arXiv：cs.LG· Isabella C. Maia, Salem Said, Pedro L. C. Rodrigues, Marco Congedo·· 5 小时前AI 评分34
SCAP：在 Stiefel 流形上路由以突破双线性 SPD 层的容量上限
Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers
AI 导读
针对 SPD 流形上 BiMap 层堆叠因 ReEig 极少激活而退化为单层的问题，研究者提出 SCAP（Stiefel Cross-Attention Pool），通过交叉注意力将 K 个专家池组合成样本特定的双线性映射，实现一族 Stiefel 滤波器。SCAP 在五个跨域 EEG 运动想象数据集上均显著优于固定滤波器的 SPDNet，并在其中四个上追平或超过三个域自适应基线。
正文
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 (Stiefel Cross-Attention Pool), a layer implementing a family of Stiefel filters by combining a pool of $K$ experts into a sample-specific bilinear map via cross-attention. We show that it matches a per-domain filter bank to first order with fewer experts than domains when domain-optimal filters span few directions near a shared tangent-space basepoint; in the worst case, its alignment empirically stays nearly flat as domains grow, escaping the fixed-filter ceiling. Naively trained, however, this routing can collapse to a fixed filter; we diagnose why and adapt three mechanisms to mitigate it. SCAP significantly improves balanced accuracy over fixed-filter SPDNet on all five cross-domain EEG motor-imagery datasets, and matches or exceeds three domain-adaptive baselines on four out of five.
| Subjects: | Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.31043 [stat.ML] |
| (or arXiv:2605.31043v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2605.31043 arXiv-issued DOI via DataCite |
Submission history
From: Isabella Costa Maia [view email]
[v1]
Fri, 29 May 2026 09:20:25 UTC (24 KB)
[v2]
Fri, 2 Oct 2026 12:59:28 UTC (83 KB)
来源：arXiv：cs.LG · arxiv.org