CutWorld: A Latent Dynamics Model for Unified Branch-and-Cut Control

Branch-and-Cut solvers repeatedly choose a branching variable, a cutting plane, and an open search node. These choices reshape an exponentially large search tree, but standard learned branching rules score candidates only from the current relaxation. We present , a latent decision-dynamics model that plans over candidate branching actions without solving their child linear programs. A bipartite GATv2 encoder maps the current relaxation to a global latent and per-variable embeddings. A causal Transformer then predicts the latent successor and its variable embeddings conditioned on a candidate and branch direction, allowing the policy to be re-applied to imagined states. We combine the resulting rollout value with the predicted dual-bound progress and cost-to-go, and use the shared representation to order nodes and select the root Gomory cut. Because the learned components only select among valid branches, globally valid cuts, and open-node orderings, they do not alter feasibility or bound tests. On fixed Set Cover benchmarks generated with one seed, the neural configurations complete all 10 medium instances ($500\times 1000$, 300 s limit) and all 5 hard instances ($1000\times 2000$, 600 s limit) in the Python/HiGHS harness, whereas the classical rules reach their time limits. A depth-one rollout reduces the medium-tier shifted-geometric-mean tree-node count by $44.2\%$ relative to imitation (3,197 versus 5,733); at hard scale, combining rollout and root cuts reaches 2,603 nodes versus 4,633 for imitation. We report completion, tree-node counts, wall-clock time, LP time, and cuts, and explicitly separate completed-tree measurements from timeout lower bounds. The benchmark is intended as a controlled feasibility study; its small, single-seed evaluation does not establish statistical superiority over industrial MIP solvers.