Logic and learning in network cascades

Galen J Wilkerson,Sotiris Moschoyiannis

doi:10.1017/nws.2021.3

Abstract

AbstractCritical cascades are found in many self-organizing systems. Here, we examine critical cascades as a design paradigm for logic and learning under the linear threshold model (LTM), and simple biologically inspired variants of it as sources of computational power, learning efficiency, and robustness. First, we show that the LTM can compute logic, and with a small modification, universal Boolean logic, examining its stability and cascade frequency. We then frame it formally as a binary classifier and remark on implications for accuracy. Second, we examine the LTM as a statistical learning model, studying benefits of spatial constraints and criticality to efficiency. We also discuss implications for robustness in information encoding. Our experiments show that spatial constraints can greatly increase efficiency. Theoretical investigation and initial experimental results also indicate that criticality can result in a sudden increase in accuracy.

Highlights

Critical network cascades are ubiquitous, found in brain function, social and biological systems, epidemics (SIR model), and many other selforganizing systems where there is interaction between entities (Bak et al, 1987; Easley et al, 2010; Newman, 2018)
A very simple Boolean model that undergoes critical cascades as a function of network topology is available (Watts, 2002) as a networked version of the linear threshold model (LTM) (Sakoda, 1971; Schelling, 1971; Granovetter, 1978), which we use as a basis for simple, biologically motivated learning
We develop an antagonistic linear threshold model (ALTM), by taking the complement of the original labeling rule, and show that it can compute universal logic

Summary

Introduction

Critical network cascades are ubiquitous, found in brain function (neuronal avalanches), social and biological systems (information cascades), epidemics (SIR model), and many other selforganizing systems where there is interaction between entities (Bak et al, 1987; Easley et al, 2010; Newman, 2018). A very simple Boolean model that undergoes critical cascades ( known as avalanches) as a function of network topology is available (Watts, 2002) as a networked version of the linear threshold model (LTM) (Sakoda, 1971; Schelling, 1971; Granovetter, 1978), which we use as a basis for simple, biologically motivated learning. Of particular interest are logic computation, spatial (geometric) constraints, criticality, lack of type I error, and information encoding This is a preliminary investigation of these simple modifications, how they scale over large networks, and their effect on the network’s ability to solve problems. Information coding may be important as an efficient way for the network to take in information or express its action (Dayan & Abbott, 2001)

Methods

Results

Discussion

Conclusion