Illusory perception of latent probabilistic structures

Inferring hidden environmental structures, which commonly involves learning arbitrary probability distributions from limited samples, is essential to optimal and adaptive behaviors across various cognitive domains. However, it remains largely unknown how the internal representations humans develop may deviate from actual probabilistic structures, and what computational processes, operated under inherent cognitive limitations, give rise to these representations. We developed a structured distribution report task to reveal human participants' internal representations and further verified our findings in a distribution recognition task. Across eight behavioral experiments (including one pre-registered study) in two modalities, participants made systematic errors in reporting the probabilistic structures, typically overestimating the cluster number, despite estimating overall probability density reasonably well. We developed a series of learning models in the framework of approximate Bayesian inference. Through model comparisons, we reconstructed the prior beliefs guiding the evolution of participants' internal representations. The best-fitting model for human reports reduces structure growth rate as complexity increases, effectively constraining the complexity of internal representations within memory limitations.