上下文依赖的时间序列预测：基于HyperReservoirs方法

中文摘要 AI 辅助

时间序列预测是储层计算的一个常见应用。当训练和测试时间序列数据包含多个动力学机制时，例如由于底层参数变化，或数据实际上由多个不同系统组成，简单应用储层计算原理会产生较高的预测误差。在此，我们提出了一种HyperReservoir，作为储层计算的扩展模型，专门针对此类情况设计。HyperReservoir将一个主储层与一个较小的上下文储层相结合，后者调制前者的输出权重。这种结构类似于深度神经网络文献中的超网络。然而，与之相反，HyperReservoirs保留了标准储层计算通过线性回归进行简单训练的特点。我们将所提出的架构与传统的回声状态网络（ESN）进行比较，其中上下文作用于输入；以及与全矩阵Conceptor进行比较，其中上下文调制储层状态空间。我们在基于Lorenz和Rössler系统的时间序列预测任务上评估了所有三种模型，包括变化的分岔参数和时间采样尺度。我们发现，HyperReservoir在所有三个任务中均实现了最低的平均测试误差，特别是在从同一吸引子但不同时间尺度采样的数据上，其性能优于conceptors。

英文摘要

Time series prediction is a common application of reservoir computing. When the training and testing time series data contains multiple dynamical regimes, because an underlying parameter is changing, or the data in fact consists of multiple distinct systems, simple application of the reservoir computing principle produces high prediction errors. Here, we propose a HyperReservoir as an extended model of reservoir computing especially designed for such cases. The HyperReservoir combines a main reservoir with a smaller context reservoir, where the latter modulates the output weights of the former. This structure resembles the hypernetworks from deep neural network literature. However, in contrast, HyperReservoirs retain the simple training via linear regression of standard reservoir computing. We compare the proposed architecture with a conventional ESN, in which context acts at the input, and a full-matrix Conceptor, in which context modulates the reservoir state space. We evaluate all three models on time-series prediction tasks based on Lorenz and Rössler systems, including for varying bifurcation parameters and time sampling scales. We find that the HyperReservoir achieves the lowest mean test error in all three tasks, and particularly outperforms conceptors on data that is sampled from the same attractor but at different time scales.

发表机构

• The University of Tokyo（东京大学）

机构由 AI 辅助整理，请以论文原文为准。