{
  "abstract": "We derive exact local responses for attention interventions, allowing candidate edits to be scored from a cached baseline and one backward pass. The starting point is the RoPE derivative $\\partial_p z(p) = A z(p)$: its integral gives the finite positional displacement, which we carry through the softmax without linearising either rotation or normalisation. The resulting predictions achieve 95.36--96.52% sign accuracy across 92,160 executed positional edits on 768 held-out prompt sets, reducing answer-margin MAE by 73.6--82.5% against the positional Jacobian and by 36.2--50.9% against zero. For simultaneous key and value edits, the same divided-difference calculus isolates the interaction term $C_{KV} = \\sum_j (p'_j - p_j)\\,\\varepsilon_j$, which is omitted by adding separate attributions. Retaining it reduces downstream margin MAE by more than a factor of nine in every setting of a 5,120-intervention sweep across two Qwen sizes, two tasks, and multiple layers; reductions against a quadratic interaction correction are 75.9--98.5%. Exactness concerns the edited attention write; downstream predictions contract that response with a baseline gradient and are evaluated by native execution. The calculus also yields a KL certificate for local approximation error, an exact query-conditioned gradient-step representation whose curvature identifies attention-preserving query directions, and minimum-norm query control. Sparse evaluation supports candidate ranking and cache decisions under explicit local distortion criteria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14127",
  "author_total": 4,
  "authors": [
    {
      "name": "Julie Huang"
    },
    {
      "name": "Maggie Chlon"
    },
    {
      "name": "Gregory Gutin"
    },
    {
      "name": "Leon Chlon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahr3evsqnjcp5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14127",
  "fulltext_url": null,
  "id": "ahr3evsqnjcp5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14127",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Explainable Artificial Intelligence (XAI)"
    ]
  ],
  "openalex": "W7213358501",
  "pdf_url": "https://arxiv.org/pdf/2609.14127",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahr3evsqnjcp5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2609.14127",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14127"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Exact Finite Attention Responses From RoPE Derivatives",
  "title_text": "Exact Finite Attention Responses From RoPE Derivatives",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/ahr3evsqnjcp5",
  "venue": "arXiv",
  "versions": []
}