---
res:
  bibo_abstract:
  - 'We address the following question:  How redundant is the parameterisation of
    ReLU networks? Specifically, we consider transformations of the weight space which
    leave the function implemented by the network intact.  Two such transformations
    are known for feed-forward architectures:  permutation of neurons within a layer,
    and positive scaling of all incoming weights of a neuron coupled with inverse
    scaling of its outgoing weights. In this work, we show for architectures with
    non-increasing widths that permutation and scaling are in fact the only function-preserving
    weight transformations.  For any eligible architecture we give an explicit construction
    of a neural network such that any other network that implements the same function
    can be obtained from the original one by the application of permutations and rescaling.  The
    proof relies on a geometric understanding of boundaries between linear regions
    of ReLU networks, and we hope the developed mathematical tools are of independent
    interest.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Phuong
      foaf_name: Bui Thi Mai, Phuong
      foaf_surname: Bui Thi Mai
      foaf_workInfoHomepage: http://www.librecat.org/personId=3EC6EE64-F248-11E8-B48F-1D18A9856A87
  - 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
  dct_date: 2020^xs_gYear
  dct_language: eng
  dct_title: Functional vs. parametric equivalence of ReLU networks@
...