arXiv:2407. 00966v3 Announce Type: replace Abstract: In traditional models of supervised learning, the goal of a learner-- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$-- is to output a hypothesis that is competitive (to within $\epsilon$) of the best fitting concept from some class.
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.
arXiv:2604. 21174v3 Announce Type: replace-cross Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis.
arXiv:2312. 14889v4 Announce Type: replace-cross Abstract: In this paper we revisit the classical method of partitioning classification and prove novel convergence rates under relaxed conditions, both for observable (non-privatised) and for privatised data.
arXiv:2512. 09084v3 Announce Type: replace Abstract: The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes.
arXiv:2602. 00511v3 Announce Type: replace Abstract: We introduce \emph{Partition of Unity Neural Networks} (PUNNs), a neural-network architecture for multiclass classification based on the classical mathematical notion of a partition of unity.
arXiv:2510. 22021v3 Announce Type: replace Abstract: Safety-critical applications of machine learning require uncertainty estimates that support reliable worst-case analysis.
arXiv:2605. 18662v2 Announce Type: replace Abstract: Noise-tolerant PAC learning of linear models has been of central interests in machine learning community since the last century.
RecKAN introduces a learnable recursive polynomial basis for Kolmogorov–Arnold Networks, replacing fixed bases like B-splines or Chebyshev polynomials. The basis is defined by a second‑order polynomial recurrence whose five coefficients are jointly learned with the network, enabling it to encompass classical families such as Chebyshev, Fibonacci, Pell, and Jacobsthal. Experiments across image, text, biomedical time‑series classification, and forecasting tasks show RecKAN outperforming parameter‑matched KAN baselines and achieving state‑of‑the‑art results on several benchmarks.
arXiv:2607. 15645v1 Announce Type: cross Abstract: Motivated by the challenge of testing distributions over high-dimensional or continuous domains, we study distribution testing with respect to bounded classes of distinguishers.
arXiv:2607. 01266v1 Announce Type: cross Abstract: We study binary classification problems whose decision sets are given by definable sets in o-minimal expansions of the real field.
arXiv:2509. 19830v3 Announce Type: replace Abstract: Kolmogorov-Arnold Networks (KANs) approximate multivariate functions by composing univariate transformations through additive or multiplicative aggregation.