Stochastic models of recurrent neural networks

Abstract

Event Abstract Back to Event Stochastic models of recurrent neural networks Stefano Cardanobile1, 2* 1 Bernstein Center Freiburg, Germany 2 University of Freiburg, Faculty of Biology, Germany Stochastic models of neural activity have a long standing tradition in the neuroscientific research, especially with regards to analysis of neural data. Analysis of recurrent neural networks models, in contrast, has been proven difficult. The main tools in the analysis are Fokker-Planck equations. Fokker-Planck theory have made possible to study stability properties and, at least partially, correlations in recurrent neural networks of leaky integrate-and-fire neurons. Here we report on recent progresses regarding rate based, non Gaussian models of spiking neural networks. We address two different types of models: linear and nonlinear. The prototype for linear models of recurrent spiking networks are the Hawkes networks. In Hawkes networks, input spikes produce a linear transient in the rate of the post-synaptic neuron. Transients caused by different spikes superimpose linearly. A complete theory for pairwise correlations in Hawkes networks exist and can be exploited to study the links between structural properties and dynamical properties of networks. Nonlinear models exist in several different forms and variants. We describe here multiplicatively interacting point processes and their connection to Lotka-Volterra equations, a type of equations that have been extensively used in the neuroscientific literature, based on phenomenological considerations. In recurrent networks of multiplicatively interacting processes, input spikes have a multiplicative effect on the rate of the post-synaptic neuron. They are linear in the logarithm of the rate and correspond to non leaky integrate-and-fire neurons with exponential escape noise. Recurrent networks of such neurons naturally display complex properties like multistability and chaos and can be used to construct networks with contrast invariant input-output tuning. Acknowledgements Supported by the German Federal Ministry of Education and Research, grant 01GQ0420 "BCCN Freiburg", and grant 01GW0730 "Impulse Control". Keywords: Neural Dynamics in Cortical Networks Conference: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011. Presentation Type: Keynote Topic: other Citation: Cardanobile S (2011). Stochastic models of recurrent neural networks. Front. Comput. Neurosci. Conference Abstract: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011. doi: 10.3389/conf.fncom.2011.53.00017 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 26 Sep 2011; Published Online: 04 Oct 2011. * Correspondence: Dr. Stefano Cardanobile, Bernstein Center Freiburg, Freiburg, Germany, cardanobile@bcf.uni-freiburg.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Stefano Cardanobile Google Stefano Cardanobile Google Scholar Stefano Cardanobile PubMed Stefano Cardanobile Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.