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BP: Fachverband Biologische Physik
BP 15: Focus session: Collective Dynamics in Neural Networks
BP 15.5: Vortrag
Mittwoch, 3. April 2019, 10:45–11:00, H11
Functional Renormalization Group for Stochastic Rate Neurons — •Tobias Kühn1, Jonas Stapmanns1,2, David Dahmen1, Carsten Honerkamp2, and Moritz Helias1,3 — 1Institute of Neuroscience and Medicine (INM-6), Forschungszentrum Juelich, Germany — 2Institute for Theoretical Solid State Physics, RWTH Aachen, Germany — 3Department of Physics, Faculty 1, RWTH Aachen, Germany
It is often suggested that the cortex operates close to a critical point at which linear response theory fails since the neural dynamics is dominated by large fluctuations on all length scales. The functional Renormalization Group (fRG) is not stained with this flaw because in principle it treats statistics of arbitrary order in an unbiased and self-consistent way. We apply fRG to a self-interacting, stochastic, quadratic rate neuron and show how this method incorporates corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To obtain a simplified treatment of the frequency-dependence of all observables, we adapt the Blaizot Méndez-Galain Wschebor (BMW) scheme to the vertex expansion, which yields good predictions.
We expect that the insights into fRG-techniques gained within our study will help to tackle challenges occurring in the description of phenomena in spatially extended networks, notably the calculation of critical exponents and the coarse-graining of microscopic models.