Spontaneous Emergence of Computation, Classification, and Learning in Network Cascades
Creators: name: WILKERSON, GALEN JUSTUS
Publisher: name: University of Surrey
Year: 2022

description: Critical network cascades, as an instance of percolation, are ubiquitous in nature. As
description: such, they occur in the brain, and nearly any self-organized or naturally-occurring system
description: characterized by interactions.
description: Cascades have also been described as a simple model of decision making. Together
description: with information diffusion, their simplicity, and their ubiquity in nature, this makes them
description: a very interesting starting point for a theory of information processing in natural systems.
description: In the brain cascades may occur as neuronal avalanches, while in social networks they
description: can be manifested as epidemics, idea or rumor spreading, or viral consumption behavior.
description: Of course, they may occur in granular media such as sand or snow as avalanches, or in
description: chemical processes or many other systems.
description: Therefore, we may also reasonably ask why cascades do not play a large role in modern
description: artificial statistical- or machine- learning, and how we may conduct basic research into
description: information processing by natural systems. Here we take some steps to understand how
description: critical network cascades can process information. We do this by studying a simple,
description: theoretical model of critical network cascades, the Linear Threshold Model (LTM).
description: We show that Boolean logic can be computed by the LTM. Also a universal basis
description: (functional completeness) can be obtained by the LTM, by including a new type of
description: antagonistic node to create the antagonistic LTM (ALTM). We observe that the global
description: cascade frequency in the ALTM is approximately the inverse of that in the LTM.
description: Subsequently, we investigate the LTM as a classification and learning model, with
description: global cascades as the classifier, and identify sources of efficiency in learning. We
description: observe that certain types of error do not exist, and that Euclidean constraints can
description: increase efficiency significantly. We also note that the LTM automatically maps between
description: information encodings.
description: We then examine the phase space of Boolean functions computed by nodes in the
description: LTM (and mix of LTM/ALTM nodes), observing a decreasing exponential rank-ordering
description: of function frequency, inversely related to a function’s decision tree complexity. Thus
description: the LTM performs computational cascades, computed by simple sub-networks which are
description: logical automata or logic motifs. Using these motifs, we predict function probability by
description: the number of required paths, and that the number of paths of a function is its decision
description: tree complexity. We show that the Boolean function’s reflection asymmetry gives us this
description: complexity, and that the probability is proportional to that of the nodes belonging to
description: the giant connected component (GCC). Thus we arrive at the deeper observation that
description: symmetry breaking in the system (formation of the GCC) leads to symmetry breaking of
description: functions (complexity) computed.