Ricci Curvature and the Stream of Thought

Abstract

This paper investigates the dynamics of semantic associations by exploring the interplay between continuity and direction, in a geometric semantic space. While acknowledging the role of continuity in guiding associations, our work introduces the notion of Direction as a crucial factor influencing transitions. Conceptually, we define the stream of associations as movement along a sequence of objects, with attention amplifying dissimilarity and progressing in the direction of maximal resolution. The direction of maximal resolution is conceptualized as the most "stretched" direction, representing the focal point of our study. Methodologically, we propose a unique version of discrete Ricci curvature to measure the direction of maximal resolution, adapting traditional curvature concepts to a hypergraph framework. Empirically, our investigation involves a categorical fluency task where participants name animals, constructing a hypergraph for transition analysis. We evaluate two hypotheses: the relationship between edge "stretchiness" and transition probability, and the enhanced explanatory power of considering Similarity + Direction over similarity alone. Our model challenges the standard view by proposing that the stream of thought moves in the direction of maximal resolution. We introduce the novel idea of Ricci curvature of a hypernetwork to quantify resolution and demonstrate its application in the context of semantic space.