Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Nikolaos Karalias, Joshua Robinson, Andreas Loukas, Stefanie Jegelka

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

2 Zitate (Scopus)

Abstract

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep learning architectures that rely on representations in high-dimensional vector spaces. In this work, we address both difficulties for set functions, which capture many important discrete problems. First, we develop a framework for extending set functions onto low-dimensional continuous domains, where many extensions are naturally defined. Our framework subsumes many well-known extensions as special cases. Second, to avoid undesirable low-dimensional neural network bottlenecks, we convert low-dimensional extensions into representations in high-dimensional spaces, taking inspiration from the success of semidefinite programs for combinatorial optimization. Empirically, we observe benefits of our extensions for unsupervised neural combinatorial optimization, in particular with high-dimensional representations.

OriginalspracheEnglisch
TitelAdvances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Redakteure/-innenS. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
Herausgeber (Verlag)Neural information processing systems foundation
ISBN (elektronisch)9781713871088
PublikationsstatusVeröffentlicht - 2022
Extern publiziertJa
Veranstaltung36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, USA/Vereinigte Staaten
Dauer: 28 Nov. 20229 Dez. 2022

Publikationsreihe

NameAdvances in Neural Information Processing Systems
Band35
ISSN (Print)1049-5258

Konferenz

Konferenz36th Conference on Neural Information Processing Systems, NeurIPS 2022
Land/GebietUSA/Vereinigte Staaten
OrtNew Orleans
Zeitraum28/11/229/12/22

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