Kobayashi Shumpei, Tran Quoc Hoan, Nakajima Kohei
Department of Creative Informatics, <a href="https://ror.org/057zh3y96">The University of Tokyo</a>, Bunkyo-ku, Tokyo 113-8656, Japan.
Next Generation Artificial Intelligence Research Center (AI Center), <a href="https://ror.org/057zh3y96">The University of Tokyo</a>, Bunkyo-ku, Tokyo 113-8656, Japan.
Phys Rev E. 2024 Aug;110(2-1):024207. doi: 10.1103/PhysRevE.110.024207.
The echo state property (ESP) represents a fundamental concept in the reservoir computing (RC) framework that ensures output-only training of reservoir networks by being agnostic to the initial states and far past inputs. However, the traditional definition of ESP does not describe possible nonstationary systems in which statistical properties evolve. To address this issue, we present two categories of ESP: nonstationary ESP, designed for potentially nonstationary systems, and subspace and subset ESP, designed for systems whose subsystems have ESP. Following the definitions, we numerically demonstrate the correspondence between nonstationary ESP in the quantum reservoir computer (QRC) framework with typical Hamiltonian dynamics and input encoding methods using nonlinear autoregressive moving-average tasks. We also confirm the correspondence by computing linear or nonlinear memory capacities that quantify input-dependent components within reservoir states. Our study presents an understanding of the practical design of QRC and other possibly nonstationary RC systems in which nonstationary systems and subsystems are exploited.
回声状态属性（ESP）是储层计算（RC）框架中的一个基本概念，它通过对初始状态和过去的输入不敏感，确保储层网络仅基于输出进行训练。然而，ESP的传统定义并未描述统计属性会发生演变的可能的非平稳系统。为了解决这个问题，我们提出了两类ESP：为潜在非平稳系统设计的非平稳ESP，以及为其子系统具有ESP的系统设计的子空间和子集ESP。根据这些定义，我们通过使用非线性自回归移动平均任务，在具有典型哈密顿动力学和输入编码方法的量子储层计算机（QRC）框架中，以数值方式证明了非平稳ESP之间的对应关系。我们还通过计算量化储层状态内输入相关组件的线性或非线性记忆容量来确认这种对应关系。我们的研究展示了对QRC和其他可能的非平稳RC系统实际设计的理解，其中会利用非平稳系统和子系统。
