A Formal Approach to Optimally Configure a Fully Connected Multilayer Hybrid Neural Network

Goutam Chakraborty (), Vadim Azhmyakov () and Luz Adriana Guzman Trujillo
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Goutam Chakraborty: Department of Software & Information Science, Iwate Prefectural University, Iwate Ken, Takizawa 020-0693, Japan
Vadim Azhmyakov: Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, A.P., India
Luz Adriana Guzman Trujillo: LARIS, University of Angers, 49000 Angers, France

Mathematics, 2024, vol. 13, issue 1, 1-18

Abstract: This paper is devoted to a novel formal analysis, optimizing the learning models for feedforward multilayer neural networks with hybrid structures. The proposed mathematical description replicates a specific switched-type optimal control problem (OCP). We have developed an equivalent, optimal control-based formulation of the given problem of training a hybrid feedforward multilayer neural network, to train the target mapping function constrained by the training samples. This novel formal approach makes it possible to apply some well-established optimal control techniques to design a versatile type of full connection neural networks. We next discuss the irrelevance of the necessity of Pontryagin-type optimality conditions for the construction of the obtained switched-type OCP. This fact motivated us to consider the so-called direct-solution approaches to the switched OCPs, which can be associated with the learning of hybrid neural networks. Concretely, we consider the generalized reduced-gradient algorithm in the framework of the auxiliary switched OCP.

Keywords: feedforward network; hybrid activation layers; deep network; discrete dynamic systems; switched optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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