Viktor Ørduk Sandberg, BCCN Berlin / TU Berlin

Mean-field Limit of Binary Recurrent Neural Networks: Analysis of Conditions for Existence

We study the role of network structure on average population activity dynamics of binary neurons. We formulate a general mean-field theory (MFT) with conditions on the network structure statistics for which the dynamics converge to a deterministic value in the limit of infinite population size. Here, we calculate the input moments of all orders in a systemic derivation of the MFT, similar to reference [9]. The method there is extended to networks that exhibit an inhomogeneity of in-degrees. Additionally, we study the Gram-Charlier expansion of the input statistics to develop an arbitrarily precise computation of the mean-field limit. We also recover the classical results for the cortical balanced state networks, where the connectivity is assumed to be a directed
Erdős–Rényi graph [31, 18].

The results in this work uncover the necessary conditions for the existence of a deterministic mean-field limit for recurrent binary neurons. Therefore, the approach here is useful for the investigation of the implications of connectivity motifs in cortical circuits.

Additional Information

MSc thesis defence in the international master program "Computational Neuroscience"

Organized by

Wilhelm Stannat / Robert Martin