{
  "abstract": "The block generalized-power method pairs threshold-based support selection with inexpensive Stiefel updates, but the standard block formulation conflates two nonequivalent objectives and leaves inactive components, threshold ties, and post-selection refitting ill-specified. We rebuild the model from the primal. Eliminating each loading column from the normalized loading-ball problem gives a sum of soft-thresholded Euclidean norms (A-SUM); the squared-threshold objective in common use arises from a quadratic lift (A-SQ). We prove both identities, exhibit a two-component instance whose maximizers disagree, and specify explicit conventions for zero-response columns, ties, rank deficiency, and mask-before-refit. For A-SQ we separate the historical full-polar iteration from a safeguarded Riemannian ascent and prove, for the latter, whole-sequence convergence via a sufficient-ascent lemma, a relative-error lemma, and the Kurdyka-Lojasiewicz property, which applies because the soft-threshold objective and the Stiefel constraint are semi-algebraic. A strict threshold margin then forces finite identification of the support and sign pattern. The post-identification map is ordinary power iteration on the active covariance for a rank-one hard threshold, and the Frechet derivative of a coupled polar map for component-specific supports; a radius-based safe-screening rule follows from the same local analysis. Planted-spike experiments match the predicted identification time and local rates. On modern-AI panels (GPT-2 residual stream, ViT CLS stream, Pitprops) the thresholded block-sparse components match dense PCA on reconstruction and improve on it in monosemanticity and class specialisation. On three native-label scRNA datasets (Zheng17 FACS-sorted PBMCs, 68k donor-A with FACS-correlated labels, Tabula Muris) A-SQ beats dense PCA on cluster-recovery AMI by +0.023 to +0.044 at matched sparsity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25721",
  "author_total": 1,
  "authors": [
    {
      "name": "Omid Shams Solari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78qgw90m4tskj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25721",
  "fulltext_url": null,
  "id": "78qgw90m4tskj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25721",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
    ]
  ],
  "openalex": "W7223056243",
  "pdf_url": "https://arxiv.org/pdf/2610.25721",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78qgw90m4tskj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25721",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25721"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Corrected Block Sparse Spectral Optimization: Exact Models, Finite Identification, and Local Dynamics",
  "title_text": "Corrected Block Sparse Spectral Optimization: Exact Models, Finite Identification, and Local Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/78qgw90m4tskj",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.5281/zenodo.23460513",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}