{
  "abstract": "Estimating a decision threshold requires locating observations near an unknown boundary. We study how gradient-based pretraining learns this statistical rule in a two-parameter softmax-attention model with a fixed feature and inequality direction. Pretraining uses labeled contexts and their true thresholds; a fresh threshold must be inferred from context alone. Under a large-resolution initialization, constant-step gradient descent on $m$ tasks with $n$ examples each produces a frozen estimator with error $\\widetilde O((m\\wedge n)^{-1}+N^{-1})$ for each fixed interior threshold and every fresh-context size $N$. The two terms separate finite-pretraining accuracy from fresh-context localization. The mechanism is coordinated parameter divergence: population training calibrates the relative label and feature scores, then increases the attention scale as $t^{1/4}$, giving population threshold error $O(t^{-1/4})$. To transfer this mechanism to a fixed finite corpus, we control gradient errors relative to the shrinking directions of progress at successive parameter scales. This certifies a growing training interval without requiring long-time tracking of the population trajectory. We also identify the boundary limitation of the one-head model and explain statistically what a reflected symmetrization could achieve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07074",
  "author_total": 4,
  "authors": [
    {
      "name": "Hong Ha Le"
    },
    {
      "name": "Jackie Lok"
    },
    {
      "name": "Atsushi Nitanda"
    },
    {
      "name": "Yan Shuo Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0qdetsh59ekr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07074",
  "fulltext_url": null,
  "id": "c0qdetsh59ekr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07074",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7220977935",
  "pdf_url": "https://arxiv.org/pdf/2610.07074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0qdetsh59ekr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:32Z",
      "native_id": "2610.07074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07074"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Learning Decision-Stump Thresholds in Context: Dynamics of Softmax Attention",
  "title_text": "Learning Decision-Stump Thresholds in Context: Dynamics of Softmax Attention",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/c0qdetsh59ekr",
  "venue": "arXiv",
  "versions": []
}