A FUNCTIONAL EQUATION WITH POLYNOMIAL SOLUTIONS AND APPLICATION TO NEURAL NETWORKS - Sorbonne Université
Journal Articles Comptes Rendus. Mathématique Year : 2020

A FUNCTIONAL EQUATION WITH POLYNOMIAL SOLUTIONS AND APPLICATION TO NEURAL NETWORKS

Abstract

We construct and discuss a functional equation with contraction property. The solutions are real univariate polynomials. The series solving the natural fixed point iterations have immediate interpretation in terms of Neural Networks with recursive properties and controlled accuracy.
We construct and discuss a functional equation with contraction property. The solutions are real univariate polynomials. The series solving the natural fixed point iterations have immediate interpretation in terms of Neural Networks with recursive properties and controlled accuracy.

Domains

Numerical Analysis [math.NA] Artificial Intelligence [cs.AI]
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https://hal.sorbonne-universite.fr/hal-02959678

Submitted on : Tuesday, November 24, 2020-9:37:59 AM

Last modification on : Tuesday, July 16, 2024-11:20:03 AM

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Dates and versions

hal-02959678 , version 1 (07-10-2020)
hal-02959678 , version 2 (09-10-2020)
hal-02959678 , version 3 (24-11-2020)

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Bruno Després, Matthieu Ancellin. A FUNCTIONAL EQUATION WITH POLYNOMIAL SOLUTIONS AND APPLICATION TO NEURAL NETWORKS. Comptes Rendus. Mathématique, 2020, Tome 358 (2020) no. 9-10, pp. 1059-1072, ⟨10.5802/CRMATH.124⟩. ⟨hal-02959678v3⟩

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