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Abstract:
The Divisive Normalization (DN) function is often viewed as a canonical neural encoding mechanism. However, DN maximizes mutual information, and thus is efficient, only for input stimuli coming from a very specific class of inputs: heavy-tailed multivariate Pareto distributions. Given the same infomax criterion, DN is not efficient for stimuli or rewards coming from other distributions. Using a behavioral paradigm and computational modeling of our results, we tested whether the brain uses DN both in environments in which it is and in which it is not efficient. That is, we ask whether choices are well described as arising from a DN representation even when that mechanism is inefficient - evidence of a physiological constraint that requires DN. We perform our experiment in a biphasic risky-choice experiment, where subjects had to choose amongst lotteries drawn from four different types of input distributions. In Phase 1 of our experiment, subjects (N=78) reported the most they would pay to purchase a given lottery, using a Becker-DeGroot-Marschak (1964) auction with a large set of lotteries. The subject-specific estimates from these valuations were used to generate two classes of continuous distributions of subjective valuations (SVs): (1) Uniform distributions, for which the DN encoding function is inefficient; and (2) multivariate Pareto type-III distributions, for which the DN function is efficient. These distributions were then used in Phase 2, where subjects made 1,280 choices in a 2*2 design (320 trials per treatment) that manipulated the number of choice options (2 vs. 6), as well as the class of SVs distributions (uniform vs Pareto). We used pooled and hierarchical maximum likelihood estimations to recover the DN functional parameters. The pattern of stochasticity in the choices of our subjects clearly indicated that subjects employed a divisive representation under both classes of input distributions. This was true regardless of the computational method used to estimate the underlying normalization, in both the pooled and hierarchical estimations. The magnitude of the curvature of the DN function, however, did vary across treatments, suggesting that subjects adapted to the different choice environments. Our results suggest that people are obligate DN-choosers, and that at least for adaptation periods of this duration, a certain degree of embedded inefficiency exists in choice induced by DN. These findings correspond to previous empirical results, which showed that many real-world naturalistic stimuli have long-tail asymmetric distributions, and perhaps imply an evolutionary origin of the neural encoding mechanism that constrains it to employ DN.
