Perceptual Compression of Evidence in Intuitive Model Selection
Francesco G. Rinaldi*1, Eugenio Piasini1
1Neuroscience Area, International School for Advanced Studies (SISSA), Trieste, Italy
*Email:frinaldi@sissa.it
Introduction To survive, animals constantly face decisions between competing interpretations for noisy and sparse sensory data. In statistics, this problem is known as Model Selection (MS). Formal frameworks like the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) address this by balancing a model's goodness-of-fit with a penalty for its complexity, inherently promoting simpler models-a concept known as simplicity bias. The same bias has been observed in human MS strategies [1,2], and quantitatively described [3,4] using a linear combination of the models Maximum Log-Likelihood (L) and terms penalizing model complexity, showing a strong sensitivity in humans to model dimensionality, or number of parameters.
Methods Model dimensionality is penalized differently across various MS frameworks. The penalty associated to a model with D parameters is simply D in AIC, while in BIC it also scales logarithmically with the sample size N (number of data points). To investigate how human behavior depends on D and N, we designed an experiment in which 100 naïve participants performed MS. The task involved inferring the number of hidden generative sources in noisy datasets of variable size. We then modelled human choices using both AIC-like and BIC-like descriptions. Moreover, we leveraged Gaussian Processes to flexibly characterize the functional dependence of human strategies on N. Results Initial analyses suggested that human choices exhibit a BIC-like behavior. However, deeper examination of the underlying components revealed that this apparent BIC-like pattern was not due to the complexity penalty D gaining weight with N, but rather resulted from a slower-than-expected growth of L. In theoretical MS frameworks the log-likelihood L, representing the weight of goodness-of-fit to sensory evidence, grows linearly with N on average. Our data however shows that human strategies effectively weight the likelihood with a function exhibiting sublinear growth in N, resembling a logarithm. This observed sublinear scaling of perceived likelihood closely aligns with the well-established sublinear perception of numerosity in humans [5]. Discussion Our study reveals that, even when not explicitly engaged in counting, the brain's internal representation of evidence (L) is subject to the same compressive nonlinearities observed in basic quantitative judgments. This suggests that MS is not a compartmentalized brain function, but potentially leverages, and is thus constrained by, lower-level cognitive processes like numerosity perception. Overall, our findings reveal a significant departure from normative theories of model selection; however, these differences might not stem from a fundamentally distinct strategy, but from limitations due to the repurposing of more elementary cognitive functions.
