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 direct evidence for the universal law in a naturalistic high-dimensional regime by analyzing an existing dataset of 214,200 human similarity judgments and a newly collected dataset of 390,819 human generalization judgments (N=2406 US participants) across three sets of natural images.

翻译：谢泼德的通用泛化定律是关于智能有机体应如何感知相似性的重要假设。在最广泛的形式中，该定律指出，当一对刺激嵌入适当的心理空间时，其感知相似性水平应随二者距离呈凹函数衰减。尽管已有广泛研究，但支持该定律的证据一直依赖于低维刺激和与真实世界实例差异较大的小型刺激集。这主要是因为相似性判断所需的成对比较数量随刺激数量呈二次增长。通过分析包含214,200个人类相似性判断的现有数据集以及新收集的包含390,819个人类泛化判断的数据集（N=2406名美国参与者），我们为自然高维情境下的通用定律提供了直接证据。这些判断基于三组自然图像数据集。