---
res:
  bibo_abstract:
  - This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU
    activation functions and proves that when the data distribution is well-separated,
    DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly)
    zero-training error under the lazy training regime. For this purpose, we unify
    three interrelated concepts of overparameterization, benign overfitting, and the
    Lipschitz constant of DNNs. Our results indicate that interpolating with smoother
    functions leads to better generalization. Furthermore, we investigate the special
    case where interpolating smooth ground-truth functions is performed by DNNs under
    the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates
    that the generalization error converges to a constant order that only depends
    on label noise and initialization noise, which theoretically verifies benign overfitting.
    Our analysis provides a tight lower bound on the normalized margin under non-smooth
    activation functions, as well as the minimum eigenvalue of NTK under high-dimensional
    settings, which has its own interest in learning theory.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Zhenyu
      foaf_name: Zhu, Zhenyu
      foaf_surname: Zhu
  - foaf_Person:
      foaf_givenName: Fanghui
      foaf_name: Liu, Fanghui
      foaf_surname: Liu
  - foaf_Person:
      foaf_givenName: Grigorios G
      foaf_name: Chrysos, Grigorios G
      foaf_surname: Chrysos
  - foaf_Person:
      foaf_givenName: Francesco
      foaf_name: Locatello, Francesco
      foaf_surname: Locatello
      foaf_workInfoHomepage: http://www.librecat.org/personId=26cfd52f-2483-11ee-8040-88983bcc06d4
    orcid: 0000-0002-4850-0683
  - foaf_Person:
      foaf_givenName: Volkan
      foaf_name: Cevher, Volkan
      foaf_surname: Cevher
  bibo_volume: 202
  dct_date: 2023^xs_gYear
  dct_language: eng
  dct_publisher: ML Research Press@
  dct_title: Benign overfitting in deep neural networks under lazy training@
...