Learning to Sample from Power Distributions for Amortized MPE Inference in Probabilistic Graphical Models

We propose a neural sampling approach for repeated most probable explanation (MPE) inference on a fixed probabilistic graphical model (PGM). Our approach learns to sample from the power family \(P_\beta(q\mide) \propto P(q\mide)^\beta\), where increasing \(\beta\) concentrates probability on high-probability configurations and progressively biases sampling toward MPE solutions. We instantiate this formulation with a factor-reading neural sampler that directly uses the PGM's potentials to generate assignments conditioned on the observed evidence. The sampler is amortized across evidence queries and trained with a reverse-KL objective and a curriculum that progressively increases \(\beta\), requiring neither labeled MPE solutions nor computation of normalizing constants. At inference time, we draw samples from the learned proposal and return the highest-scoring assignment, with optional query-specific test-time refinement using the same objective to further improve solution quality. Across nine PGMs, a single sample per query achieves higher mean solution quality than the evaluated neural MPE baselines. With query-specific refinement, our method also outperforms the evaluated branch-and-bound solvers on six benchmark PGMs under matched wall-clock budgets. Beyond direct MPE inference, we analyze how the power parameter \(\beta\) affects distributional fidelity and MPE solution quality, and show that the learned proposals can improve existing inference procedures by warm-starting annealed sequential Monte Carlo and guiding branch-and-bound search.