A Weisfeiler-Leman Characterization of Global-Attention Graph Transformers for Mixed-Integer Linear Programs
Graph foundation models (GFMs) with global attention are increasingly used to represent mixed-integer linear programs (MILPs), aiming to capture structure beyond the locality of standard graph neural networks. We study their expressive power through graph isomorphism testing, asking which MILP instances they map to identical representations. We prove that a broad class of hierarchical graph transformers combining global linear attention, edge-weighted cross-attention, and bipartite message passing is bounded by the one-dimensional Weisfeiler-Leman (1-WL) test: under any parameter setting, 1-WL-equivalent MILP graphs receive identical graph embeddings. Our compositional proof shows that ea...
| Authors | Md Abrar Jahin, Craig A. Knoblock, Jay Pujara |
|---|---|
| Primary category | cs.LG |
| Published | 20 July 2026 |
| Last updated at source | 20 July 2026 |
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