Necessary and Sufficient Reservoir Condition for Universal Reservoir Computing

Shuhei Sugiura, Ryo Ariizumi (), Toru Asai and Shun-ichi Azuma
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Shuhei Sugiura: Department of Mechanical and Aerospace Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
Ryo Ariizumi: Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Koganei 184-8588, Japan
Toru Asai: Department of Mechanical Engineering, College of Engineering, Chubu University, Kasugai 487-8501, Japan
Shun-ichi Azuma: Department of Informatics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

Mathematics, 2025, vol. 13, issue 21, 1-13

Abstract: We discuss necessary and sufficient conditions for universal approximation using reservoir computing. Reservoir computing is a machine learning method used to train a dynamical system model by tuning only the static part of the model. The universality is the ability of the model to approximate any dynamical system with any precision. In the previous studies, we provided two sufficient conditions for the universality. We employed the universality definition that has been discussed since the earliest studies on reservoir computing. In this present paper, we prove that these two conditions and the universality are equivalent to one another. Using this equivalence, we show that a universal model must have a “pathological” property that can only be achieved or approached by chaotic reservoirs.

Keywords: machine learning; reservoir computing; neural network; nonlinear dynamical system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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