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.
Demonstrating the efficacy of kolmogorov-arnold networks in vision tasks
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The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
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 practitioner's selection guide plus open challenges.
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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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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
P1-KAN introduces a new KAN architecture with theoretical approximation guarantees that outperforms MLPs and prior KAN variants on irregular functions while matching spline KAN accuracy on smooth ones, demonstrated on hydraulic optimization.
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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 practitioner's selection guide plus open challenges.