Berlin 2024 – scientific programme
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BP: Fachverband Biologische Physik
BP 13: Statistical Physics of Biological Systems I (joint session DY/BP)
BP 13.9: Talk
Tuesday, March 19, 2024, 12:00–12:15, BH-N 334
Low-dimensional stochastic dynamics of finite-size, spiking-neuron populations via eigenmode expansion — •Tilo Schwalger1,2 and Bastian Pietras3 — 1Technical University Berlin, 10623 Berlin, Germany — 2Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany — 3Universitat Pompeu Fabra, Barcelona, Spain
Low-dimensional neural population models in the form of nonlinear Langevin equations provide an effective description of the collective stochastic dynamics of neural networks in the brain. However, existing population models are largely heuristic without a clear link to the underlying neuronal and synaptic mechanisms. Here, we derive a system of Langevin equations at the mesoscopic scale from a microscopic model of a finite-size, fully-connected network of integrate-and-fire neurons with escape noise. The theory is based on a stochastic integral equation for the mesoscopic dynamics of the neural network (Schwalger et al. PloS Comput Biol. 2017) and an eigenmode expansion of the corresponding refractory-density equation (Pietras at al., Phys. Rev. E 2020). Truncating the hierarchy of coupled spectral modes after the first M modes yields a 2M-dimensional Langevin equation, permitting a systematic model reduction. Retaining only the dominant spectral mode, M=1, already captures well oscillatory transients and finite-size fluctuations when compared to microscopic simulations. Our bottom-up theory thus connects biologically plausible spiking neural networks to the efficient firing-rate models often used in applcations.
Keywords: neural population dynamics; finite-size fluctuations; spectral decomposition; dimensionality reduction; spiking-neuron dynamics