Learning to integrate parts for whole through correlated neural variability

Neural activity in the cortex exhibits a wide range of firing variability and rich correlation structures. Studies on neural coding indicate that correlated neural variability can influence the quality of neural codes, either beneficially or adversely. However, the mechanisms by which correlated neural variability is transformed and processed across neural populations to achieve meaningful computation remain largely unclear. Here we propose a theory of covariance computation with spiking neurons which offers a unifying perspective on neural representation and computation with correlated noise. We employ a recently proposed computational framework known as the moment neural network to resolve the nonlinear coupling of correlated neural variability with a task-driven approach to constructing neural network models for performing covariance-based perceptual tasks. In particular, we demonstrate how perceptual information initially encoded entirely within the covariance of upstream neurons' spiking activity can be passed, in a near-lossless manner, to the mean firing rate of downstream neurons, which in turn can be used to inform inference. The proposed theory of covariance computation addresses an important question of how the brain extracts perceptual information from noisy sensory stimuli to generate a stable perceptual whole and indicates a more direct role that correlated variability plays in cortical information processing. Understanding how the brain represents and processes perceptual information through neuronal firing patterns is at the heart of neuroscience. The prevailing idea suggests that the information is primarily encoded in mean firing rates, whereas correlations among neurons may play a secondary role. However, given that firing variability is ubiquitously observed in cortical neurons, one wonders if correlated noise may play a more central role in neural computation than previously thought. Here, we propose that perceptual information can be encoded in part or even entirely in the correlated variability of spiking neurons. Through a combination of theoretical modeling and machine learning approaches, we construct neural network models capable of processing correlated variability in a task-driven way. We demonstrate that the trained network is able to learn to extract covariance-encoded perceptual information to generate stimulus-selectivity in their mean firing rates, thanks to the nonlinear coupling of statistical moments of their activity. Information-theoretic analysis reveals a near-lossless transfer of perceptual information from the covariance of upstream neurons to the mean firing rate of downstream neurons. Our work offers new insights into the role of correlated variability in cortical processing and hints towards a task-driven paradigm for studying cortical computation with biologically plausible neural network models.