First population risk bounds for KANs under mini-batch DP-SGD with correlated noise, using a new non-convex optimization analysis combined with stability-based generalization.
On the rate of convergence of K olmogorov-Arnold Network regression estimators,
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Deep KANs with edge functions from a finite affine family plus one fixed non-affine continuous function σ are dense in C(K) for compact K precisely when σ is non-affine.
For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.
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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Population Risk Bounds for Kolmogorov-Arnold Networks Trained by DP-SGD with Correlated Noise
First population risk bounds for KANs under mini-batch DP-SGD with correlated noise, using a new non-convex optimization analysis combined with stability-based generalization.
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Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks
Deep KANs with edge functions from a finite affine family plus one fixed non-affine continuous function σ are dense in C(K) for compact K precisely when σ is non-affine.
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Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks
For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.
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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.