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- Calvin Tsay Department of Computing, Imperial College London
Department of Computing, Imperial College London
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- Jan Kronqvist Department of Mathematics, KTH Royal Institute of Technology
Department of Mathematics, KTH Royal Institute of Technology
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- Alexander Thebelt Department of Computing, Imperial College London
Department of Computing, Imperial College London
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- Ruth Misener Department of Computing, Imperial College London
Department of Computing, Imperial College London
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NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing SystemsDecember 2021Article No.: 235Pages 3068–3080
Published:10 June 2024Publication History
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NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing Systems
Partition-based formulations for mixed-integer optimization of trained ReLU neural networks
Pages 3068–3080
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ABSTRACT
This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions via disjunctive programming. At one extreme, one partition per input recovers the convex hull of a node, i.e., the tightest possible formulation for each node. For fewer partitions, we develop smaller relaxations that approximate the convex hull, and show that they outperform existing formulations. Specifically, we propose strategies for partitioning variables based on theoretical motivations and validate these strategies using extensive computational experiments. Furthermore, the proposed scheme complements known algorithmic approaches, e.g., optimization-based bound tightening captures dependencies within a partition.
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NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing Systems
December 2021
30517 pages
ISBN:9781713845393
- Editors:
- M. Ranzato,
- A. Beygelzimer,
- Y. Dauphin,
- P.S. Liang,
- J. Wortman Vaughan
Copyright © 2021 Neural Information Processing Systems Foundation, Inc.
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- Published: 10 June 2024
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