biLorentzFM: Hyperbolic Multi-Objective Deep Learning for Reciprocal Recommendation

Reciprocal recommendation requires satisfying preferences on both sides of a match, which differs from standard one-sided settings and often involves hierarchical structure (e.g., skills, seniority, education). We present biLorentzFM, which is a multi-objective framework that integrates hyperbolic geometry into factorization machine architectures using Lorentz embeddings with learnable curvature and manifold-aware optimization. The approach addresses whether a geometric structure aligned with hierarchical relationships can improve reciprocal matching without requiring major architectural changes. On a large-scale recruitment dataset from Kariyer.Net (1,150,302 interactions, 229,805 candidates), the model achieves candidate and company AUCs of 0.9964 and 0.9913 respectively, representing 6.6% and 6.0% improvements over the strongest Euclidean baseline while maintaining practical inference latency (2.1 ms per batch). Cross-validation analysis confirms robustness (5-fold: 0.9813 ± 0.0002; 3-seed: 0.9964 ± 0.0012) with very large effect sizes (Cohen’s d = 2.89–3.08). Although the per-epoch training time increases by 23.5% due to manifold operations, faster convergence (12 vs. 18 epochs) reduces the total training time by 17.8%. Cross-domain evaluation on Speed Dating data demonstrates generalization beyond explicit hierarchies with a 2.8% AUC improvement despite lacking structured taxonomies. Learned curvature parameters differ by entity type, providing interpretable indicators of hierarchical structure strength. Ablation studies isolate contributions from geometric structure (6.6%), learnable curvature (4.7%), multi-objective learning (2.1%), and explicit feature interactions (0.6%). A systematic comparison reveals that Lorentz embeddings outperform Poincaré ball implementations by 4.4% AUC under identical conditions, which is attributed to numerical stability advantages. The results indicate that pairing standard recommendation architectures with geometry reflecting hierarchical relationships can provide consistent improvements for reciprocal matching, while limitations including cold-start performance, computational overhead at an extreme scale, and static hierarchy assumptions suggest directions for future work on adaptive curvature, fairness constraints, and dynamic taxonomies.