2019/06/30 by Feng Pan, Pengfei Zhou, Haijun Zhou +2 · 14 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Autocorrelation #Autoregressive model #Complex Network Analysis Techniques #Computer science #Graph #Mathematics #Neural Networks and Applications #Physics #Sparse approximation #Statistical mechanics #Statistical physics #Statistics #Theoretical computer science #Topological and Geometric Data Analysis #Vertex (graph theory) #cond-mat.dis-nn #cond-mat.stat-mech #cs.LG #stat.ML
paper · pdf · doi:10.1103/physreve.103.012103
published in Physical review. E 103(1), 012103 (American Physical Society) · 13 pages, 5 figures
arxiv created 2020/05/22 · openalex publication_date 2021/01/05 · arxiv updated 2021/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small feedback vertex set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learns a variational distribution parametrized using neural networks to approximate the original Boltzmann distribution. The method is able to estimate free energy, compute observables, and generate unbiased samples via direct sampling without autocorrelation. Extensive experiments show that our approach is more accurate than existing approaches for sparse spin glasses. On random graphs and real-world networks, our approach significantly outperforms the standard methods for sparse systems, such as the belief-propagation algorithm; on structured sparse systems, such as two-dimensional lattices our approach is significantly faster and more accurate than recently proposed variational autoregressive networks using convolution neural networks.