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.
By Clemens Kinn, Philipp Petersen
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.
By Bal\'azs Csan\'ad Cs\'aji, L\'aszl\'o Gy\"orfi, Ambrus Tam\'as, Harro Walk
The paper introduces TOUCKANs, a variant of Kolmogorov–Arnold networks that use finite‑degree polynomial outer functions to create a decomposable sum–product structure. This design allows expectations, variances, and higher moments to be computed via deterministic recursions over one‑dimensional integrals, eliminating the need for costly Monte Carlo sampling even in high dimensions. Experiments on uniform and Gaussian benchmarks up to 50 dimensions show deterministic mean and variance errors below those of fixed‑budget Monte Carlo, and the method successfully enforces conservation laws and normalization constraints in physical simulations such as Cahn–Hilliard mass conservation and Schrödinger eigenpair computation.
By Juan Diego Toscano, Sascha Ranft, Zhiwei Gao, Li-Lian Wang, George Em Karniadakis
arXiv:2606.28444v2 Announce Type: replace-cross
Abstract: Classical universal approximation theorems (UAT) establish the expressive power of sigmoidal multilayer perceptrons, but they do not specify...
By Yi-Shan Chu
arXiv:2609.37958v1 Announce Type: new
Abstract: As the input dimension $n$ grows, rule-based machine learning, such as Learning Classifier Systems (LCSs), faces a fundamental scalability bottleneck f...
By Hiroki Shiraishi, Hisao Ishibuchi, Masaya Nakata
arXiv:2510.17072v2 Announce Type: replace
Abstract: Regression with non-Euclidean responses---e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions---has b...
By Kyum Kim, Yaqing Chen, Paromita Dubey