Delay-embedded reservoir computing with single memristor for scale-efficient temporal signal processing

Reservoir computing (RC) is a computational framework characterized by low training cost and high efficiency in processing temporal signals. In conventional memristor-based RC systems, only the current input at each time step is injected into the reservoir, and performance improvement is often achieved through large-scale parallel reservoir arrays. However, such an injection scheme inadequately captures the temporal dependencies of the input sequences while simultaneously increasing system complexity and resource consumption. To address these limitations, we propose a delay-embedded RC framework. By incorporating delay embedding at the input layer, the original one-dimensional time series is reconstructed into a high-dimensional vector comprising the current sample and a set of historical inputs. This vector is then multiplied by a randomly generated mask matrix with matched dimensions, enabling the current input to be enriched with its local temporal context before entering the reservoir. Numerical results demonstrate that the delay-embedded RC implemented with a single memristor outperforms conventional large-scale parallel RC system in both Mackey–Glass time-series prediction and waveform classification tasks. Furthermore, introducing this architecture into conventional parallel RC system can also significantly enhance performance. The proposed design enables RC systems to enhance their ability to represent complex temporal signals while maintaining or even reducing the reservoir size, thereby enhancing computational performance while simplifying the system hardware architecture. This study provides an effective and feasible performance-enhancement strategy for breaking the scale-performance trade-off and valuable guidance for the design of physical RC systems under resource-constrained conditions.