The responses of sensory neurons in cortex are variable, and this variability is often correlated [Cohen and Kohn, 2011]. While correlations were initially seen as primarily detrimental to the ability of neuronal populations to carry information about an external stimulus [Zohary et al., 1994], more recent studies have shown that they need not be information-limiting in populations of neurons with heterogenous tuning curves [Shamir and Sompolinsky, 2006, Ecker et al., 2011]. In general, information about some variable of interest, s, is only limited by correlations — sometimes called ’bad correlations’ (Pitkow et al., SfN 2013) — that are equivalent to correlations induced by external uncertainty in s. The greater the magnitude of these correlations, the less information about s can be represented by the population. We show in the context of a 2AFC task that correlations of the ’bad noise’ structure are induced by feedback connections in a sensory population of neurons involved in probabilistic inference. However, unlike in the traditional encoding/decoding framework, here their presence reflects the fact that the brain has learnt the task. In fact, perceptual learning will increase their magnitude such that stronger ’bad’ correlations are simply a side-effect of better psychophysical performance. We further show that increasing ’bad correlations’ entails a steeper relationship between choice probabilities (CP) and neurometric performance as has been observed empirically during perceptual learning [Law and Gold, 2008]. Finally, we derive the results of classic reverse correlation techniques as applied to a neural system performing probabilistic inference and relate them to the bottom-up and top-down information flow as predicted by the normative model. Interestingly, we find that despite the fact that CPs are primarily caused by the top-down influence of the decision on sensory responses, they can nonetheless be used to infer the influence of an individual neuron onto the subject’s decision.

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