{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.31043",
  "author_total": 4,
  "authors": [
    {
      "name": "Isabella C. Maia"
    },
    {
      "name": "Salem Said"
    },
    {
      "name": "Pedro L. C. Rodrigues"
    },
    {
      "name": "Marco Congedo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnagz5m3qv625.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.31043",
  "fulltext_url": null,
  "id": "bnagz5m3qv625",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.31043",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2805|EEG and Brain-Computer Interfaces"
    ]
  ],
  "openalex": "W7163036531",
  "pdf_url": "https://arxiv.org/pdf/2605.31043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnagz5m3qv625.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:56Z",
      "native_id": "2605.31043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.31043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers",
  "title_text": "Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/bnagz5m3qv625",
  "venue": "arXiv",
  "versions": []
}