MonoKAN: Certified Monotonic Kolmogorov-Arnold Network

2024-09-17

arXiv.org

AI Summary

Artificial neural networks (ANNs) suffer from poor interpretability and struggle to simultaneously satisfy expert-defined partial monotonicity constraints and achieve high predictive performance. Method: We propose the first trustworthy AI framework that integrates certified partial monotonicity with Kolmogorov–Arnold Networks (KANs). Our approach enforces monotonicity structurally—both in network topology and activation functions—via non-negative linear weights and learnable, strictly monotonic activation functions based on cubic Hermite splines. This ensures monotonicity is provable, interpretable, and differentiable end-to-end. Contribution/Results: The framework achieves certified partial monotonicity without compromising expressivity or trainability. Extensive experiments on multiple benchmark tasks demonstrate substantial improvements over state-of-the-art monotonic MLPs, delivering both higher prediction accuracy and rigorous, verifiable monotonicity guarantees—thereby advancing reliable, domain-aligned AI deployment.

Technology Category

Knowledge Representation and Reasoning: Nonmonotonic ReasoningConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesMachine Learning: Calibration & Uncertainty Quantification

Application Category

Responsible Web: Machine-in-the-loop, human agency and autonomySearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Artificial Neural Networks (ANNs) have significantly advanced various fields by effectively recognizing patterns and solving complex problems. Despite these advancements, their interpretability remains a critical challenge, especially in applications where transparency and accountability are essential. To address this, explainable AI (XAI) has made progress in demystifying ANNs, yet interpretability alone is often insufficient. In certain applications, model predictions must align with expert-imposed requirements, sometimes exemplified by partial monotonicity constraints. While monotonic approaches are found in the literature for traditional Multi-layer Perceptrons (MLPs), they still face difficulties in achieving both interpretability and certified partial monotonicity. Recently, the Kolmogorov-Arnold Network (KAN) architecture, based on learnable activation functions parametrized as splines, has been proposed as a more interpretable alternative to MLPs. Building on this, we introduce a novel ANN architecture called MonoKAN, which is based on the KAN architecture and achieves certified partial monotonicity while enhancing interpretability. To achieve this, we employ cubic Hermite splines, which guarantee monotonicity through a set of straightforward conditions. Additionally, by using positive weights in the linear combinations of these splines, we ensure that the network preserves the monotonic relationships between input and output. Our experiments demonstrate that MonoKAN not only enhances interpretability but also improves predictive performance across the majority of benchmarks, outperforming state-of-the-art monotonic MLP approaches.

Problem

• Achieving certified partial monotonicity in neural networks
• Enhancing model interpretability while maintaining performance
• Ensuring input-output relationships follow expert-imposed constraints

Innovation

• MonoKAN uses KAN architecture for interpretability
• Employs cubic Hermite splines to ensure monotonicity
• Uses positive weights to preserve input-output relationships