Hierarchical Co-Embedding of Font Shapes and Impression Tags

Font shapes can evoke a wide range of impressions, but the correspondence between fonts and impression descriptions is not one-to-one: some impressions are broadly compatible with diverse styles, whereas others strongly constrain the set of plausible fonts. We refer to this graded constraint strength as style specificity. In this paper, we propose a hyperbolic co-embedding framework that models font--impression correspondence through entailment rather than simple paired alignment. Font images and impression descriptions, represented as single tags or tag sets, are embedded in a shared hyperbolic space with two complementary entailment constraints: impression-to-font entailment and low-to-high style-specificity entailment among impressions. This formulation induces a radial structure in which low style-specificity impressions lie near the origin and high style-specificity impressions lie farther away, yielding an interpretable geometric measure of how strongly an impression constrains font style. Experiments on the MyFonts dataset demonstrate improved bidirectional retrieval over strong one-to-one baselines. In addition, traversal and tag-level analyses show that the learned space captures a coherent progression from ambiguous to more style-specific impressions and provides a meaningful, data-driven quantification of style specificity.