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Poster
Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions
Nikolaos Karalias · Joshua Robinson · Andreas Loukas · Stefanie Jegelka

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #305
in Poster Session 4 »

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) 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.

Keywords: Combinatorial Optimization · Deep Learning · Unsupervised Learning · algorithmic reasoning

Author Information

Nikolaos Karalias (EPFL)
Joshua Robinson (MIT)
Andreas Loukas (Prescient Design, gRED, Roche)
Stefanie Jegelka (MIT)

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