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Intelligent systems. Theory and applications, 2022, Volume 26, Issue 4, Pages 173–196
(Mi ista495)
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This article is cited in 1 scientific paper (total in 1 paper)
Part 3. Mathematical models
Convex CPL-functions recovering by neural networks on RELU-bases
V. G. Shishlyakov Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
The present paper considers a problem of functional classes obtained by using neural networks on max non-linearities bases. firstly, some properties of CPL-functions and equivalence classes generating them are investigated. Proceeding from these properties a theorem is proved that neural networks built on the basis of linear and max non-linearity functions can exactly recover any convex CPL-function.
Secondly, RELU-basis, a special case of max non-linearities bases, is investigated, with a theorem similar to the previous one mentioned above proved. The question of estimating the number of neurons and layers in obtained architectures is also discussed.
All the mentioned theorems have a constructive proof, i.e. neural network architectures with mentioned features are built explicitly.
Keywords:
Neural networks, architecture, functions recovery, functions expressibility, convex functions, particle-linear functions, ReLU function, max function.
Citation:
V. G. Shishlyakov, “Convex CPL-functions recovering by neural networks on RELU-bases”, Intelligent systems. Theory and applications, 26:4 (2022), 173–196
Linking options:
https://www.mathnet.ru/eng/ista495 https://www.mathnet.ru/eng/ista/v26/i4/p173
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Abstract page: | 23 | Full-text PDF : | 14 | References: | 7 |
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