Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers

arXiv:2605.31043v2 Announce Type: replace-cross Abstract: Deep networks on the symmetric positive-definite (SPD) manifold promise expressive representations by encoding data geometry as an inductive bias, but stacking BiMap layers with the standard ReEig nonlinearity often adds no capacity: on real, preconditioned EEG data, ReEig rarely activates, so the stack behaves as a single layer at any depth. In the worst case, when domains share no discriminative directions, we prove a single filter has a capacity ceiling, so it cannot fully align every domain at once. To overcome that, we propose SCAP

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