Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability

TL;DR

This paper critically evaluates Kolmogorov-Arnold Networks, revealing they excel only in symbolic regression and face significant limitations in other domains due to computational costs and unsubstantiated theoretical claims.

Contribution

It provides a systematic, fair comparison of KANs against traditional models, clarifies their actual performance, and identifies conditions for their effective use and research gaps.

Findings

KANs outperform MLPs only in symbolic regression

KANs are 1.36-100x slower than traditional models

Theoretical claims about breaking the curse of dimensionality are unsubstantiated

Abstract

Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation functions. However, recent systematic evaluations reveal substantial discrepancies between theoretical claims and empirical evidence. This critical assessment examines KANs' actual performance across diverse domains using fair comparison methodologies that control for parameters and computational costs. Our analysis demonstrates that KANs outperform MLPs only in symbolic regression tasks, while consistently underperforming in machine learning, computer vision, and natural language processing benchmarks. The claimed advantages largely stem from B-spline activation functions rather than architectural innovations, and computational overhead (1.36-100x slower) severely limits practical deployment. Furthermore, theoretical claims about breaking the "curse of dimensionality" lack rigorous mathematical foundation. We systematically identify the conditions under which KANs provide value versus traditional approaches, establish evaluation standards for future research, and propose a priority-based roadmap for addressing fundamental limitations. This work provides researchers and practitioners with evidence-based guidance for the rational adoption of KANs while highlighting critical research gaps that must be addressed for broader applicability.