Graph neural networks and the energetic cavity method for combinatorial optimization
We study the use of graph neural networks (GNNs) for finding approximate ground states of Ising models. Efficiently finding these ground states is of broad significance because many combinatorial optimization problems can be formulated as an Ising model with the appropriate choice of couplings and fields. Exactly solving these problems is hard but there are many good heuristic methods. A lineage of these heuristics build from mean-field approximations: one approach uses the leading eigenvector of an appropriately defined matrix, another is the min-sum algorithm, also known as the energetic cavity method. Without modification, GNNs perform worse than both of these methods. We consider smal...
| Authors | Joe Bacchus George, George T. Cantwell |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 7 September 2026 |
| Last updated at source | 7 September 2026 |
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