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Modelling metric violations in (geometric) conceptual spaces

Abstract

Understanding how people represent similarity relations between concepts is one of the most fundamental problems in cognitive science, with implications for many theories of learning and reasoning. Human judgments of similarity violate basic metric assumptions, leading to effects such as judgment asymmetry and the triangle inequality. These effects have been difficult to capture with modern geometric representations of conceptual structure such as vector embeddings. Here we introduce a similarity function related to a feature-based view of concepts. We show how this function can be applied to geometric representations and that the resulting algorithm can account for classic judgment effects. Using representations extracted from a Large Language Model, we computed the predictions of this approach to similarity relations among a set of everyday concepts (world countries), and evaluated these predictions against human judgments of similarity in a behavioral experiment. The model's predictions correlate with human judgments. These results offer insight into human judgments of similarity relations and the design of algorithms that align with human reasoning.

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