Pattern theory: the mathematics of perception

TL;DR

This paper explores the mathematical foundations of perception and intelligence, emphasizing Bayesian inference and stochastic models like hidden Markov models to understand sensory signals and their relation to the external world.

Contribution

It provides a mathematical framework for perception based on stochastic models, highlighting the role of Bayesian inference in understanding sensory signals and world structures.

Findings

Bayesian inference is central to perception modeling.

Hidden Markov models effectively represent speech signals.

Mathematical challenges in perception modeling are discussed.

Abstract

Is there a mathematical theory underlying intelligence? Control theory addresses the output side, motor control, but the work of the last 30 years has made clear that perception is a matter of Bayesian statistical inference, based on stochastic models of the signals delivered by our senses and the structures in the world producing them. We will start by sketching the simplest such model, the hidden Markov model for speech, and then go on illustrate the complications, mathematical issues and challenges that this has led to.