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.

翻译：Hopfield网络因其提供了一种生物合理机制而成为解决许多类型计算问题的有吸引力的选择。自优化模型通过使用基于生物学的Hebbian学习规则，结合对任意初始状态的重复网络重置，对Hopfield网络进行了扩展，以优化其自身行为朝向网络中编码的某个期望目标状态。为了更好理解该过程，我们首先通过“说谎者问题”和“地图着色问题”两个实例，证明自优化模型能够解决合取范式形式的组合问题。此外，我们展示了在某些条件下，关键信息如何可能永久丢失，导致学习后的网络产生看似最优的解决方案，而这些方案实际上并不适合其被要求解决的问题。这种看似是自优化模型的不良副作用的现象，可以为其解决棘手的计算问题提供深入见解。