arXiv Machine Learning By Wei Liu, Eleni Chatzi, Zhilu Lai

On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators

Read the original on arXiv Machine Learning →

arXiv:2509. 19830v3 Announce Type: replace Abstract: Kolmogorov-Arnold Networks (KANs) approximate multivariate functions by composing univariate transformations through additive or multiplicative aggregation.

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arXiv Machine Learning
Sep 2

Dense Weak Hiding: Closing Complexity Gaps in Nonconvex and PL Finite-Sum Optimization under Individual Smoothness

The paper establishes the optimal incremental first‑order oracle (IFO) complexity for nonconvex finite‑sum optimization under individual smoothness, proving a matching lower bound that closes a previously missing √{n} factor. It also refines the analysis of the PAGE algorithm under the global Polyak‑Lojasiewicz condition, providing tighter guarantees for different ranges of the condition number. The authors introduce a novel dense weak hiding construction that yields these lower bounds and demonstrates the limits of existing methods.

By Yuxing Peng, Zhiqing Tang, Weijia Jia
arXiv Machine Learning
Sep 4

A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations

arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.

By Ruiyang Hong, Hrad Ghoukasian, Anastasis Kratsios