Solving Statistical Mechanics on Sparse Graphs with Feedback Set Variational Autoregressive Networks [article]

Feng Pan, Pengfei Zhou, Hai-Jun Zhou, Pan Zhang
2020 arXiv   pre-print
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 parameterized using neural networks to approximate the original Boltzmann distribution. The method is able to estimate free energy, compute
more » ... , and generate unbiased samples via direct sampling without auto-correlation. 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.
arXiv:1906.10935v2 fatcat:zt3notnp7fewtitf2pq2bat4oa