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: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: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.
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.
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...
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...
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...
arXiv:2608.31120v1 Announce Type: new Abstract: The motivation for this paper is the investigation of the trade-offs implicit in probabilistic models used in machine learning. Models are often used t...
arXiv:2505. 24849v2 Announce Type: replace-cross Abstract: For three decades statistical mechanics has been providing a framework to analyse neural networks.
arXiv:2610.08592v1 Announce Type: new Abstract: CNet is a C++/CUDA framework for building and training deep complex-valued neural networks (CVNNs) and, more generally, for optimizing complex-valued f...
arXiv:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.
arXiv:2610.28025v1 Announce Type: cross Abstract: This paper studies the problem of aggregation in multiclass classification, generalizing existing results for binary classification. Given a finite d...
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.