Hülser Tobias, Köster Felix, Lüdge Kathy, Jaurigue Lina
Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.
Technische Universität Ilmenau, Institute of Physics, Ilmenau, Germany.
Nanophotonics. 2022 Oct 3;12(5):937-947. doi: 10.1515/nanoph-2022-0415. eCollection 2023 Mar.
In the reservoir computing literature, the information processing capacity is frequently used to characterize the computing capabilities of a reservoir. However, it remains unclear how the information processing capacity connects to the performance on specific tasks. We demonstrate on a set of standard benchmark tasks that the total information processing capacity correlates poorly with task specific performance. Further, we derive an expression for the normalized mean square error of a task as a weighted function of the individual information processing capacities. Mathematically, the derivation requires the task to have the same input distribution as used to calculate the information processing capacities. We test our method on a range of tasks that violate this requirement and find good qualitative agreement between the predicted and the actual errors as long as the task input sequences do not have long autocorrelation times. Our method offers deeper insight into the principles governing reservoir computing performance. It also increases the utility of the evaluation of information processing capacities, which are typically defined on i.i.d. input, even if specific tasks deliver inputs stemming from different distributions. Moreover, it offers the possibility of reducing the experimental cost of optimizing physical reservoirs, such as those implemented in photonic systems.
在水库计算文献中，信息处理能力经常被用来表征水库的计算能力。然而，信息处理能力如何与特定任务的性能相关联仍不清楚。我们在一组标准基准任务上证明，总信息处理能力与任务特定性能的相关性很差。此外，我们推导出一个任务的归一化均方误差作为各个信息处理能力的加权函数的表达式。在数学上，推导要求任务具有与用于计算信息处理能力相同的输入分布。我们在一系列违反此要求的任务上测试我们的方法，并且只要任务输入序列没有长自相关时间，就会发现预测误差与实际误差之间有良好的定性一致性。我们的方法为控制水库计算性能的原理提供了更深入的见解。它还增加了信息处理能力评估的效用，信息处理能力通常是在独立同分布输入上定义的，即使特定任务提供来自不同分布的输入。此外，它提供了降低优化物理水库（例如在光子系统中实现的那些）实验成本的可能性。
