Combining Learned Representations for Combinatorial Optimization
This work addresses combinatorial optimization for AI/ML researchers by offering an incremental improvement in efficiency for specific problems like boolean satisfiability.
The authors tackled combinatorial optimization problems by combining pretrained Restricted Boltzmann Machines (RBMs) to bypass learning in large models, enabling the solution of 64-bit addition and 16-bit factorization problems with more accurate results compared to fully trained models at the same sample size.
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.