Power-law efficient neural codes provide general link between perceptual bias and discriminability

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Recent work in theoretical neuroscience has shown that efficient neural codes, which allocate neural resources to maximize the mutual information between stimuli and neural responses, give rise to a lawful relationship between perceptual bias and discriminability in psychophysical measurements (Wei & Stocker 2017). Here we generalize these results to show that the same law arises under a much larger family of optimal neural codes, which we call power-law efficient codes. These codes provide a unifying framework for understanding the relationship between perceptual bias and discriminability, and how it depends on the allocation of neural resources. Specifically, we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution. This family includes neural codes that are optimal for minimizing Lp error for any p, indicating that the lawful relationship observed in human psychophysical data does not require information-theoretically optimal neural codes. Furthermore, we derive the exact constant of proportionality governing the relationship between bias and discriminability for different choices of power law exponent q, which includes information-theoretic (q = 2) as well as “discrimax” (q = 1/2) neural codes, and different choices of decoder. As a bonus, our framework provides new insights into “anti-Bayesian” perceptual biases, in which percepts are biased away from the center of mass of the prior. We derive an explicit formula that clarifies precisely which combinations of neural encoder and decoder can give rise to such biases.