On the use of associative memory in Hopfield networks designed to solve propositional satisfiability problems
This work addresses the reliability of biologically inspired neural networks for solving intractable combinatorial problems, though it is incremental in exploring the limitations of an existing model.
The authors demonstrated that the Self-Optimization model, an extension of Hopfield networks using Hebbian learning and resets, can solve combinatorial SAT problems like the Liars and map coloring problems, but also identified conditions where it loses critical information, leading to inappropriate solutions.
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 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. In order to better understand that process, we demonstrate first that the SO model can solve concrete combinatorial problems in SAT form, using two examples of the Liars problem and the map coloring problem. In addition, we show how under some 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.