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

Area of Science:

• Machine Learning
• Graph Representation Learning
• Geometric Deep Learning

Background:

• Hyperbolic Graph Neural Networks (GNNs) utilize learnable curvature for complex graph modeling.
• Standard single-global-curvature settings often show a performance-geometry decoupling, leading to degraded embedding geometry.
• Lack of explicit geometric control can cause substantial degradation even when task performance saturates.

Purpose of the Study:

• To address the decoupling between task performance and geometric fidelity in learnable-curvature hyperbolic GNNs.
• To propose a novel method for stable and reliable curvature learning in hyperbolic GNNs.
• To improve the geometric integrity of embeddings during the training of hyperbolic GNNs.

Main Methods:

• Formulating curvature learning as a distortion-feedback control problem.
• Introducing a Distortion-Aware Adaptive Controller that uses embedding distortion as a feedback signal.
• Balancing geometric fidelity and statistical complexity using a curvature-dependent trade-off.

Main Results:

• The proposed controller mitigates late-stage geometric degradation in link prediction tasks.
• Significantly reduced variance in curvature during training.
• Maintained competitive task performance while improving geometric reliability.

Conclusions:

• Explicit geometry-aware feedback is crucial for stable and reliable curvature learning in hyperbolic GNNs.
• The Distortion-Aware Adaptive Controller enhances the trustworthiness of geometric embeddings.
• This approach offers a more robust method for applying hyperbolic GNNs to complex graph data.