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Abstract

Shepard’s universal law of generalization is a remarkable hypothesis about how intelligent organisms should perceive similarity. In its broadest form, the universal law states that the level of perceived similarity between a pair of stimuli should decay as a concave function of their distance when embedded in an appropriate psychological space. While extensively studied, evidence in support of the universal law has relied on low-dimensional stimuli and small stimulus sets that are very different from their real-world counterparts. This is largely because pairwise comparisons—as required for similarity judgments—scale quadratically in the number of stimuli. We provide strong evidence for the universal law in a naturalistic high-dimensional regime by analyzing an existing data set of 214,200 human similarity judgments and a newly collected data set of 390,819 human generalization judgments (N = 2,406 U.S. participants) across three sets of natural images.