11:00 am Tuesday, February 16, 2016
Math-Nuro-CS Seminar: A Phase Transition in Neural Coding by Thibaud Taillefumier (Princeton University) in GDC 2.216
The human brain comprises about 100 billion neurons connected via 100 trillion synapses. In principle, the comprehensive mapping of an organism’s entire neural connectome should elucidate how brains function. However, relating biological functions to network structures hinges on uncovering behaviorally relevant patterns of neural activity, i.e. on understanding the neural code. Here, we argue that the statistical regularity of neurals input controls whether a noisy integrate-and-fire neuron acts as a rate coder, with smooth firing probabilities, or as a temporal coder, with sharply defined spiking times. Mathematically, this coding dichotomy is due to a phase transition affecting the first-passage-time (FPT) distribution of a diffusive process with barriers of varying roughness. The critical behavior occurs when the roughness of the barrier equals the roughness of the diffusive process, which corresponds to uncorrelated balanced neural inputs. For smoother barriers, the FPT distribution has a continuous probability density; for rougher barriers, the FPT distribution is concentrated on a Cantor-like set of zero measure. Our result suggests that the relation between input statistics and neural network structure determines whether a neuron conveys information via spiking times or firing rate. To explore this relation in modeled assemblies of noisy spiking neurons, we have developed exact simulation methods that generalize the Gillespie algorithm to reacting systems with memory. We anticipate that analyzing neural network dynamics will require new macroscopic limits that depart from traditional mean-field models. Submitted by
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