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We propose an analytically tractable neural connectivity model with power-lawdistributed synaptic strengths. When threshold neurons with biologicallyplausible number of incoming connections are considered, our model features acontinuous transition to chaos and can reproduce biologically relevant lowactivity levels and scale-free avalanches, i.e. bursts of activity withpower-law distributions of sizes and lifetimes. In contrast, the Gaussiancounterpart exhibits a discontinuous transition to chaos and thus cannot bepoised near the edge of chaos. We validate our predictions in simulations ofnetworks of binary as well as leaky integrate-and-fire neurons. Our resultssuggest that heavy-tailed synaptic distribution may form a weakly informativesparse-connectivity prior that can be useful in biological and artificialadaptive systems.

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