A convergent Deep Learning algorithm for approximation of polynomials
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 con...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.462/ |
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| Summary: | 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^\infty $ 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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| ISSN: | 1778-3569 |