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：霍普菲尔德网络因其提供生物合理机制，成为解决多种计算问题的理想选择。自我优化（SO）模型通过采用基于生物学的赫布学习规则，结合网络反复重置至任意初始状态，进一步完善了霍普菲尔德网络，使其能够向编码于网络中的理想目标状态优化自身行为。为深入理解这一过程，我们首先通过“说谎者问题”和“地图着色问题”两个实例，证明SO模型能够求解SAT形式的组合问题。此外，我们揭示了在某些条件下，关键信息可能永久丢失，导致学习后的网络产生看似最优实则与任务要求不符的解决方案。这种看似是SO模型不良副作用的特性，反而能为其解决难解问题的机制提供重要洞察。