A mathematical framework for time-delay reservoir computing analysis
Reservoir computing is a well-established approach for processing data with a much lower complexity compared to traditional neural networks. Despite two decades of experimental progress, the core properties of reservoir computing (namely separation, robustness, and fading memory) still lack rigorous mathematical foundations. This paper addresses this gap by providing a control-theoretic framework for the analysis of time-delay-based reservoir computers. We introduce formal definitions of the separation property and fading memory in terms of functional norms, and establish their connection to well-known stability notions for time-delay systems as incremental input-to-state stability. For a class of linear reservoirs, we derive an explicit lower bound for the separation distance via Fourier analysis, offering a computable criterion for reservoir design. Numerical results on the NARMA10 benchmark and continuous-time system prediction validate the approach with a minimal digital implementation.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Efficient Optimisation of Physical Reservoir Computers using only a Delayed Input
We present an experimental validation of a recently proposed optimization technique for reservoir computing, using an optoelectronic setup. Reservoir computing is a robust framework for signal processing applications, an…
Embedding Theory of Reservoir Computing and Reducing Reservoir Network Using Time Delays
Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems…
Performance boost of time-delay reservoir computing by non-resonant clock cycle
The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, unti…
Techniques for Enhancing Memory Capacity of Reservoir Computing
Reservoir Computing (RC) is a bio-inspired machine learning framework, and various models have been proposed. RC is a well-suited model for time series data processing, but there is a trade-off between memory capacity an…
A Novel Reservoir Computing Framework for Chaotic Time Series Prediction Using Time Delay Embedding and Random Fourier Features
Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that …
Time Series Prediction