标题： 过去的回声：衰减记忆和回声状态的统一观点 显示英文标题

标题： Echoes of the past: A unified perspective on fading memory and echo states

摘要： 递归神经网络（RNNs）在涉及时间序列和时间数据的信息处理任务中变得越来越流行。 RNNs 的一个基本特性是它们能够创建可靠的输入/输出响应，这通常与网络如何处理其处理过的信息的记忆有关。 已经提出了各种概念来概念化 RNNs 中记忆的行为，包括稳态、回声状态、状态遗忘、输入遗忘和衰减记忆。 尽管这些概念经常被互换使用，但它们的确切关系仍然不清楚。 本工作旨在用一种共同的语言统一这些概念，推导它们之间的新含义和等价性，并提供一些现有结果的替代证明。 通过澄清这些概念之间的关系，这项研究有助于更深入地理解 RNNs 及其时间信息处理能力。 显示英文摘要

摘要： Recurrent neural networks (RNNs) have become increasingly popular in information processing tasks involving time series and temporal data. A fundamental property of RNNs is their ability to create reliable input/output responses, often linked to how the network handles its memory of the information it processed. Various notions have been proposed to conceptualize the behavior of memory in RNNs, including steady states, echo states, state forgetting, input forgetting, and fading memory. Although these notions are often used interchangeably, their precise relationships remain unclear. This work aims to unify these notions in a common language, derive new implications and equivalences between them, and provide alternative proofs to some existing results. By clarifying the relationships between these concepts, this research contributes to a deeper understanding of RNNs and their temporal information processing capabilities.