arXiv AI July 22, 2026 By Anuragine S A, Prem Jagadeesan

Functional Equivalence and Geometric Diversity in Neural Network Approximations: An Empirical Characterization

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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Jul 21

Functional Equivalence and Geometric Diversity in Neural Network Approximations: An Empirical Characterization

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 Machine Learning

2d ago

Not all solutions are created equal: An analytical dissociation of functional and representational similarity in deep linear neural networks

arXiv:2609.38998v1 Announce Type: new Abstract: A foundational principle of connectionism is that perception, action, and cognition emerge from parallel computations among simple, interconnected unit...

By Lukas Braun, Erin Grant, Andrew M. Saxe

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arXiv Machine Learning

Sep 22

Approximating Smooth Functionals with ReLU Networks

arXiv:2609.15355v2 Announce Type: replace-cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by ReLU neural netw...

By Shuhao Jiao

arXiv Machine Learning

Sep 15

ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis

arXiv:2609.15355v1 Announce Type: cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural network...

By Shuhao Jiao

arXiv AI

Jun 26

Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation

arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.

By Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim, Gregory Cousins, Haitz S\'aez de Oc\'ariz Borde

arXiv Machine Learning

Jun 17

A Dynamical Systems Perspective on the Analysis of Neural Networks

arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.

By Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz

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Functional Equivalence and Geometric Diversity in Neural Network Approximations: An Empirical Characterization

Not all solutions are created equal: An analytical dissociation of functional and representational similarity in deep linear neural networks

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