---
res:
  bibo_abstract:
  - "The empirical emergence of neural collapse—a surprising symmetry in the feature
    representations of the training data in the penultimate layer of deep neural\r\nnetworks—has
    spurred a line of theoretical research aimed at its understanding.\r\nHowever,
    existing work focuses on data-agnostic models or, when data structure is\r\ntaken
    into account, it remains limited to multi-layer perceptrons. Our paper fills\r\nboth
    these gaps by analyzing modern architectures in a data-aware regime: we\r\nprove
    that global optima of deep regularized transformers and residual networks\r\n(ResNets)
    with LayerNorm trained with cross entropy or mean squared error loss\r\nare approximately
    collapsed, and the approximation gets tighter as the depth grows.\r\nMore generally,
    we formally reduce any end-to-end large-depth ResNet or transformer training into
    an equivalent unconstrained features model, thus justifying its\r\nwide use in
    the literature even beyond data-agnostic settings. Our theoretical results\r\nare
    supported by experiments on computer vision and language datasets showing\r\nthat,
    as the depth grows, neural collapse indeed becomes more prominent.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Peter
      foaf_name: Súkeník, Peter
      foaf_surname: Súkeník
      foaf_workInfoHomepage: http://www.librecat.org/personId=d64d6a8d-eb8e-11eb-b029-96fd216dec3c
  - foaf_Person:
      foaf_givenName: Christoph
      foaf_name: Lampert, Christoph
      foaf_surname: Lampert
      foaf_workInfoHomepage: http://www.librecat.org/personId=40C20FD2-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-8622-7887
  - foaf_Person:
      foaf_givenName: Marco
      foaf_name: Mondelli, Marco
      foaf_surname: Mondelli
      foaf_workInfoHomepage: http://www.librecat.org/personId=27EB676C-8706-11E9-9510-7717E6697425
    orcid: 0000-0002-3242-7020
  bibo_doi: 10.52202/085713-1450
  bibo_volume: 38
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1049-5258
  - http://id.crossref.org/issn/9798331338275
  dct_language: eng
  dct_publisher: Neural Information Processing Systems Foundation@
  dct_title: Neural collapse is globally optimal in deep regularized ResNets and transformers@
...