Convolutional Fractional Stochastic Fields and their Deep Learning

In a stochastic environment where reality is described through samples or examples, artificial intelligence learns by penalizing weighted differential and/or integral viewpoints. The convolutional neural framework is relevant to encompass the mathematical operations performed by such an artificial intelligence. Conversely, mathematical compositions alternating convolutions and non linear operators are powerful tools for generating complex artificial realities.

This book proposes a stochastic integral perspective of deep machine learning in artificial intelligence. The organization of the book is as follows. Chapter 1 introduces the basics of stochastic reasoning and the most useful properties of stochastic processes. Chapters 2 and 3 derive stochastic convoluted models for the construction, analysis and simulation of fractionally integrated fields. Chapter 4 highlights how some deep artificial neurons can disentangle the very long-range stochastic dependencies, when these neurons are parameterized to integrate spectral responses.