Heavy-tailed connections support robust neural communication

In the synaptic wiring between neurons, some rare connections are orders of magnitude stronger than most. This heavy-tailed connectivity is ubiquitous across different species, brain regions, and cell types, suggesting that it serves a general purpose for neural function. Here, we show, both analytically and in simulations, that heavy-tailed connections reduce communication errors in the presence of synaptic noise. In minimal models of individual neurons, noisy connections induce errors at a rate that depends only on a simple network statistic, which we refer to as robustness. For a fixed number of incoming synapses, neurons with broader distributions of connection strength are more robust and, therefore, admit fewer errors. Across several connectomes, we find that real neurons are consistently more robust than comparable null networks. In the whole brain of the fruit fly Drosophila, robustness increases with distance from the sensory periphery, such that central neurons are more robust than those involved in sensory processing. Together, these results indicate that heavy-tailed connections may arise universally to fortify the brain against noise in communication.