When task performance deceives: Task-geometry decoupling in learnable-curvature hyperbolic GNNs

Treating curvature as a learnable parameter in Hyperbolic Graph Neural Networks (GNNs) has become a useful approach for modeling complex graphs. However, in the standard single-global-curvature setting, improved task performance does not necessarily guarantee geometric fidelity. Our empirical analysis reveals a decoupling between these objectives: without explicit geometric control, the embedding geometry may degrade substantially even after validation performance has largely saturated. To address this issue, we formulate curvature learning as a distortion-feedback control problem and propose a Distortion-Aware Adaptive Controller. Guided by a curvature-dependent trade-off between geometric fidelity and statistical complexity, the method uses embedding distortion as a feedback signal to regulate curvature during training, improving the stability and reliability of curvature learning while retaining competitive task performance. Across the evaluated link prediction benchmarks, the proposed controller mitigates late-stage geometric degradation and substantially reduces curvature variance, highlighting the value of explicit geometry-aware feedback in learnable-curvature hyperbolic GNNs.