{
  "abstract": "The ℓ1,∞ norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, O nm log(nm) for a matrix in R n×m . In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the ℓ1,∞ norm is only O nm for a matrix in R n×m . Moreover, we provide a new ℓ1,∞ identity with mathematical proof and experimental validation. Experiments show that our bi-level ℓ1,∞ projection is O log(nm) times faster than the actual fastest algorithm. Our bi-level ℓ1,∞ projection outperforms the sparsity of the usual ℓ1,∞ projection while keeping the same or slightly better accuracy in classification applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Michel Barlaud"
    },
    {
      "name": "Jean-Paul Marmorat"
    },
    {
      "name": "Guillaume Perez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eqw4tekmyjzy1.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "eqw4tekmyjzy1",
  "issns": [],
  "landing_url": "https://hal.science/hal-05303330v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.stat"
    ],
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      "hal",
      "1.stat.ml"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05303330/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eqw4tekmyjzy1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "hal-05303330",
      "source": "hal",
      "url": "https://hal.science/hal-05303330v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Linear-Time Bilevel Clipping operators for Structured Sparsity in Neural Networks",
  "title_text": "Linear-Time Bilevel Clipping operators for Structured Sparsity in Neural Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:21Z",
  "url": "https://research.draconitic.com/paper/eqw4tekmyjzy1",
  "venue": "HAL",
  "versions": []
}