{
  "abstract": "Training-free source selection for LLM families with shared vocabularies arises in scientific string domains such as SMILES, protein, and genomic sequences, where candidate corpora share a tokenizer but differ in prediction targets. This creates an activation-dark regime: representation-similarity metrics can be uninformative without assumptions about label-conditioned error geometry, while classical update-geometry metrics are computationally prohibitive at vocabulary scale. We show that, in a shared-output head setting, representation metrics (e.g., CKA) are non-identifiable for transfer; models can share identical representations yet have orthogonal head updates. The key identity is that head Fisher alignment is exactly a cosine between kernel mean embeddings in the joint activation-error space, exposing activation, error, and coupling factors rather than requiring a materialized Fisher matrix. FisherSketch estimates this cosine directly in a single streaming pass, making K=128,256 head Fisher alignment practical with a 16 KB task signature (m=4096) and a 192 KB per-task streaming state, small enough to store next to a model hash, but encoding transfer-relevant update structure. Beyond source selection, the same signatures and marginals provide a diagnostic instrument for studying whether LLM task similarity is driven by activations, errors, or their coupling; shared-parameter and internal-layer validations, together with Llama-3.1-8B verbalizer-shift experiments, show that FisherSketch remains informative when activation similarity cannot distinguish tasks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:117826-117889, 2026",
  "arxiv": "2606.27242",
  "author_total": 1,
  "authors": [
    {
      "name": "John Sweeney"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c88yg580c745.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.27242",
  "fulltext_url": null,
  "id": "9c88yg580c745",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.27242",
  "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.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Domain Adaptation and Few-Shot Learning"
    ]
  ],
  "openalex": "W7166099324",
  "pdf_url": "https://arxiv.org/pdf/2606.27242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c88yg580c745.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2606.27242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.27242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "The Geometry of Updates: Fisher Alignment at Vocabulary Scale",
  "title_text": "The Geometry of Updates: Fisher Alignment at Vocabulary Scale",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/9c88yg580c745",
  "venue": "arXiv",
  "versions": []
}