Nested Inductive Bias Framework for SPD Manifold Learning

תקציר מקורי באנגליתarXiv:2609.04466v1 Announce Type: new Abstract: 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 Poincar\'e metric are widely utilized to induce domain-aligned relational priors, generalizing them from standard vector representations to the SPD manifold has remained a challenge. To bridge this gap, we introduce a Nested Inductive Bias framework t