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Area of Science:

Computational neuroscience
Complex systems analysis
Machine learning theory

Background:

Reservoir computing, particularly delay-based systems, is a powerful tool for time-series processing.
Characterizing memory capacity in these systems is crucial for understanding their performance.
Existing methods for memory capacity analysis can be computationally intensive or limited in scope.

Purpose of the Study:

To introduce a universal master memory function (MMF) for delay-based reservoir computers.
To provide an efficient analytical method for computing linear memory capacity.
To demonstrate the broad applicability of the MMF across different reservoir types.

Main Methods:

Derivation of a universal master memory function (MMF) applicable to a wide range of delay-based reservoirs.
Development of an analytical description for the MMF enabling efficient computation.
Validation of the MMF using known dynamical systems like Mackey-Glass and Stuart-Landau models.

Main Results:

Demonstration that numerous delay-based reservoir computers share a common MMF.
The MMF allows for the linear memory capacity calculation based on two parameters.
The proposed analytical method significantly speeds up the computation of memory capacity.

Conclusions:

The MMF offers a unified framework for analyzing memory capacity in delay-based reservoir computers.
The efficient computation method makes memory capacity analysis more accessible.
This approach extends to reservoirs with unknown dynamical models, broadening its practical utility.