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Pré-Publication, Document De Travail Année : 2022

A CONVERGENT DEEP LEARNING ALGORITHM FOR APPROXIMATION OF POLYNOMIALS

Bruno Després
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Résumé

We start from the contractive functional equation proposed in [4], where it was shown that the polynomial solution of functional equation can be used to initialize a Neural Network structure, with a controlled accuracy. We propose a novel algorithm, where the functional equation is solved with a converging iterative algorithm which can be realized as a Machine Learning training method iteratively with respect to the number of layers. The proof of convergence is performed with respect to the L ∞ norm. Numerical tests illustrate the theory and show that stochastic gradient descent methods can be used with good accuracy for this problem.
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Dates et versions

hal-03762185 , version 1 (26-08-2022)

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  • HAL Id : hal-03762185 , version 1

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Bruno Després. A CONVERGENT DEEP LEARNING ALGORITHM FOR APPROXIMATION OF POLYNOMIALS. 2022. ⟨hal-03762185⟩
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