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

arXiv: https://arxiv.org/abs/2407.11075 · HTML: https://mlsanity.com/paper/2407.11075/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2024.

## Built on by (most cited first, 23 of 23)

- [KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation](https://mlsanity.com/paper/2512.12850/) (2025)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [Residual Kolmogorov-Arnold Network for Enhanced Deep Learning](https://mlsanity.com/paper/2410.05500/) (2024)
- [Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement](https://mlsanity.com/paper/2505.18131/) (2025)
- [Towards Intrinsic Interpretability of Large Language Models:A Survey of Design Principles and Architectures](https://mlsanity.com/paper/2604.16042/) (2026)
- [KACQ-DCNN: Uncertainty-Aware Interpretable Kolmogorov-Arnold Classical-Quantum Dual-Channel Neural Network for Heart Disease Detection](https://mlsanity.com/paper/2410.07446/) (2024)
- [KANs for Computer Vision: An Experimental Study](https://mlsanity.com/paper/2411.18224/) (2024)
- [Geometric Kolmogorov-Arnold Superposition Theorem](https://mlsanity.com/paper/2502.16664/) (2025)
- [Integrating Symbolic Neural Networks with Building Physics: A Study and Proposal](https://mlsanity.com/paper/2411.00800/) (2024)
- [KAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forward](https://mlsanity.com/paper/2411.10622/) (2024)
- [Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2502.06153/) (2025)
- [Enhancing Federated Learning with Kolmogorov-Arnold Networks: A Comparative Study Across Diverse Aggregation Strategies](https://mlsanity.com/paper/2505.07629/) (2025)
- [Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment](https://mlsanity.com/paper/2505.21592/) (2025)
- [Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.03345/) (2026)
- [On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2410.08041/) (2024)
- [KAN KAN Buff Signed Graph Neural Networks?](https://mlsanity.com/paper/2501.00709/) (2025)
- [TrafficKAN-GCN: Graph Convolutional-based Kolmogorov-Arnold Network for Traffic Flow Optimization](https://mlsanity.com/paper/2503.03276/) (2025)
- [Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective](https://mlsanity.com/paper/2507.14121/) (2025)
- [An Interpretable Multi-Plane Fusion Framework With Kolmogorov-Arnold Network Guided Attention Enhancement for Alzheimer's Disease Diagnosis](https://mlsanity.com/paper/2508.06157/) (2025)
- [Ultrafast On-Chip Online Learning via Spline Locality in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.02056/) (2026)
- [DualFlexKAN: Dual-stage Kolmogorov-Arnold Networks with Independent Function Control](https://mlsanity.com/paper/2603.08583/) (2026)
- [A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions](https://mlsanity.com/paper/2603.15307/) (2026)
- [KAN-CL: Per-Knot Importance Regularization for Continual Learning with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2605.12306/) (2026)

## Abstract (arXiv)

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.