On the Use of Associative Memory in Hopfield Networks Designed to Solve Propositional Satisfiability Problems
Natalya Weber, Werner Koch, Ozan Erdem, Tom Froese · 2023
Hopfield networks are an attractive choice for solving many types of computational problems because they provide a biologically plausible mechanism. The Self-Optimization (SO) model adds to the Hopfield network (HN) by using a biologically founded Hebbian learning rule, in combination with repeated network resets to arbitrary initial states, for optimizing its own behavior towards some desirable goal state encoded in the network. However, the solutions to the abstract problems used in the literature offer little insight into how HN arrive at solutions or partial solutions. In order to better understand that process, we demonstrate first that the SO model can solve concrete combinatorial satisfiability problems: The Liars problem and the map coloring problem. Based on these solutions, we discuss how under certain conditions critical information might get lost forever with the learned network producing seemingly optimal solutions that are in fact inappropriate for the problem it was tasked to solve. What appears to be an undesirable side-effect of the SO model, can provide insight into its process for solving intractable problems.