Doubly distributional population codes: simultaneous representation of uncertainty and multiplicity.

Perceptual inference fundamentally involves uncertainty, arising from noise in sensation and the ill-posed nature of many perceptual problems. Accurate perception requires that this uncertainty be correctly represented, manipulated, and learned about. The choices subjects make in various psychophysical experiments suggest that they do indeed take such uncertainty into account when making perceptual inferences, posing the question as to how uncertainty is represented in the activities of neuronal populations. Most theoretical investigations of population coding have ignored this issue altogether; the few existing proposals that address it do so in such a way that it is fatally conflated with another facet of perceptual problems that also needs correct handling: multiplicity (that is, the simultaneous presence of multiple distinct stimuli). We present and validate a more powerful proposal for the way that population activity may encode uncertainty, both distinctly from and simultaneously with multiplicity.