{
  "abstract": "Full-parameter fine-tuning of large language models (LLMs) incurs substantial optimizer state memory overhead, limiting the model sizes that fit on modern GPUs. Existing approaches either compress optimizer state, abandon first-order gradients, or change the update geometry while retaining dense state. The recently introduced Muon optimizer reduces optimizer memory through matrix-valued updates. Still, its geometry differs from AdamW and can lead to performance degradation when fine-tuning AdamW-pretrained models. To reduce optimizer memory without sacrificing accuracy or computational efficiency in LLM fine-tuning, we propose Ternary Absolute-max Column-wise One-sparse optimizer, or TACO, which follows Muon's operator-norm steepest-descent view but takes the geometric route further. TACO computes the exact steepest-descent direction under a dimension-normalized $1\\to1$ operator norm by selecting the sign of the largest magnitude entry in each column of two-dimensional weight matrices. This retains first-order gradients while making optimizer state memory nearly negligible. Our practical TACO optimizer maintains only a small set of low precision gradient components per column, reducing persistent optimizer state by $174\\times$ relative to AdamW8bit (from 27.7 GB to 0.16 GB) and peak training memory by $2.9\\times$ (from 80.6 GB to 27.5 GB) on OPT-13B, while achieving comparable accuracy and runtime. TACO further enables full-parameter fine-tuning of 30-32B-parameter models on a single 80 GB H100 GPU across multiple model families and tasks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02199",
  "author_total": 5,
  "authors": [
    {
      "name": "Jichao Jiang"
    },
    {
      "name": "Cristian McGee"
    },
    {
      "name": "El Houcine Bergou"
    },
    {
      "name": "HanQin Cai"
    },
    {
      "name": "Aritra Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ka8fnaw659ee.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02199",
  "fulltext_url": null,
  "id": "8ka8fnaw659ee",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02199",
  "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.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7219155420",
  "pdf_url": "https://arxiv.org/pdf/2610.02199",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ka8fnaw659ee.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.02199",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02199"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "TACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-Tuning",
  "title_text": "TACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-Tuning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/8ka8fnaw659ee",
  "venue": "arXiv",
  "versions": []
}