Modeling learning and strategy formation as phase transitions in cortical networks

Abstract

Abstract-Learning in the mammalian brain is commonly modeled through changing synaptic connections in cortical networks. Dynamical brain models indicate that learning leads to the formation of limit cycle oscillations across cortical areas and that the oscillatory regimes re-emerge when the learnt input is presented to the system. In this work, learning is modeled using a graph-theoretical model, which captures salient characteristics of the learning process. We introduce a random graph that combines a torus with lattice edges and additional random edges, which have power law length distribution. On this graph, we consider bootstrap percolation with excitatory and inhibitory vertices. Theoretical and numerical studies indicate the presence of various dynamical regimes on these graphs. Here, the transitions between fixed-point and limit cycle attractors are analyzed. We link this transition to changes in cortical networks during category learning, which have been observed in animal experiments using electro-cortiograph (ECoG) arrays over sensory cortices. We discuss how learning leads to categorization and strategy formation, and how the theoretical modeling results can be used for designing learning and adaptation in computationally aware intelligent machines.

State Transitions During Discrimination Learning in the Gerbil Auditory Cortex Analyzed by Network Causality Metrics

“…This work is the extension of the preliminary results reported by Kozma et al (2016b) at IEEE SMC2016 conference, with permission. We thank Kathrin Ohl for performing animal surgeries and technical assistance.…”

“…It is possible to describe the dynamics of BP with two types of (excitatory and inhibitory) nodes (Kozma et al, 2016b). In this case, one needs to find the solutions of the following set of fixed-point equations, for the mathematically derived nonlinear mapping functions f 1 (x, y) and f 2 (x, y):…”

“…The fixed point can be either stable or unstable, which determines the nature of the percolation dynamics, e.g., fixed point, limit cycle, or non-periodic oscillations (Kozma et al, 2016b). Numerical examination of BP with two types of vertices shows dynamic behavior that is richer than in BP with only one type of vertices.…”

“…We introduce a mathematical model of neurodynamical processes across the cortical layers, based on percolation processes in graphs and networks (Balister et al, 2006;Kozma et al, 2016b;Janson et al, 2019). Of special interest is the adaptation of brain networks during the learning process.…”

“…Zero fixed point (light green) is shown in the lower segment of the phase diagram. The region corresponding to the hypothetic cognitive phase transitions is illustrated by pink arrows; modified and reprinted with permission fromKozma et al (2016b).…”