Neural Dual Bounds: Valid-by-Construction JGLP Warm-Starts for MAP and Constrained MAP

We present Neural Dual Bounds, a calibration-free framework that produces deterministic upper bounds for MAP inference in probabilistic graphical models using a single neural-network forward pass. The framework trains a network to output the edge messages of a mini-bucket style upper bound on a given join-graph decomposition in a self-supervised manner by directly minimizing the a smooth dual objective. The output of this network can be used at test time to warm-start a standard JGLP optimizer. Across diverse benchmarks, this warm start yields dual gaps that are orders of magnitude tighter than those from zero initialization, with the largest gains in the early-iteration regime. We also apply our framework for the constrained MAP (CMPE) task, and we show that neural warm starts with test-time adaptation consistently achieve the tightest dual gaps across all iteration budgets against an adaptive baseline.