{
  "abstract": "Post-training pruning enables efficient deployment, but conventional methods do not explicitly preserve internal-gradient alignment between sparse and dense models. We study novel connections between downstream performance of compressed models and the ability to retain gradient information via influence-function preservation. Central to this connection is a curvature-aware objective that accounts for both layer activations and backpropagated gradients. Despite its promise, this objective remains underexplored in pruning due to a lack of efficient solvers. We introduce $\\texttt{CACTUS}$, a novel ADMM-based optimizer supporting both pruning and sparse-plus-low-rank decompositions of pre-trained weights. Compared to LLM-Surgeon which targets the same objective, $\\texttt{CACTUS}$ can achieve over an order-of-magnitude speedup. At $50\\%$ pruning of Qwen3-4B, $\\texttt{CACTUS}$ reduces the C4 perplexity gap to the dense model by $45\\%$, improves compressed-to-dense per-sample gradient cosine similarity on WikiText-2 from $0.670$ to $0.755$, and runs over $28\\times$ faster than LLM-Surgeon on substantially weaker hardware. By preserving influence functions, $\\texttt{CACTUS}$ supports effective data selection. On Llama-3.2-3B, fine-tuning a fresh dense model on the $5\\%$ of data selected by $\\texttt{CACTUS}$ achieves $49.44\\%$ accuracy on BIG-Bench Hard, compared with $47.22\\%$ using ALPS and $49.54\\%$ using dense-model selection. Finally, integrating $\\texttt{CACTUS}$ with LoGRA, a recent gradient-projection strategy, on Qwen3-4B with MLP layers pruned to 2:4 sparsity and a rank-64 correction retains a $0.711$ cosine alignment with dense LoGRA-projected C4 gradients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18516",
  "author_total": 3,
  "authors": [
    {
      "name": "Mehdi Makni"
    },
    {
      "name": "Natalia Ponomareva"
    },
    {
      "name": "Rahul Mazumder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86my4jvesj8eq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18516",
  "fulltext_url": null,
  "id": "86my4jvesj8eq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18516",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1707|Advanced Neural Network Applications"
    ]
  ],
  "openalex": "W7221752953",
  "pdf_url": "https://arxiv.org/pdf/2610.18516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86my4jvesj8eq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.18516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Two For The Price Of One: Curvature-Aware Pruning Preserves Influence Functions Too",
  "title_text": "Two For The Price Of One: Curvature-Aware Pruning Preserves Influence Functions Too",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/86my4jvesj8eq",
  "venue": "arXiv",
  "versions": []
}