SCoR: Unsupervised State-Conditioned Refinement for Integer Linear Programming

Integer linear programming (ILP) is a general framework for combinatorial optimization. Unsupervised approaches learn to solve ILPs without solver-generated supervision, but their updates often rely on aggregate signals that obscure the prediction-dependent states of individual constraints and their effects across variables. We propose State-Conditioned Refinement (SCoR), which incorporates localized constraint feedback into unsupervised ILP optimization. Given a relaxed prediction, SCoR encodes normalized constraint residuals and propagates them to incident variables through sparse attention over the bipartite incidence graph. This feedback and the current optimization state parameterize a bounded positive diagonal preconditioner that adapts the base update to heterogeneous local conditions. We characterize the refinement's boundedness and descent compatibility and show that, under a matched update budget, variable-wise preconditioning admits a broader allocation set than uniform scaling and can yield a strictly larger local-model decrease. SCoR preserves the underlying unsupervised objective and can be integrated with different optimization schemes. Experiments on standard benchmarks and real-world instances demonstrate improvements across representative unsupervised ILP optimizers.