The novel architecture balances predictive accuracy with crucial transparency and constraint satisfaction.
• MonoKAN advances the field of explainable AI by providing a practical approach to certified partial monotonicity.