Statistical Field Theory and Networks of Spiking Neurons

Abstract

This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems in interaction [45][46]. Our model keeps track of individual interacting neurons dynamics but also preserves some of the features and goals of neural field dynamics, such as indexing a large number of neurons by a space variable. Thus, this paper bridges the scale of individual interacting neurons and the macro-scale modelling of neural field theory.

Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons

“…For better or worse, the situation resembles the “zoo of particle physics” prior to the introduction of the Standard Model. In this paper we introduce a lattice field theory (LFT) [ 21 , 23 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ] that is tailored to interpret data from multisite brain–computer interfaces (BCIs) in a systematic and physically grounded way that links the microscopic parameters to the experimental observations through well-known renormalization procedures. In short, LFTs discretize the space–time into a lattice grid and are commonly used in theoretical particle physics to facilitate numerical simulations and intractable calculations.…”