Human learning of probability distributions is biased toward moderate structural complexity

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 constructed by humans may deviate from actual probabilistic structures, and what computational processes, operated under inherent cognitive limitations, give rise to these representations. We first develop a structured distribution report task to reveal human participants' internal representations, with findings verified in a further distribution recognition task. Across eight behavioral experiments (including one pre-registered study) in two modalities, participants estimate the overall probability density reasonably well, but exhibit a systematic bias toward moderate structural complexity, reporting too many clusters when the true distribution is a single Gaussian and too few when it contains many clusters. We then build a series of learning models in the framework of approximate Bayesian inference fit to our behavioral data. Through model comparisons, we reconstruct 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.