提出同步更新机制，加速霍普菲尔德网络计算并保证收敛。
New Synchronous Computation Dynamics for Hopfield Networks
- 用离散微分滤波器（DDF）求解同步更新时的能量最小化问题。
- 新方法在实验中实现显著提速，且每步能量下降最大。
- 适合需要快速求解优化问题的场景，如模式识别与存储重建。
原始霍普菲尔德网络采用异步动态（每次仅更新一个神经元）。本文提出一种新工具和新动态，通过每步同步更新一个或多个神经元，在确保收敛的前提下最大化每步能量下降，从而缩短总处理时间。从同步动态视角看，寻找使能量下降最多的下一时序状态本身是一个组合优化问题。为此，我们开发了离散微分滤波器（DDF），并基于此构建新的同步动态SD-DDF。本文回顾了原始异步动态，给出了新工具与新动态的理论依据，并通过四项计算实验实证其处理速度提升效果。
原文摘要 · Abstract (English)
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.
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