Benchmarking Embedding Geometries and Clustering Algorithms for Unsupervised Patent Claim Classification

Prior-art retrieval systems are structurally organized around classification codes, making cross-code discovery difficult. This paper asks if an unsupervised representation trained on patent text can recover relevant connections that code-restricted search cannot, and if hyperbolic space helps. We trained a hyperbolic and a matched Euclidean Variational Autoencoder (VAE) on 45,000 US patents (96 runs, 6 seeds). The hyperbolic model retrieves genuinely cross-category prior art 52% more often than the Euclidean model (18.76% vs. 12.34% of top-10 results, 3,000 queries). This represents a practical gain for the motivating search problem. The hyperbolic model agrees less with official classification (NMI 0.2392 vs. 0.3206), which we explain geometrically: the two measures capture different goals, and only one aligns with prior-art search needs. In a study of 10 technology domains (50,000 more patents), we find that a domain's classification breadth--the number of distinct CPC subgroups spanned--predicts approach performance (Pearson r=-0.642, p=0.045, N=10), and that patents per subgroup is an even stronger predictor (r=0.715, p=0.020). This provides a checkable signal for practitioners to determine where the method is most valuable. We report all findings with statistical transparency and release a complete, 91-test automated implementation.