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

Author

Listed:
  • Goutam Chakraborty

    (Department of Software & Information Science, Iwate Prefectural University, Iwate Ken, Takizawa 020-0693, Japan
    Department of Computer Science & Engineering, Madanapalle Institute of Technology & Science, Madanapalle 517325, A.P., India
    These authors contributed equally to this work.)

  • Vadim Azhmyakov

    (Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, A.P., India
    These authors contributed equally to this work.)

  • Luz Adriana Guzman Trujillo

    (LARIS, University of Angers, 49000 Angers, France
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Goutam Chakraborty & Vadim Azhmyakov & Luz Adriana Guzman Trujillo, 2024. "A Formal Approach to Optimally Configure a Fully Connected Multilayer Hybrid Neural Network," Mathematics, MDPI, vol. 13(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:129-:d:1557983
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