scholarly journals Replica-Mean-Field Limits for Intensity-Based Neural Networks

2019 ◽  
Vol 18 (4) ◽  
pp. 1756-1797
Author(s):  
François Baccelli ◽  
Thibaud Taillefumier
Keyword(s):  
Neural Networks ◽  
Mean Field ◽  
Mean Field Limits

scholarly journals Stochastic mean-field formulation of the dynamics of diluted neural networks

2015 ◽  
Vol 16 (S1) ◽  
Author(s):  
David Angulo-Garcia ◽  
Alessandro Torcini
Keyword(s):  
Neural Networks ◽  
Mean Field

scholarly journals Mean field limits for interacting Hawkes processes in a diffusive regime

Bernoulli ◽  
2022 ◽  
Vol 28 (1) ◽  
Author(s):  
Xavier Erny ◽  
Eva Löcherbach ◽  
Dasha Loukianova
Keyword(s):  
Mean Field ◽  
Hawkes Processes ◽  
Diffusive Regime ◽  
Mean Field Limits

scholarly journals Neutral Stability, Rate Propagation, and Critical Branching in Feedforward Networks

2013 ◽  
Vol 25 (7) ◽  
pp. 1768-1806 ◽  
Author(s):  
N. Alex Cayco-Gajic ◽  
Eric Shea-Brown
Keyword(s):  
Neural Networks ◽  
Markov Chain ◽  
Mean Field ◽  
Neutral Stability ◽  
Feedforward Networks ◽  
Firing Rates ◽  
Wide Range ◽  
Complex Models ◽  
Dynamical Properties ◽  
Parameter Ranges

Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing patterns. We seek the simplest setting in which these properties emerge, clarifying their origin and relationship in random, feedforward networks of McCullochs-Pitts neurons. Two key parameters are the thresholds at which neurons fire spikes and the overall level of feedforward connectivity. When neurons have low thresholds, we show that there is always a connectivity for which the properties in question all occur, that is, these networks preserve overall firing rates from layer to layer and produce broad distributions of activity in each layer. This fails to occur, however, when neurons have high thresholds. A key tool in explaining this difference is the eigenstructure of the resulting mean-field Markov chain, as this reveals which activity modes will be preserved from layer to layer. We extend our analysis from purely excitatory networks to more complex models that include inhibition and local noise, and find that both of these features extend the parameter ranges over which networks produce the properties of interest.

scholarly journals Mean-field limits of the quantum Potts model

1983 ◽  
Vol 90 (3) ◽  
pp. 373-387 ◽  
Author(s):  
A. Cant ◽  
Paul A. Pearce
Keyword(s):  
Potts Model ◽  
Mean Field ◽  
Mean Field Limits
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