# Asymptotic evaluation of the information processing capacity in reservoir computing

arXiv: https://arxiv.org/abs/2502.15769 · HTML: https://mlsanity.com/paper/2502.15769/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Builds on (most cited first, 5 of 5)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [A Unifying Framework for Information Processing in Stochastically Driven Dynamical Systems](https://mlsanity.com/paper/1906.04608/) (2019)
- [Memory Capacity of Nonlinear Recurrent Networks: Is it Informative?](https://mlsanity.com/paper/2502.04832/) (2025)

## Built on by (most cited first, 3 of 3)

- [Techniques for Enhancing Memory Capacity of Reservoir Computing](https://mlsanity.com/paper/2502.17923/) (2025)
- [Information Processing Capacity of Stationary Physical Systems: Theory, Data-efficient Estimation Methods, and Photonic Demonstration](https://mlsanity.com/paper/2605.19152/) (2026)
- [Organization of computation in reservoir computing](https://mlsanity.com/paper/2607.17858/) (2026)

## Abstract (arXiv)

Reservoir computing (RC) is becoming increasingly important because of its short training time. The squared error normalized by the target output is called the information processing capacity (IPC) and is used to evaluate the performance of an RC system. Since RC aims to learn the relationship between input and output time series, we should evaluate the IPC for infinitely long data rather than the IPC for finite-length data. However, a method for estimating it has not been established. We evaluated the IPC for infinitely long data using the asymptotic expansion of the IPC and weighted least-squares fitting. Then, we showed the validity of our method by numerical simulations. This work makes the performance evaluation of RC more evident.