{
  "abstract": "As large language models (LLMs) are increasingly deployed across heterogeneous hardware with varying resource constraints, the ability to adaptively manage the performance-efficiency trade-off without retraining is critical. We propose Drop-by-Drop, a novel multi-bitwidth post-training quantization framework enabling inference-time precision control over LLM weights from a single quantized model. As theoretical motivation, we prove that Gaussian sources are successively refinable under a weighted mean squared error distortion motivated by LLM loss functions: successive refinement across distortion levels incurs no rate penalty relative to encoding at each level separately. Drop-by-Drop approximates this hierarchical structure in practice by incorporating Matryoshka-style supervision into additive codebook training, inducing an ordering in which codebook prefixes yield accurate partial reconstructions at each precision level. Furthermore, a block-Hadamard rotation brings the weight distribution closer to our Gaussian source assumption. The result is a single model that serves multiple bitwidths by dropping codebooks, reducing storage and quantization cost relative to the static per-bitwidth models. Across Qwen, LLaMA, Gemma, and Mistral, Drop-by-Drop achieves lower perplexity than state-of-the-art multi-bitwidth methods with competitive zero-shot accuracy, while our specialized kernels further reduce decoding latency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.12876",
  "author_total": 3,
  "authors": [
    {
      "name": "Liza Babaoglu"
    },
    {
      "name": "Shuangyi Chen"
    },
    {
      "name": "Ashish Khisti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m1x2sz7th9em.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12876",
  "fulltext_url": null,
  "id": "7m1x2sz7th9em",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12876",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1707|Advanced Neural Network Applications"
    ]
  ],
  "openalex": "W7164591065",
  "pdf_url": "https://arxiv.org/pdf/2606.12876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m1x2sz7th9em.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2606.12876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Multi-Bitwidth Quantization for LLMs Using Additive Codebooks",
  "title_text": "Multi-Bitwidth Quantization for LLMs Using Additive Codebooks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/7m1x2sz7th9em",
  "venue": "arXiv",
  "versions": []
}