Difference Equations and Machine Learning

This book presents in-depth explanations of well-known and recognized behaviors of neural networks in machine learning.  In addition, the author provides novel technical analyses of behaviors of discrete-time dynamical systems modeled as difference equations.  These analyses and their outcomes are closely related to models of very well-known neural networks such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) neural networks, which are widely used in machine learning and artificial intelligence (AI) applications.  The author also discusses difference equations and their relevance to neural networks, machine learning, and AI.

Introduction.- Linear Difference Equations.- Nonlinear Difference Equations.- Stability and Chaotic Behaviors of Difference Equations.- Control of Difference Equations.- Applications to Neural Networks and Machine Learning.- Conclusions.

Dušan Stipanovic, Ph.D., is a Professor in the Coordinated Science Laboratory and Department of Industrial and Enterprise Systems Engineering at University of Illinois Urbana-Champaign.  He received his B.S. in Electrical Engineering from the University of Belgrade, Serbia and his M.S.E.E. and Ph.D. in Electrical Engineering from Santa Clara University, California.  Dr. Stipanovic’s research interests include differential and difference equations, control and stability theory, neural networks, and differential games with applications in control of autonomous vehicles, machine learning and AI, precision agriculture, circuits, and medical robotics.