FEKAN: Feature-Enriched Kolmogorov-Arnold Networks

2026-02-18

AI Summary

This work proposes Feature-Enhanced Kolmogorov–Arnold Networks (FEKAN) to address the limitations of existing Kolmogorov–Arnold Networks (KANs), which suffer from high computational cost and slow convergence, hindering their scalability. FEKAN enhances model expressivity and accelerates convergence through a feature augmentation mechanism without introducing additional trainable parameters, while preserving the interpretability inherent to KANs. Grounded in the Kolmogorov–Arnold representation theorem, FEKAN is well-suited for tasks such as function approximation, physics-informed neural networks, and neural operators. Experimental results demonstrate that FEKAN consistently outperforms current KAN variants across multiple benchmarks, achieving both higher accuracy and faster convergence.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Kolmogorov-Arnold Networks (KANs) have recently emerged as a compelling alternative to multilayer perceptrons, offering enhanced interpretability via functional decomposition. However, existing KAN architectures, including spline-, wavelet-, radial-basis variants, etc., suffer from high computational cost and slow convergence, limiting scalability and practical applicability. Here, we introduce Feature-Enriched Kolmogorov-Arnold Networks (FEKAN), a simple yet effective extension that preserves all the advantages of KAN while improving computational efficiency and predictive accuracy through feature enrichment, without increasing the number of trainable parameters. By incorporating these additional features, FEKAN accelerates convergence, increases representation capacity, and substantially mitigates the computational overhead characteristic of state-of-the-art KAN architectures. We investigate FEKAN across a comprehensive set of benchmarks, including function-approximation tasks, physics-informed formulations for diverse partial differential equations (PDEs), and neural operator settings that map between input and output function spaces. For function approximation, we systematically compare FEKAN against a broad family of KAN variants, FastKAN, WavKAN, ReLUKAN, HRKAN, ChebyshevKAN, RBFKAN, and the original SplineKAN. Across all tasks, FEKAN demonstrates substantially faster convergence and consistently higher approximation accuracy than the underlying baseline architectures. We also establish the theoretical foundations for FEKAN, showing its superior representation capacity compared to KAN, which contributes to improved accuracy and efficiency.

Problem

• Kolmogorov-Arnold Networks
• computational cost
• slow convergence
• scalability
• practical applicability

Innovation

• Feature Enrichment
• Kolmogorov-Arnold Networks
• Computational Efficiency
• Representation Capacity
• Convergence Acceleration