{
  "abstract": "A core tenet of filterbank design is to minimize discrepancies in group delay, defined as the negative derivative of each filter's phase response with respect to frequency. Yet, in a convolutional neural network (convnet) layer, finite impulse responses (FIRs) are initialized with i.i.d. random Gaussian weights, thereby making group delay a random function of frequency. In the context of machine learning for signal processing, our article conducts a probabilistic analysis of group delay in convnets. We find that a zero-mean initialization causes heavy tails in the distribution of group delay. To reduce the probability of large deviations, a simple workaround is to introduce residual connections, as in residual neural networks (ResNets).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Vincent Lostanlen"
    },
    {
      "name": "Daniel Haider"
    },
    {
      "name": "Peter Balazs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28kyzs2bt6ape.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "28kyzs2bt6ape",
  "issns": [],
  "landing_url": "https://hal.science/hal-05847165v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.stat"
    ],
    [
      "hal",
      "1.info.info-ts"
    ],
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      "hal",
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    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05847165/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28kyzs2bt6ape.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:44Z",
      "native_id": "hal-05847165",
      "source": "hal",
      "url": "https://hal.science/hal-05847165v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Understanding Group Delay in Random Convnets",
  "title_text": "Understanding Group Delay in Random Convnets",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:47Z",
  "url": "https://research.draconitic.com/paper/28kyzs2bt6ape",
  "venue": "HAL",
  "versions": []
}