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arXiv · 1910.05780

Edge of chaos and avalanches in neural networks with heavy-tailed synaptic weight distribution

Łukasz Kuśmierz·Shun Ogawa·Taro Toyoizumi
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Abstract

We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous transition to chaos and can reproduce biologically relevant low activity levels and scale-free avalanches, i.e. bursts of activity with power-law distributions of sizes and lifetimes. In contrast, the Gaussian counterpart exhibits a discontinuous transition to chaos and thus cannot be poised near the edge of chaos. We validate our predictions in simulations of networks of binary as well as leaky integrate-and-fire neurons. Our results suggest that heavy-tailed synaptic distribution may form a weakly informative sparse-connectivity prior that can be useful in biological and artificial adaptive systems.

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Łukasz Kuśmierz, Shun Ogawa, Taro Toyoizumi. 2019-10-13. Edge of chaos and avalanches in neural networks with heavy-tailed synaptic weight distribution. https://doi.org/10.1103/physrevlett.125.028101

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