CBB seminar Arthur Prat-Carrabin (Harvard)

Arthur Prat-Carrabin  Harvard University

Topic: The Number Sense under Limited Resources 

The brain needs to represent important information from the outside world, but it has limited resources to do so. As a considerable fraction of our decisions depend on environmental variables, a crucial objective is to characterize how these limited resources shape the brain's internal representations of external variables. The variability of human responses in psychophysical experiments, and that of the activity of sensory neurons in neurophysiological studies, both suggest an inherent imprecision in the representation of sensory magnitudes. Similar results obtained in numerosity studies indicate in addition the existence of a ‘number sense’ in the brain. The principle of efficient coding, according to which the imprecision reflects an optimal allocation of limited cognitive resources, implies that subjective representations should be context-dependent. We test this in an estimation task and a discrimination task, both involving numerosities. Human subjects appear to reallocate their representational resources, when the range of the prior distribution of numbers changes. Specifically, I exhibit a sublinear scaling law relating the scale of subjects' variability to the width of the prior range. This sublinear scaling, moreover, depends on the objective of the task — estimation or discrimination. This double dependence — on the prior, but also on the task objective — is consistent with an efficient coding strategy that optimizes a tradeoff between the expected reward, different for each task, and a resource cost of the activity of the neurons that encode the numerosity. Contrasting the two tasks allows us to clarify the form of the resource constraint. Furthermore, a possible strategy for the reallocation of resources is to rescale the neuronal encoding to adapt to the range, by shifting accordingly the preferred numerosities of the encoding neurons. In an fMRI study (with collaborators at the University of Zurich), we examine the numerical receptive fields of number-sensitive neural populations in the parietal cortex. We find a shift of the population-level ‘preferred numerosities’, when the prior range changes, suggesting a scalable representation of numbers in the brain. Together, these results suggest that the brain's representations quickly adapt to the current context, with a degree of perceptual noise that is determined endogenously.