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.
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:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv:2606. 30935v1 Announce Type: cross Abstract: While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints.
arXiv:2607. 09710v1 Announce Type: new Abstract: Tabular classification is often governed by local, condition-triggered rules rather than smooth global patterns.
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
arXiv:2512. 24780v2 Announce Type: replace Abstract: Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking.
arXiv:2606. 28444v1 Announce Type: cross Abstract: Classical universal approximation theorems establish the expressive power of sigmoidal multilayer perceptrons, but they do not prescribe how initial weights should encode the geometry of a data distribution.