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

TL;DR

This paper conducts a rigorous, evidence-based critique of Kolmogorov-Arnold Networks (KANs), interrogating claims of universal superiority and interpretability. It shows that, when fairness in parameter and compute costs is enforced, KANs rival MLPs only in symbolic regression, while underperforming in machine learning, computer vision, NLP, and audio domains due to misaligned data properties and substantial overhead. The analysis attributes much of KANs' apparent advantages to the B-spline activation choice rather than architectural innovation and highlights theoretical gaps in their supposed 'curse-breaking' capabilities. The work culminates in a domain-aware roadmap, advocating specialized use in mathematical and scientific computing while charting practical improvements and rigorous evaluation standards for future research.

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.

Figures (4)

• Figure 1: Hierarchical Architecture of Kolmogorov-Arnold Networks: From Theoretical Foundations to Practical Implementation
• Figure 2: Performance Comparison Across Different Application Domains. The radar chart illustrates the relative performance of KAN (red) vs MLP (blue) across five major domains. KAN shows clear advantage only in symbolic regression, while consistently underperforming in other domains. Data derived from Yu et al. yu2024kan.
• Figure 3: Specialized KAN Applications Across Domains: A Comprehensive Taxonomy of Physics-Informed, Medical, Time Series, and Emerging Applications. This taxonomy presents the landscape of specialized KAN applications, categorized by domain expertise and demonstrating the focused nature of successful KAN deployments.
• Figure 4: KAN Performance Evaluation Across Application Domains: Success Patterns, Computational Overhead, and Critical Limitations. Performance assessment reveals domain-dependent KAN effectiveness, with clear success in mathematical domains (+150% to +600%) but systematic underperformance in mainstream ML applications, accompanied by significant computational overhead (1.36-100× training time).