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A Power Law Keeps the Brain’s Perceptions Balanced
- haltingproblem 6y agoOriginal article: https://www.biorxiv.org/content/10.1101/374090v1 https://www.biorxiv.org/content/10.1101/374090v1 Abstract: A neuronal population encodes information most efficiently when its activity is uncorrelated and high-dimensional, but correlated lower-dimensional codes provide robustness against noise. Here, we analyzed the correlation structure of natural image coding, in large visual cortical populations recorded from awake mice. Evoked population activity was high dimensional, with correlations obeying an unexpected power-law: the nth principal component variance scaled as 1/n. This was not inherited from the 1/f spectrum of natural images, because it persisted after stimulus whitening. We proved mathematically that the variance spectrum must decay at least this fast if a population code is smooth, i.e. if small changes in input cannot dominate population activity. The theory also predicted larger power-law exponents for lower-dimensional stimulus ensembles, which we validated experimentally. These results suggest that coding smoothness represents a fundamental constraint governing correlations in neural population codes.