We propose a new approach to combine Restricted Boltzmann Machines (RBMs)
that can be used to solve combinatorial optimization problems. This allows
synthesis of larger models from smaller RBMs that have been pretrained, thus
effectively bypassing the problem of learning in large RBMs, and creating a
system able to model a large, complex multi-modal space. We validate this
approach by using learned representations to create ``invertible boolean
logic'', where we can use Markov chain Monte Carlo (MCMC) approaches to find
the solution to large scale boolean satisfiability problems and show viability
towards other combinatorial optimization problems. Using this method, we are
able to solve 64 bit addition based problems, as well as factorize 16 bit
numbers. We find that these combined representations can provide a more
accurate result for the same sample size as compared to a fully trained model.

本研究提出了一种新方法，使用受限玻尔兹曼机（RBMs）来解决组合优化问题，从而有效地绕过在大型 RBMs 中学习的问题，并创建一个能够建模大型复杂多模态空间的系统。研究结果表明，这种方法可以有效地解决布尔可满足性问题和其他组合优化问题，对于相同的样本大小，这种方法可以提供比完全训练模型更准确的结果。