Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating computational intensive heuristics like strong branching, which entails solving multiple linear optimization problems (LPs). Despite the empirical success, the reasons behind MPNNs’ effectiveness in emulating linear optimization remain largely unclear. Here, we show that MPNNs can simulate standard interior-point methods for LPs, explaining their practical success. Furthermore, we highlight how MPNNs can serve as a lightweight proxy for solving LPs, adapting to a given problem instance distribution. Empirically, we show that MPNNs solve LP relaxations of standard combinatorial optimization problems close to optimality, often surpassing conventional solvers and competing approaches in solving time.
Future Directions in Foundations of Graph Machine Learning
Christopher Morris, Nadav Dym, Haggai Maron, and 7 more authors
CoRR, 02–04 may 2024
Weisfeiler-Leman at the margin: When more expressivity matters
Billy J. Franks, Christopher Morris, Ameya Velingker, and 1 more author
CoRR, 02–04 may 2024
2023
Arxiv
Attending to Graph Transformers
Luis Müller, Mikhail Galkin, Christopher Morris, and 1 more author
MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers
Elias B. Khalil, Christopher Morris, and Andrea Lodi
In Thirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2022, Thirty-Fourth Conference on Innovative Applications of Artificial Intelligence, IAAI 2022, The Twelveth Symposium on Educational Advances in Artificial Intelligence, EAAI 2022 Virtual Event, February 22 - March 1, 2022, 02–04 may 2022
Combinatorial Optimization and Reasoning with Graph Neural Networks
Quentin Cappart, Didier Chételat, Elias B. Khalil, and 3 more authors
In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event / Montreal, Canada, 19-27 August 2021, 02–04 may 2021
The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs
Christopher Morris, Matthias Fey, and Nils M. Kriege
In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event / Montreal, Canada, 19-27 August 2021, 02–04 may 2021
Leonardo Cotta, Christopher Morris, and Bruno Ribeiro
In Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, 02–04 may 2021
Weisfeiler and Leman go sparse: Towards scalable higher-order graph embeddings
Christopher Morris, Gaurav Rattan, and Petra Mutzel
In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 02–04 may 2020
Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks
Christopher Morris, Martin Ritzert, Matthias Fey, and 4 more authors
In The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019, The Thirty-First Innovative Applications of Artificial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019, Honolulu, Hawaii, USA, January 27 - February 1, 2019, 02–04 may 2019
A Property Testing Framework for the Theoretical Expressivity of Graph Kernels
Nils M. Kriege, Christopher Morris, Anja Rey, and 1 more author
In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden, 02–04 may 2018
Hierarchical Graph Representation Learning with Differentiable Pooling
Zhitao Ying, Jiaxuan You, Christopher Morris, and 3 more authors
In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, 02–04 may 2018
Recent Advances in Kernel-Based Graph Classification
Nils M. Kriege, and Christopher Morris
In Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2017, Skopje, Macedonia, September 18-22, 2017, Proceedings, Part III, 02–04 may 2017