Mathematical foundations of neural networks for modeling human cognition in AI systems

Malwade, Sulakshana; Lavate, Santosh H.; Borkar, Pradnya; Jadhav, Pundlik Dattatray

doi:10.47974/JIM-2500

Open Access Research Article

Mathematical foundations of neural networks for modeling human cognition in AI systems

Sulakshana Malwadesulakshana.malwade@mitwpu.edu.inDepartment of Computer Engineering School of Polytechnic and Skill Development Dr. Vishwanath Karad MIT World Peace UniversityDepartment of Polytechnic Dr. Vishwanath Karad MIT World Peace UniversityPune, Maharashtra, 411038, IndiaView full profile → , ^*Santosh H. LavateCorresponding authorlavate.santosh@gmail.comDepartment of Electronics and Telecommunication Engineering AISSMS College of EngineeringPune, Maharashtra, 411001, IndiaView full profile → , Pradnya Borkarpradnyaborkar2@gmail.comDepartment of Computer Science and Engineering Symbiosis Institute of Technology Nagpur Campus Symbiosis International (Deemed University)Department of Computer Science and Engineering Symbiosis Institute of Technology Nagpur Campus Symbiosis International (Deemed University)Pune, Maharashtra, 440027, IndiaView full profile → , Pundlik Dattatray Jadhavpdjadhav17@gmail.comDepartment of Computer Applications Institute of Engineering Bhujbal Knowledge City Department of Computer Applications Institute of Engineering Nashik, Maharashtra, 422002, IndiaView full profile →

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pp. 655–662Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2500XML

Received:: 01 Mar 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2500
Pages:: 655–662

Abstract

In this paper it examines the mathematical principles of the neural networks and how these can be applied to simulate the thoughts of people in computer systems that are expected to be intelligent. Certain significant aspects of the learning process are considered, such as linear algebra (with an emphasis on the operations of vectors and matrices) and calculus techniques such as the differentiation and gradients. The backpropagation technique is discussed in detail as one of the simplest approaches to training neural networks to minimize the error. There are also several optimization techniques including gradient descent and more advanced versions, which are considered to enhance the speed and precision of learning.

Keywords

Neural networks Vector metric space Orthogonal sequences Backpropagation Gradient descent

Subject Classifications

68T10 P68T27

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