Message Passing Variational Autoregressive Network for Solving
  Intractable Ising Models
Qunlong Ma Zhi Ma Jinlong Xu Hairui Zhang Ming Gao
Many deep neural networks have been used to solve Ising models, including
autoregressive neural networks, convolutional neural networks, recurrent neural
networks, and graph neural networks. Learning a probability distribution of
energy configuration or finding the ground states of a disordered, fully
connected Ising model is essential for statistical mechanics and NP-hard
problems. Despite tremendous efforts, a neural network architecture with the
ability to high-accurately solve these fully connected and extremely
intractable problems on larger systems is still lacking. Here we propose a
variational autoregressive architecture with a message passing mechanism, which
can effectively utilize the interactions between spin variables. The new
network trained under an annealing framework outperforms existing methods in
solving several prototypical Ising spin Hamiltonians, especially for larger
spin systems at low temperatures. The advantages also come from the great
mitigation of mode collapse during the training process of deep neural
networks. Considering these extremely difficult problems to be solved, our
method extends the current computational limits of unsupervised neural networks
to solve combinatorial optimization problems.