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.
Figures & tables
Fig. 1: End-to-end pipeline. Only the latent-model stage differs between the Euclidean and hyperbolic conditions compared throughout this paper.
Fig. 2: A tree embedded in flat Euclidean space (a) crowds together as it branches; the same tree in the Poincaré disk (b) has room to spread, since available area grows exponentially, not polynomially, with radius.
Fig. 3: VAE architecture. Encoding, sampling, and the KL term are geometry-specific (hyperbolic or Euclidean); the decoder is Euclidean in both conditions, a deliberate simplification we note in Section VIII .
Fig. 4: (a) Hyperbolic diverges from CPC classification more than Euclidean, consistent with organizing along technical rather than administrative structure (0.2392 vs. 0.3206 NMI, non-overlapping across 6 seeds). (b) Hyperbolic outperforms Euclidean on cross-category retrieval (18.76% vs. 12.34%, +52% relative) — this paper’s central practical result.
Method
NMI vs. fine CPC
Note
BERTopic
0.6114
267 clusters, ∼ 50% outliers — different regime
Raw SBERT + KMeans
0.3766
No VAE training
Raw-hyperbolic
0.3513
Untrained, Poincaré-mapped
Euclidean VAE
0.3206
Trained
LDA
0.2775
Classical topic model
Hyperbolic VAE
0.2392
Trained, best variant
TABLE I: Baseline comparison: NMI vs. fine CPC codes.
Domain
CPC Code(s)
AI / Software (original)
G06N, G06F, G06Q
Semiconductors
H01L
Pharmaceutical
A61K
Medical devices
A61B
Digital communications
H04L
Camera / imaging
H04N
TABLE II: Technology domains and their CPC codes for Study 2.
Fig. 5: v2 geometry comparison, Phase 1 (n=30 per bar, error bars show one standard deviation). Directionally consistent with Study 1 but noisier at this smaller per-domain scale.
Fig. 6: Winning Phase-1 configuration (MiniLM, Euclidean) applied to all 10 domains, 6 seeds each. Pharmaceutical scores lowest, electric vehicles highest (3.7 × higher); AI and software patents sit near, not at, the bottom.
Fig. 7: Real patents per distinct CPC subgroup vs. mean representation-quality score. Pearson r=0.715, p=0.020, N=10 domains.