{
  "abstract": "Mixed-precision weight quantization is commonly formulated as a Multiple-Choice Knapsack Problem (MCKP), yet existing solvers rely on scalar sensitivity proxies that collapse each weight matrix's Hessian into a single number and treat every module independently. We prove that even the optimal scalar proxy incurs multiplicative distortion up to $\\sqrt{κ(\\mathbf{A})κ(\\mathbf{B})}$ relative to the full activation-aware quadratic, where $κ(\\mathbf{A})$ and $κ(\\mathbf{B})$ denote the condition numbers of the input- and output-side Hessian factors. This bound varies from $10^1$ to $10^{13}$ for typical LLM modules, making inter-module sensitivity ranking unreliable. To address these limitations, we propose Cross-layer Activation-aware Sensitivity Allocation (CASA), a two-phase method. In Stage 1, the scalar proxy is replaced by an activation-aware metric derived from the Kronecker-factored Hessian, reducing the MCKP to a form whose continuous relaxation admits a closed-form solution. In Stage 2, a cross-layer-aware local search evaluates bit-width updates using the end-to-end model loss. Experiments on multiple LLMs across different bit budgets show that CASA achieves lower perplexity than the latest scalar-proxy baselines, especially at ultra-low bit-widths ($<3$ bits per weight). Moreover, the performance gain in zero-shot accuracy tracks the per-model average condition-number over modules, confirming the distortion bound as a practical indicator of scalar-proxy failure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25916",
  "author_total": 2,
  "authors": [
    {
      "name": "Akihiro Yoshida"
    },
    {
      "name": "Yuma Ichikawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7yf96sza1v8w0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25916",
  "fulltext_url": null,
  "id": "7yf96sza1v8w0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25916",
  "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.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1707|Advanced Neural Network Applications"
    ]
  ],
  "openalex": "W7214113829",
  "pdf_url": "https://arxiv.org/pdf/2609.25916",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7yf96sza1v8w0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:49Z",
      "native_id": "2609.25916",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25916"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond Scalar Sensitivity: Activation-Aware Mixed-Precision LLM Quantization with Cross-Layer Refinement",
  "title_text": "Beyond Scalar Sensitivity: Activation-Aware Mixed-Precision LLM Quantization with Cross-Layer Refinement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:49Z",
  "url": "https://research.draconitic.com/paper/7yf96sza1v8w0",
  "venue": "arXiv",
  "versions": []
}