Conceptual similarity as aggregation over feature sets in geometric spaces

Understanding how people judge whether two concepts are similar is a fundamental problem in cognitive science, with implications for theories of learning and reasoning. Human judgments of conceptual similarity often conflict with basic metric assumptions, leading to effects such as judgment asymmetry and violations of the triangle inequality. Classical models of conceptual structure explained these effects via set-based logic applied to manually constructed feature-set representations of concepts. Modern geometric models of conceptual structure offer a scalable, data-driven alternative, but struggle to capture judgment asymmetries via metric-based similarity measures. Here we introduce a modeling framework that combines the merits of these two approaches. Our approach represents concepts as sets of high-dimensional feature embeddings extracted from geometric models via natural language descriptions (e.g. has legs, likes coffee). We present a similarity function appropriate to this setting and show how it can account for classic judgment effects. We evaluate the predictions of this approach against human judgment in two studies: (1) a behavioral study of human similarity judgments among abstract concepts (world countries), and (2) the Nelson free word association dataset. We also formalize a link between our approach and Tversky's classic Contrast Model. Our model outperforms alternatives and establishes a generally-applicable framework that integrates classic and contemporary approaches to conceptual structure.