Fixed-point theorems in training deep neural networks

Patil, Praniti Ram; Rajpurohit, Suresh Singh; Joshi, Manthan; Dave, Harsha; Gojare, Aakash Mansaram; Parkar, Ashwini Prasad

doi:10.47974/JIM-2505

Open Access Research Article

Fixed-point theorems in training deep neural networks

Praniti Ram Patilpranitirpatil@gmail.comDepartment of Information TechnologyDwarkadas Jivanlal Sanghvi College of EngineeringMumbai, Maharashtra, 400056, IndiaView full profile → , ^*Suresh Singh RajpurohitCorresponding authorsrajpurohit422@gmail.comDepartment of Artificial Intelligence and Machine LearningKandivaliThakur Shyamnarayan Engineering CollegeMumbai, Maharashtra, 400101, IndiaView full profile → , Manthan Joshimanthan.joshi@slrtce.inDepartment of Information TechnologyShree L.R. Tiwari College of EngineeringThane, Maharashtra, 401107, IndiaView full profile → , Harsha Davedaveharsha.dave@gmail.comDepartment of Computer EngineeringShree L. R. Tiwari College of EngineeringThane, Maharashtra, 401107, IndiaView full profile → , Aakash Mansaram Gojareaakashgojare10@gmail.comDepartment of Computer EngineeringShree L. R. Tiwari College of EngineeringThane, Maharashtra, 401107, IndiaView full profile → , Ashwini Prasad Parkarparkarashwini14@gmail.comDepartment of Computer Science and Engineering (Data Science)Parshvanath Charitable Trust’s A. P. Shah Institute of TechnologyThane, Maharashtra, 400615, IndiaView full profile →

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pp. 701–708Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2505XML

Received:: 01 Mar 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2505
Pages:: 701–708

Abstract

This paper discuss fixed-point theories can be used to train deep neural networks. We find a mathematical link between nonlinear analysis and learning dynamics by looking at neural network optimisation as a fixed-point problem. In repeated training processes, fixed-point formulas ensure convergence, stability, and equilibrium in a theoretical sense. The results of experiments show that fixed-point–based algorithms are faster and more stable than standard optimisation methods such as Adam and gradient descent. This study shows how fixed-point principles can help make learning methods for complicated neural systems more accurate, easy to understand, and effective.

Keywords

Fixed-Point theorems Deep learning Convergence Stability Optimization

Subject Classifications

37C2568T07

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