Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons

Abstract

Two facts about cortex are widely accepted: neuronal responses show large spiking variability with near Poisson statistics and cortical circuits feature abundant recurrent connections between neurons. How these spiking and circuit properties combine to support sensory representation and information processing is not well understood. We build a theoretical framework showing that these two ubiquitous features of cortex combine to produce optimal sampling-based Bayesian inference. Recurrent connections store an internal model of the external world, and Poissonian variability of spike responses drives flexible sampling from the posterior stimulus distributions obtained by combining feedforward and recurrent neuronal inputs. We illustrate how this frame-work for sampling-based inference can be used by cortex to represent latent multivariate stimuli organized either hierarchically or in parallel. A neural signature of such network sampling are internally generated differential correlations whose amplitude is determined by the prior stored in the circuit, which provides an experimentally testable prediction for our framework.

Visual-Based Spatial Coordinate Dominates Probabilistic Multisensory Inference in Macaque MST-d Disparity Encoding

“…We chose the functional Monte-Carlo sampling method in the framework because the sampling of response provides a concrete neuronal implementation to represent the randomization of perceiving the external world state. It was proposed that the probability of neuronal spiking is indeed computing the posterior probability of perception through response sampling [ 28 , 29 , 30 , 31 ]. As the main encoding components, different probability distributions of preference were observed empirically but the explicit mathematical description of the distribution was not accessible.…”

“…As we seek to provide a general principle for biophysical sampling-based processes, the present work suffers from several limitations. It has been demonstrated that real decision processes in the brain also involve sampling of neuronal responses [ 31 ]. In MST-d, the neuronal response shows complex modulation of preferences and inputs, and the response decay may not be symmetrical when the inputs deviate from the preference of each input modality.…”

Natural gradient enables fast sampling in spiking neural networks

“…such that the acceptance ratio is 24) Therefore, this model differs from the perfect integrator model of §B.1 only in the voltage dynamics; the perfect integrator is recovered exactly if we set η = 0. As in the perfect integrator model, the natural generalization of these leaky dynamics to time-varying mean signal θ t is to take…”

“…Several neural architectures for probabilistic computation have been proposed, including: probabilistic population codes [13], which allow a direct readout of uncertainty under some assumptions; direct encoding of metacognitive variables, such as the confidence (the probability of being correct) in a decision [3,4,7]; doubly distributional codes [14,15] which distinguish uncertainty from multiplicity; sampling-based codes [8,[16][17][18][19][20][21][22][23] where the variability in neural dynamics corresponds to a signature of exploration of the posterior probability. Of these approaches, sampling-based codes are rooted in the strongest theoretical framework in the statistics and machine learning literature [24][25][26][27][28][29], and have been used to perform inference at scale [30][31][32].…”

“…Several neural architectures for probabilistic computation have been proposed, including: probabilistic population codes [13], which in certain cases allow a direct readout of uncertainty; direct encoding of metacognitive variables, such as decision confidence [4,5,8]; doubly distributional codes [14,15] which distinguish uncertainty from multiplicity; and sampling-based codes [9,[16][17][18][19][20][21][22][23][24][25], where the variability in neural dynamics corresponds to a signature of exploration of the posterior probability. Most experiments quantifying uncertainty representations in single biological neurons have only varied parameters along one or two dimensions, such as in Bayesian cue combination [2,10,26].…”