Аннотация:
Due to the inherent complexity of neural models, relating the spiking
activity of a network to its structure requires simplifying assumptions,
such as considering models in the thermodynamic mean-field limit.
In this limit, an infinite number of neurons interact via vanishingly
small interactions, thereby erasing the finite size geometry of
interactions.
To better capture the geometry in question, we analyze the activity of
neural networks in the replica-mean-field limit regime. Such models are made
of infinitely many replicas which interact according to the same basic
structure as that of the finite network of interest. Our main contribution
is an analytical characterization of the stationary dynamics of
intensity-based
neural networks with spiking reset and heterogeneous excitatory synapses in
this replica-mean-field limit. Specifically, we functionally characterize
the stationary dynamics of these limit networks via ordinary or partial
differential equations derived from the Poisson Hypothesis of queuing
theory.
We then reduce this functional characterization to a system of
self-consistency
equations specifying the stationary neuronal firing rates.
Joint work with T. Taillefumier.
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