AI 中文总结
针对原始霍普菲尔德网络异步处理耗时问题，提出基于离散微分滤波器（DDF）的新型同步动力学SD-DDF，经四项实验实证可缩短处理时间，且保证收敛与能量最大降低。
AI 中文摘要
原始霍普菲尔德网络的动力学是异步（顺序）的（每个时间步仅更新一个神经元的状态）。本文提出一种新工具和新动力学，旨在通过每个时刻同时更新一个或多个神经元来减少处理时间，同时保证过程收敛并力求每一步实现最大能量降低，从而确保总处理时间最短。从同步动力学角度看，计算使能量较当前状态降低最多且保证收敛的下一个网络状态，本身是一个组合优化问题。我们开发并使用新工具求解该问题，将其命名为离散微分滤波器（Discrete Differential Filter, DDF），并基于此开发新型同步动力学，命名为SD-DDF（基于离散微分滤波器的同步动力学）。本文回顾了霍普菲尔德网络的原始异步动力学，提出新工具和新同步动力学，并给出其理论依据及四项计算实验，以实证评估处理时间的加速效果。
英文摘要
The dynamics of the original Hopfield network is asynchronous (sequential) (updates the state of only one neuron per time step). In this paper, we propose a new tool and a new dynamics to reduce the processing time by updating one or more neurons simultaneously per instant while ensuring process convergence and aiming for the maximum energy decrease at each step, thus guaranteeing the shortest total processing time. From the point of view of synchronous dynamics, calculating the next network state at which energy decreases the most from the current state while ensuring convergence is itself a combinatorial optimization problem. We develop and use a new tool to solve it. We call this new tool Discrete Differential Filter (DDF) and, based upon it, we develop a new synchronous dynamics which we call SD-DDF (Synchronous Dynamics based upon Discrete Differential Filter). In this paper, we review the original asynchronous dynamics for Hopfield networks and present a new tool and a new synchronous dynamics with its theoretical justification and four computational experiments to assess the speed up in processing time empirically.
