Title: NeuroLifting: Neural Inference on Markov Random Fields at Scale
Primary area: optimization
Keywords: MAP estimation, Markov Random Fields, random spanning trees

Abstract: Inference in large-scale Markov Random Fields (MRFs) remains challenging, with traditional approximate like belief propagation and exact methods such as the Toulbar2 solver often struggling to balance efficiency and solution quality at scale. This paper presents NeuroLifting, a novel approach that uses Graph Neural Networks (GNNs) to reparameterize MRF decision variables, enabling standard gradient descent optimization. By extending lifting techniques through neural networks, NeuroLifting achieves efficient, parallelizable optimization with a smooth loss landscape. Empirical results show NeuroLifting matches Toulbar2's solution quality on moderate scales while outperforming approximate methods. Notably, on large-scale MRFs, it demonstrates superior solutions compared to baselines with linear computational complexity growth, marking a significant advance in scalable MRF inference. The code of our model can be accessed at \url{https://anonymous.4open.science/status/NeuroLifting-5BC0}.