5 papers
Universality of the mean-field equations of networks of Hopfield-like neurons
Olivier Faugeras, Etienne Tanré
We revisit the problem of characterising the mean-field limit of a network of Hopfield-like neurons. Building on the previous works of Ben Arous and Guionnet we establish for a lar…
Asymptotic behavior of a network of neurons with random linear interactions
Olivier Faugeras, Émilie Soret, Etienne Tanré
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which…
Stochastic neural field equations: A rigorous footing
Olivier Faugeras, James Inglis
We extend the theory of neural fields which has been developed in a deterministic framework by considering the influence spatio-temporal noise. The outstanding problem that we here…
Correlation structure of stochastic neural networks with generic connectivity matrices
D. Fasoli, O. Faugeras
Using a perturbative expansion for weak synaptic weights and weak sources of randomness, we calculate the correlation structure of neural networks with generic connectivity matrice…
Finite size effects in the correlation structure of stochastic neural networks: analysis of different connectivity matrices and failure of the mean-field theory
D. Fasoli, O. Faugeras
We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a…