Self-organizing dynamical networks able to learn autonomously

TL;DR

This paper introduces a model for autonomous network evolution using stochastic non-markovian signals, enabling networks to self-organize and learn target functions through differential equations and algorithms.

Contribution

It develops a novel dynamical systems framework for self-organizing networks that can adapt their structure to achieve specific functionalities autonomously.

Findings

Networks can modify their structure to learn target functions.

The model applies to flow processing and chemical reaction networks.

Statistical analysis confirms effective self-organization under various parameters.

Abstract

We present a model for the time evolution of network architectures based on dynamical systems. We show that the evolution of the existence of a connection in a network can be described as a stochastic non-markovian telegraphic signal (NMTS). Such signal is formulated in two ways: as an algorithm and as the result of a system of differential equations. The autonomous learning conjecture [Phys. Rev. E \textbf{90},030901(R) (2014)] is implemented in the proposed dynamics. As a result, we construct self-organizing dynamical systems (networks) able to modify their structures in order to learn prescribed target functionalities. This theory is applied to two systems: the flow processing networks with time-programmed responses, and a system of first-order chemical reactions. In both cases, we show examples of the evolution and a statistical analysis of the obtained functional networks with respect to the model parameters.