{
  "abstract": "Transformers have revolutionized machine learning and deploying attention layers in the model is increasingly standard across a myriad of applications. Further, for large models, it is common to implement Low Rank Adaptation (LoRA), whereby a factorized parameterization of them is trained, to achieve a surprisingly beneficial accuracy-size trade-off. In this work, via a unified framework we rigorously establish trainability of such models under stochastic methods. We prove that for a class of mild regularizations, the empirical regression loss on a attention layer and LoRA on a shallow neural net, both induce Poincaré inequality for the corresponding Gibbs' measure. Crucially, we show that the Poincaré constant is free of the data dimension for LoRA and for multi-head attention it is free of the head dimensions, Then it follows, via invoking recent results, that a certain SDE, which mimics the SGD, minimizes the corresponding losses. In both the cases, our first-of-its-kind results of trainability on attention and nets, do not use any assumptions on the data or the model size.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.07959",
  "author_total": 5,
  "authors": [
    {
      "name": "Zhengkai Sun"
    },
    {
      "name": "Dibyakanti Kumar"
    },
    {
      "name": "Alejandro F Frangi"
    },
    {
      "name": "Anirbit Mukherjee"
    },
    {
      "name": "Mingfei Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eeh2dp94pm8gd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.07959",
  "fulltext_url": null,
  "id": "eeh2dp94pm8gd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.07959",
  "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",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7160839712",
  "pdf_url": "https://arxiv.org/pdf/2605.07959",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eeh2dp94pm8gd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2605.07959",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.07959"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergent Stochastic Training of Multi-Headed Attention and Understanding LoRA",
  "title_text": "Convergent Stochastic Training of Multi-Headed Attention and Understanding LoRA",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/eeh2dp94pm8gd",
  "venue": "arXiv",
  "versions": []
}