Continuous-time neural networks without local traps for solving Boolean satisfiability

Abstract

We present a deterministic continuous-time recurrent neural network similar to CNN models, which can solve Boolean satisfiability (k-SAT) problems without getting trapped in non-solution fixed points. The model can be implemented by analog circuits, in which case the algorithm would take a single operation: the template (connection weights) is set by the k-SAT instance and starting from any initial condition the system converges to a solution. We prove that there is a one-to-one correspondence between the stable fixed points of the model and the k-SAT solutions and present numerical evidence that limit cycles may also be avoided by appropriately choosing the parameters of the model. As this study opens potentially novel technical avenues to tackle hard optimization problems, we also discuss some of the arising questions that need to be investigated in future studies.