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On the limitations of representing functions on sets

Abstract:

Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed as the cardinality of the sets under consideration increases. However, we demonstrate that the analysis leading to this conjecture requires mappings which are highly discontinuous and argue that this is only of limited practical use. Motivated by this obser...

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Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Oxford college:
Pembroke College
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Engineering Science
Role:
Author
Publisher:
Journal of Machine Learning Research Publisher's website
Journal:
Proceedings of Machine Learning Research Journal website
Volume:
97
Pages:
6487-6494
Host title:
Proceedings of Machine Learning Research
Publication date:
2019-06-13
Acceptance date:
2019-04-24
ISSN:
2640-3498
Source identifiers:
1081433
Keywords:
Pubs id:
pubs:1081433
UUID:
uuid:3d5730ad-0070-46e9-b173-5b139d122dba
Local pid:
pubs:1081433
Deposit date:
2020-01-09

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