Hyperbolic Embeddings in Qdrant

Hyperbolic embeddings use negatively curved geometry to represent branching hierarchies such as product catalogs, taxonomies, and part-whole relationships more naturally than conventional Euclidean or spherical embeddings, because hyperbolic space expands exponentially with distance from its center. The discussion reports that low-dimensional Poincaré embeddings substantially outperformed higher-dimensional Euclidean embeddings when reconstructing WordNet and Google Product Taxonomy relationships, with radial position also offering an interpretable indication of specificity from broad concepts near the center to detailed descendants near the boundary. It also examines deployment challenges in Qdrant: although converting hyperbolic distance to an inner product worked in brute-force search, HNSW indexing performed poorly because vector norms varied widely. A more effective approach stores original Poincaré coordinates, uses Euclidean HNSW to prefetch candidates, and applies Qdrant Formula Query rescoring with true hyperbolic distance, reaching recall@10 of 0.920 with a prefetch of 1,000 taxonomy points. The results suggest hyperbolic embeddings can be compact and effective for genuinely hierarchical data, but require careful retrieval tuning because stronger embeddings may place more vectors near the Poincaré ball’s edge, making Euclidean candidate selection less reliable.

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