Neural population coding of multiple stimuli

In natural scenes, objects generally appear together with other objects. Yet, theoretical studies of neural population coding typically focus on the encoding of single objects in isolation. Experimental studies suggest that neural responses to multiple objects are well described by linear or nonlinear combinations of the responses to constituent objects, a phenomenon we call stimulus mixing. Here, we present a theoretical analysis of the consequences of common forms of stimulus mixing observed in cortical responses. We show that some of these mixing rules can severely compromise the brain's ability to decode the individual objects. This cost is usually greater than the cost incurred by even large reductions in the gain or large increases in neural variability, explaining why the benefits of attention can be understood primarily in terms of a stimulus selection, or demixing, mechanism rather than purely as a gain increase or noise reduction mechanism. The cost of stimulus mixing becomes even higher when the number of encoded objects increases, suggesting a novel mechanism that might contribute to set size effects observed in myriad psychophysical tasks. We further show that a specific form of neural correlation and heterogeneity in stimulus mixing among the neurons can partially alleviate the harmful effects of stimulus mixing. Finally, we derive simple conditions that must be satisfied for unharmful mixing of stimuli.