{
  "abstract": "Neural networks can leverage feature superposition to encode more concepts than dimensions, but cross-feature interference constrains the linear accessibility of simultaneously active features. By framing linear accessibility as a compressed sensing problem, we derive high-probability bounds for fixed supports under subgaussian noise, proving the sufficient dimension scales linearly ($d=O_{\\varepsilon}(k \\log m)$) rather than prior worst-case quadratic limits. We characterize the asymmetry between active and inactive interference and the trade-off between interference and observation-noise budgets. We then validate these bounds across system parameters through Gaussian-tail approximations. We also introduce IHT-SAE, which uses learned iterative refinement to improve feature recovery beyond the limits of linear availability. These results quantify the geometric constraints of the linear representation hypothesis, providing a framework for evaluating sparse autoencoders, compositional generalization, and neural interpretability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09556",
  "author_total": 1,
  "authors": [
    {
      "name": "Enrico Vompa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vd3378tyv06f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09556",
  "fulltext_url": null,
  "id": "1vd3378tyv06f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09556",
  "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": [
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      "arxiv",
      "cs.AI"
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      "arxiv",
      "math.PR"
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      "openalex",
      "2206|Sparse and Compressive Sensing Techniques"
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  "openalex": "W7212194494",
  "pdf_url": "https://arxiv.org/pdf/2609.09556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vd3378tyv06f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.09556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "High-probability guarantees for linear accessibility in feature superposition",
  "title_text": "High-probability guarantees for linear accessibility in feature superposition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/1vd3378tyv06f",
  "venue": "arXiv",
  "versions": []
}