arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.00766cs.LGmath.DSstat.ML
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稳定性和记忆丧失齐头并进:动力学和计算中的三个结果

Stability and Memory-loss go Hand-in-Hand: Three Results in Dynamics & Computation

University of Pretoria(比勒陀利亚大学)

G Manjunath

摘要:

寻找有助于建立动力学和计算之间关系的普遍规律是由最近生物启发计算的扩张主义倡议所驱动的。理解这种动力学和计算的一般设置是响应时间输入的驱动动力学系统。令人惊讶的是,我们发现记忆丧失是驱动系统忘记其内部状态的一个特征,这有助于为以下几十年来一直没有答案的基本稳定性问题提供明确的答案:什么是必要的和足够的,使得略有不同的输入仍然导致大多数相似的反应?改变驱动系统的参数如何影响稳定性?临界边缘的数学定义是什么?我们预计我们的结果是及时的理解和设计生物启发的计算机,进入专用硬件实现的时代,为类脑计算和国家的最先进的储备池计算的应用。

英文摘要:

The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and computation is a driven dynamical system that responds to a temporal input. Surprisingly, we find memory-loss a feature of driven systems to forget their internal states helps provide unambiguous answers to the following fundamental stability questions that have been unanswered for decades: what is necessary and sufficient so that slightly different inputs still lead to mostly similar responses? How does changing the driven system's parameters affect stability? What is the mathematical definition of the edge-of-criticality? We anticipate our results to be timely in understanding and designing biologically inspired computers that are entering an era of dedicated hardware implementations for neuromorphic computing and state-of-the-art reservoir computing applications.

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