Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study
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Abstract (arXiv)
Kolmogorov-Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility and interpretability. While KANs have been applied successfully across scientific and machine learning tasks, their initialization strategies remain largely unexplored. In this work, we study initialization schemes for spline-based KANs, proposing two theory-driven approaches inspired by LeCun and Glorot, as well as an empirical power-law family with tunable exponents. Our evaluation combines large-scale grid searches on function fitting and forward PDE benchmarks, an analysis of training dynamics through the lens of the Neural Tangent Kernel, and evaluations on a subset of the Feynman dataset. Our findings indicate that the Glorot-inspired initialization significantly outperforms the baseline in parameter-rich models, while power-law initialization achieves the strongest performance overall, both across tasks and for architectures of varying size. All code and data accompanying this manuscript are publicly available at https://github.com/srigas/KAN_Initialization_Schemes.
Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 20 of its 31 references that are in the map. First posted on arXiv 3 Sep 2025.
Builds on
20 of 31 references.
References · 20
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- 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
- 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
- 2024KAN: Kolmogorov-Arnold Networkscited by 634
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
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- 2015All you need is a good initcited by 124
- 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
- 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 82
- 2023Residual-based attention in physics-informed neural networkscited by 72
- 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
- 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 64
8 more
- 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
- 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 36
- 2024On the expressiveness and spectral bias of KANscited by 36
- 2024A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Datacited by 25
- 2024Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometriescited by 11
- 2024On the Robustness of Kolmogorov-Arnold Networks: An Adversarial Perspectivecited by 11
- 2024Deep Learning Alternatives of the Kolmogorov Superposition Theoremcited by 11
- 2024Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networkscited by 11
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Citing papers per year: 2025: 2; 2026: 8.
10 papers.
- 2025KANO: Kolmogorov-Arnold Neural Operatorcited by 6
- 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accuratecited by 3
- 2026SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networkscited by 2
- 2025Optimized Architectures for Kolmogorov-Arnold Networkscited by 1
- 2026Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networkscited by 1
- 2026A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networkscited by 1
- 2026Partition-of-Unity Gaussian Kolmogorov-Arnold Networkscited by 1
- 2026KANs need curvature: penalties for compositional smoothnesscited by 0
- 2026An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networkscited by 0
- 2026LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Predictioncited by 0
- 2026LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction28 Sep 2026
- 2026An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks9 Jun 2026
- 2026KANs need curvature: penalties for compositional smoothness4 May 2026
- 2026Partition-of-Unity Gaussian Kolmogorov-Arnold Networks26 Apr 2026
- 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate23 Apr 2026
- 2026SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks19 Mar 2026
- 2026A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks26 Jan 2026
- 2026Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks20 Jan 2026
- 2025Optimized Architectures for Kolmogorov-Arnold Networks13 Dec 2025
- 2025KANO: Kolmogorov-Arnold Neural Operator20 Sep 2025