Marginalization in Neural Circuits with Divisive Normalization

Abstract

A wide range of computations performed by the nervous system involves a type of probabilistic inference known as marginalization. This computation comes up in seemingly unrelated tasks, including causal reasoning, odor recognition, motor control, visual tracking, coordinate transformations, visual search, decision making, and object recognition, to name just a few. The question we address here is: how could neural circuits implement such marginalizations? We show that when spike trains exhibit a particular type of statistics – associated with constant Fano factors and gain-invariant tuning curves, as is often reported in vivo – some of the more common marginalizations can be achieved with networks that implement a quadratic nonlinearity and divisive normalization, the latter being a type of nonlinear lateral inhibition that has been widely reported in neural circuits. Previous studies have implicated divisive normalization in contrast gain control and attentional modulation. Our results raise the possibility that it is involved in yet another, highly critical, computation: near optimal marginalization in a remarkably wide range of tasks.

A computational perspective on autism

“…Importantly, this finding is not inconsistent with the hypothesis of altered divisive normalization in autism since cue integration does not theoretically require divisive normalization (42). Altered divisive normalization in autism does, however, predict changes in other forms of multisensory processing that require divisive normalization, such as cue conflict conditions and causal inference (36,38).…”

“…When the letter of interest is the global feature, the local feature is a nuisance variable in the sense that it makes no difference if it is the letter "A" or any other letter. The elimination of nuisance variables is called marginalization, and theoretical work suggests that the neural implementation of this process requires divisive normalization (38). A bias toward local feature processing in autism is therefore consistent with the possibility of impaired marginalization through altered divisive normalization.…”

“…Divisive normalization further accounts for a number of phenomena in auditory cortex (35), multisensory integration (36), and higher-order processes such as attention (37) and rationality (16). In addition, divisive normalization may be critical for neural circuits to implement marginalization, a type of probabilistic inference that eliminates irrelevant information, so-called "nuisance variables" (38).…”

“…One possibility is that population activity is decoded to determine the most probable stimulus, and the appropriate behavioral response is then selected accordingly (17,38,42). This strategy captures the intuition that greater activity in a subpopulation of neurons with similar response properties leads to greater certainty about the stimulus (SI Appendix).…”

“…A bias toward local feature processing in autism is therefore consistent with the possibility of impaired marginalization through altered divisive normalization. More generally, behaviors requiring marginalization such as social cognition (58), visual search (59), reference frame transformations (60), and causal inference (38), may be altered in autism. Consistent with this prediction, impaired social cognition is a diagnostic criterion for autism, visual search is altered in the disorder (61), and an increased egocentric perspective in autism (62) may reflect an impairment in reference frame transformations.…”