arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
arXiv:2606. 28464v1 Announce Type: new Abstract: In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture.
arXiv:2508. 03867v2 Announce Type: replace-cross Abstract: We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in parameter space.
arXiv:2604. 14037v2 Announce Type: replace Abstract: Parameter space is not function space for neural network architectures.
arXiv:2605. 09609v2 Announce Type: replace Abstract: We provide counterexamples to the unimodal minimal filling architecture conjecture for polynomial neural networks (PNNs) with power activation functions.
arXiv:2410. 04907v2 Announce Type: replace-cross Abstract: In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions.
arXiv:2606. 04327v1 Announce Type: cross Abstract: We investigate the geometric structure of stationary plateaus that arise in the loss landscape of two-layer neural networks with smooth activation functions.
arXiv:2607. 08370v1 Announce Type: cross Abstract: We derive bounds for the volume of tubular neighbourhoods of smooth Pfaffian hypersurfaces, generalising known results for algebraic varieties.
arXiv:2603. 12785v2 Announce Type: replace Abstract: Three-layer neural networks are known to form singular learning models, and their Bayesian asymptotic behavior is governed by the learning coefficient, or real log canonical threshold.
The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error. However, the uniqueness of such neural network representations is not guaranteed, raising questions about practical identifiability.
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
arXiv:2606. 04754v1 Announce Type: new Abstract: Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged.
arXiv:2607. 18930v1 Announce Type: cross Abstract: The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error.