Felix Köster

Felix Köster, Kazutaka Kanno, Jun Ohkubo et al.

Photonic reservoir computing has been successfully utilized in time-series prediction as the need for hardware implementations has increased. Prediction of chaotic time series remains a significant challenge, an area where the conventional reservoir computing framework encounters limitations of prediction accuracy. We introduce an attention mechanism to the reservoir computing model in the output stage. This attention layer is designed to prioritize distinct features and temporal sequences, thereby substantially enhancing the prediction accuracy. Our results show that a photonic reservoir computer enhanced with the attention mechanism exhibits improved prediction capabilities for smaller reservoirs. These advancements highlight the transformative possibilities of reservoir computing for practical applications where accurate prediction of chaotic time series is crucial.

Felix Köster, Serhiy Yanchuk, Kathy Lüdge

We show that many delay-based reservoir computers considered in the literature can be characterized by a universal master memory function (MMF). Once computed for two independent parameters, this function provides linear memory capacity for any delay-based single-variable reservoir with small inputs. Moreover, we propose an analytical description of the MMF that enables its efficient and fast computation. Our approach can be applied not only to reservoirs governed by known dynamical rules such as Mackey-Glass or Ikeda-like systems but also to reservoirs whose dynamical model is not available. We also present results comparing the performance of the reservoir computer and the memory capacity given by the MMF.

Felix Köster, Serhiy Yanchuk, Kathy Lüdge

In this paper we give a profound insight into the computation capability of delay-based reservoir computing via an eigenvalue analysis. We concentrate on the task-independent memory capacity to quantify the reservoir performance and compare these with the eigenvalue spectrum of the dynamical system. We show that these two quantities are deeply connected, and thus the reservoir computing performance is predictable by analyzing the small signal response of the reservoir. Our results suggest that any dynamical system used as a reservoir can be analyzed in this way. We apply our method exemplarily to a photonic laser system with feedback and compare the numerically computed recall capabilities with the eigenvalue spectrum. Optimal performance is found for a system with the eigenvalues having real parts close to zero and off-resonant imaginary parts.

Felix Köster, Dominik Ehlert, Kathy Lüdge

We analyze the memory capacity of a delay based reservoir computer with a Hopf normal form as nonlinearity and numerically compute the linear as well as the higher order recall capabilities. A possible physical realisation could be a laser with external cavity, for which the information is fed via electrical injection. A task independent quantification of the computational capability of the reservoir system is done via a complete orthonormal set of basis functions. Our results suggest that even for constant readout dimension the total memory capacity is dependent on the ratio between the information input period, also called the clock cycle, and the time delay in the system. Optimal performance is found for a time delay about 1.6 times the clock cycle

Mirko Goldmann, Felix Köster, Kathy Lüdge et al.

The Deep Time-Delay Reservoir Computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity (MC) and how that can be used for optimization. In particular, we analyze bifurcations of the corresponding autonomous system and compute conditional Lyapunov exponents, which measure the generalized synchronization between the input and the layer dynamics. We show how the MC is related to the systems distance to bifurcations or magnitude of the conditional Lyapunov exponent. The interplay of different dynamical regimes leads to a adjustable distribution between linear and nonlinear MC. Furthermore, numerical simulations show resonances between clock cycle and delays of the layers in all degrees of the MC. Contrary to MC losses in a single-layer reservoirs, these resonances can boost separate degrees of the MC and can be used, e.g., to design a system with maximum linear MC. Accordingly, we present two configurations that empower either high nonlinear MC or long time linear MC.