Optimizing for fast sampling-based inference yields oscillatory dynamics in a spiking model of primary visual cortex

ZHEN CHEN; FORREST WARGO; RODRIGO ECHEVESTE; RALF HAEFNER

(online)

Workshop; Spiking Neural networks as Universal Function Approximators; 2021

Abstract: The neural sampling hypothesis suggests that the brain?s sensory processing can be understood as implementing a sampling process that computes the posterior belief over latent variables given a sensory observation. Prior studies have examined this hypothesis in the context of the primary visual cortex (V1), and almost all of them have assumed V1 neurons to represent the continuous intensity of Gabor- shaped features either by firing rates or membrane potentials (Hoyer and Hyvärinen, 2003; Haefner et al., 2016; Orbán et al., 2016; Bányai et al., 2017). All of these models either implemented known sampling algorithms or simply ignored dynamics. Most recently, Echeveste et al. 2020 showed that a rate-based model optimized for fast sampling exhibited rich dynamics including marked stimulus-dependent transient responses and gamma oscillations.It remains unclear whether these dynamic features observed in models of continuous variables would still emerge in the case of binary latents. However, learning in Gaussian binary models of natural images also gives rise to Gabor-shaped receptive fields (Bornschein et al., 2013). Gibbs-sampling based inference in binary models has been shown to be feasible using spiking networks (Buesing et al., 2011; Pecevski, et al., 2011) and using leaky integrate-and-fire neurons (Chattoraj et al., 2019), which yielded near contrast-invariant tuning curves and realistic spiking statistics, interpretable as probabilistic population codes (PPCs, Shivkumar et al., 2018).Here, we optimized the recurrent connectivity of small networks consisting of binary excitatory and inhibitory neurons that obey Dale?s Law to maximize the speed of sampling-based inference in a generative model of retinal images. We found sampling was fastest for non-symmetric connectivity structures that implied oscillatory dynamics (Hennequin et al., 2014) with performance between Gibbs sampling and independent sampling. Importantly, unlike Gibbs sampling and independent sampling, neural responses in our network presented strong oscillations, as observed in the cortex.