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Nested Inductive Bias Framework for SPD Manifold Learning

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

In Geometric Deep Learning, inductive biases serve two primary functions: enforcing manifold constraints and embedding relational priors. Currently, representation learning on SPD manifolds frequently relies on pullback Euclidean metrics, such as the Log-Euclidean Metric, to satisfy the former. While computationally efficient in avoiding domain boundary violations, these metrics induce a flat geometry that may fail to capture the intrinsic relational priors of datasets. While metrics such as the Poincaré metric are widely utilized to induce domain-aligned relational priors, generalizing them f

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