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Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability
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Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability
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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.
Forward citations
Cited by 8 Pith papers
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KAN-CL: Per-Knot Importance Regularization for Continual Learning with Kolmogorov-Arnold Networks
KAN-CL cuts catastrophic forgetting by 88-93% on Split-CIFAR-10/5T and Split-CIFAR-100/10T by anchoring KAN parameters at per-knot granularity while matching baseline accuracy.
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KANEL\'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation
Quantized, pruned Kolmogorov-Arnold Networks can be compiled directly into FPGA lookup tables, achieving extreme latency/resource reductions and matching state-of-the-art LUT-based networks on several benchmarks.
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SCOPE and SCION: A Benchmark and an Auditable Reference Pipeline for Schema Induction and Fusion from Text
A 24-dataset benchmark for inducing schema graphs from raw text, plus an auditable LLM-based pipeline that reports the highest scores on the benchmark's four schema-similarity metrics.
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Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks
Derives generalized formulas for KAN inference complexity using RM, BOP, and NABS metrics across B-spline, GRBF, Chebyshev, and Fourier variants.
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Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models
iCKAN combines input-convex Kolmogorov-Arnold networks with a thermodynamic inelasticity framework to turn stress-strain data into symbolic elastic and inelastic potentials.
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Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks
Platform-independent formulas for KAN hardware inference complexity (RM, BOP, NABS) are derived for B-spline, GRBF, Chebyshev, and Fourier variants.
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Interpretable Clinical Classification with Kolmogorov-Arnold Networks
Logistic KAN and KAAM achieve competitive or superior accuracy on clinical datasets compared to linear, tree, and neural baselines while providing built-in interpretability via symbolic forms and feature-wise decompositions.
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A Practitioner's Guide to Kolmogorov-Arnold Networks
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a...
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