KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
The kolmogorov superposition theorem can break the curse of dimensionality when approximating high dimensional functions
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For rational multivariate functions, the Kolmogorov Superposition Theorem allows variable decoupling by inspection with no computation using the Loewner Framework.
Transformers achieve approximation and generalization error bounds for noisy manifold regression that scale with the intrinsic dimension of the task-level manifold.
Wahkon unifies Kolmogorov superposition with RKHS regularization to produce a deep network whose penalized estimator is exactly the MAP under a hierarchical GP prior and achieves minimax-optimal rates.
InfinityKAN is a variational inference method that learns the number of basis functions per layer in KANs during training, matching or exceeding fixed-basis KAN performance across 18 datasets without manual selection.
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.
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.
citing papers explorer
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KAN: Kolmogorov-Arnold Networks
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
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Variable decoupling and the Kolmogorov Superposition Theorem for rational functions
For rational multivariate functions, the Kolmogorov Superposition Theorem allows variable decoupling by inspection with no computation using the Loewner Framework.
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Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights
Transformers achieve approximation and generalization error bounds for noisy manifold regression that scale with the intrinsic dimension of the task-level manifold.
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Wahkon: A Statistically Principled Deep RKHS Superposition Network
Wahkon unifies Kolmogorov superposition with RKHS regularization to produce a deep network whose penalized estimator is exactly the MAP under a hierarchical GP prior and achieves minimax-optimal rates.
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Variational Kolmogorov-Arnold Network
InfinityKAN is a variational inference method that learns the number of basis functions per layer in KANs during training, matching or exceeding fixed-basis KAN performance across 18 datasets without manual selection.
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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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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.