Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagation
LRP-radial-all explains hyperbolic networks with attributions consistent across equivalent geometric implementations.
The paper studies explanations for hyperbolic neural networks through Geometric Representation Invariance and zero-curvature consistency. It proposes 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, unlike a conservative LRP-half baseline. On hyperbolic MNIST, sEEG, and CIFAR-10, attribution fidelity is competitive, with runtime comparable to Gradient×Input and substantially lower than Integrated Gradients.
- Equivalent geometric realizations can produce different feature attributions
- LRP-radial-all assigns relevance to the signal branch and treats scaling as modulation
- The rule meets relevance conservation and zero-curvature consistency
- Tested on hyperbolic MNIST, sEEG, and CIFAR-10 classifiers
From the original article
1 min read at arxiv.orgHyperbolic 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.
By Ping Xiong · arxiv.org
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