Beyond mean field theory: statistical field theory for neural networks

Mean field theory for asymmetric neural networks.

The computation of mean firing rates and correlations is intractable for large neural networks. For symmetric networks one can derive mean field approximations using the Taylor series expansion of the free energy as proposed by Plefka. In asymmetric networks, the concept of free energy is absent. Therefore, it is not immediately obvious how to extend this method to asymmetric networks. In this ...

Mean-field theory of fluid neural networks

Jordi Delgado and Ricard V. Solé Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord, Mòdul C6, Jordi Girona Salgado 1-3 08034 Barcelona, Spain Complex Systems Research Group, Departament de Fı́sica i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Sor Eulàlia d’ Anzizu s/n, Campus Nord, Mòdul B4, 08034 Barcelona, Spain ~Received 27 May ...

Mean Field Theory for Sigmoid Belief Networks Mean Field Theory for Sigmoid Belief Networks

We develop a mean eld theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean eld theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition|the classiication of ha...

Mean Field Theory for Random Recurrent Spiking Neural Networks

Recurrent spiking neural networks can provide biologically inspired model of robot controller. We study here the dynamics of large size randomly connected networks thanks to ”mean field theory”. Mean field theory allows to compute their dynamics under the assumption that the dynamics of individual neuronsare stochastically independent. We restrict ourselves to the simple case of homogeneous cen...

Beyond Gross-Pitaevskii Mean Field Theory