Hyperbolic neural networks explained with geometry aware attribution rules
Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagation
Machine Learning
Summary
Explaining decisions made by hyperbolic neural networks is tricky because their geometry affects how information flows inside them. The authors study how to fairly assign credit to different parts of these networks by considering their geometric properties. They propose a new method called LRP-radial-all that respects these properties and gives more consistent explanations. Their method works well compared to others and runs efficiently on image and brain signal data.
What this means in practice
- •For machine learning engineers: Explain hyperbolic neural network decisions more consistently by using geometry-aware relevance propagation rules.
- •For medical data analysts: Use improved attribution methods to interpret hyperbolic models analyzing brain signals like sEEG for more trustworthy insights.
Authors
Ping Xiong, Shanglin Li, Yi Ding, Thomas Schnake, Shinichi Nakajima
Abstract
Hyperbolic neural networks introduce geometric operations that require explicit treatment in relevance propagation. Equivalent geometric realizations can produce different feature attributions, even when local relevance is conserved. We study this problem through Geometric Representation Invariance (GRI), a specialization of Implementation Invariance, and zero-curvature consistency, which requires identity relevance propagation when a geometric module approaches the identity. We propose LRP-radial-all for origin-centered radial modules, treating geometric scaling as modulation and assigning relevance entirely to the signal branch. The rule conserves relevance, is invariant to equivalent radial factorizations, and satisfies zero-curvature consistency, yielding GRI for a specified Poincaré-Lorentz logarithmic-map construction. In contrast, a conservative LRP-half baseline can violate both consistency criteria. Experiments on hyperbolic MNIST, sEEG, and CIFAR-10 classifiers assess attribution fidelity, qualitative explanations, and runtime. LRP-radial-all achieves competitive attribution fidelity across datasets with runtime comparable to Gradient$\times$Input and substantially lower than Integrated Gradients. These findings motivate geometry-aware propagation rules that distinguish relevance conservation from consistency across equivalent computations.