论文标题
不对称神经网络中的满足性过渡
Satisfiability transition in asymmetric neural networks
论文作者
论文摘要
神经元之间突触相互作用的不对称性在确定复发神经网络的记忆存储和检索特性方面起着至关重要的作用。在这项工作中，我们分析了将随机记忆存储在由具有确定程度不对称程度的突触基质连接的神经元网络中的问题。我们研究了与在记忆中找到突触矩阵有关的约束满意度问题的解决方案空间中相应的满意度和聚类转变。除了在网络中存储的关键记忆中，我们发现，除了通常的SAT/UNSAT过渡外，还有一个非常非对称矩阵的额外过渡，其中竞争性约束（确定的不对称与记忆存储）在问题中引起了足够的挫败感，以使其无法解决。在单个内存存储的情况下，该发现尤其引人注目，因为系统中没有淬火障碍。
Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a network of neurons connected by a synaptic matrix with a definite degree of asymmetry. We study the corresponding satisfiability and clustering transitions in the space of solutions of the constraint satisfaction problem associated with finding synaptic matrices given the memories. We find, besides the usual SAT/UNSAT transition at a critical number of memories to store in the network, an additional transition for very asymmetric matrices, where the competing constraints (definite asymmetry vs. memories storage) induce enough frustration in the problem to make it impossible to solve. This finding is particularly striking in the case of a single memory to store, where no quenched disorder is present in the system.
