"Memory foam" approach to unsupervised learning

TL;DR

This paper introduces a novel unsupervised learning system modeled as a dynamical system that adapts its vector field to input signals, converging to stable patterns that represent probable data features, demonstrated with musical signals.

Contribution

It presents a new mathematical framework for unsupervised learning based on dynamical systems that automatically form stable patterns from input data.

Findings

System converges to stable fixed points representing data patterns

Automatically shapes vector fields based on input signals

Effective in modeling musical signals

Abstract

We propose an alternative approach to construct an artificial learning system, which naturally learns in an unsupervised manner. Its mathematical prototype is a dynamical system, which automatically shapes its vector field in response to the input signal. The vector field converges to a gradient of a multi-dimensional probability density distribution of the input process, taken with negative sign. The most probable patterns are represented by the stable fixed points, whose basins of attraction are formed automatically. The performance of this system is illustrated with musical signals.