Neural networks are dynamical systems that compute with their dynamics. One example is the Hopfield model, forming an associative memory which stores patterns as global attractors of the network dynamics. From studies of dynamical networks it is well known that localized attractors also exist. Yet, they have not been used in computing paradigms. Here we show that interacting localized attractors in threshold networks can result in universal computation. We develop a rewiring algorithm that builds universal Boolean gates in a biologically inspired two-dimensional threshold network with randomly placed and connected nodes using collision-based computing. We aim at demonstrating the computational capabilities and the ability to control local limit cycle attractors in such networks by creating simple Boolean gates by means of these local activations. The gates use glider guns, i.e., localized activity that periodically generates "gliders" of activity that propagate through space. Several such gliders are made to collide, and the result of their interaction is used as the output of a Boolean gate. We show that these gates can be used to build a universal computer.
翻译:神经网络是与其动态进行计算动态的动态系统。 一个例子就是Hopfield模型, 形成联动记忆, 存储着网络动态的全球吸引者模式。 从对动态网络的研究中, 众所周知, 本地吸引者也存在。 然而, 这些网络没有被用于计算范式 。 我们在这里显示, 临界网络中相互作用的地方吸引者可以导致普遍计算 。 我们开发了一种重新连线算法, 在一个生物激发的双维临界网中建立普世波林门, 用基于碰撞的计算来随机放置和连接节点 。 我们的目标是通过这些本地激活来显示计算能力和在网络中控制本地限制循环吸引者的能力。 大门使用滑翔枪, 即定期生成空间传播活动的“ 滑翔机 ” 的局部活动。 数个这样的滑翔机被制造成为串, 其相互作用的结果被用作波林门的输出结果 。 我们显示, 这些门可以用来制造通用的计算机 。