---
res:
  bibo_abstract:
  - 'A crucial property for achieving secure, trustworthy and interpretable deep learning
    systems is their robustness: small changes to a system''s inputs should not result
    in large changes to its outputs. Mathematically, this means one strives for networks
    with a small Lipschitz constant. Several recent works have focused on how to construct
    such Lipschitz networks, typically by imposing constraints on the weight matrices.
    In this work, we study an orthogonal aspect, namely the role of the activation
    function. We show that commonly used activation functions, such as MaxMin, as
    well as all piece-wise linear ones with two segments unnecessarily restrict the
    class of representable functions, even in the simplest one-dimensional setting.
    We furthermore introduce the new N-activation function that is provably more expressive
    than currently popular activation functions. We provide code at this https URL.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Bernd
      foaf_name: Prach, Bernd
      foaf_surname: Prach
      foaf_workInfoHomepage: http://www.librecat.org/personId=2D561D42-C427-11E9-89B4-9C1AE6697425
  - 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
  bibo_doi: 10.48550/ARXIV.2311.06103
  dct_date: 2023^xs_gYear
  dct_language: eng
  dct_title: 1-Lipschitz neural networks are more expressive with N-activations@
...