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

Understand

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 observables, 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.