Device Variability and Uncertainty Propagation in Memristive Reservoir Computing

Memristive crossbar arrays provide an efficient hardware substrate for in-memory and neuromorphic computing architectures. Reservoir Computing (RC) is particularly well suited for such systems because only the output layer requires training, making it attractive for hardware implementations. However, memristive devices exhibit intrinsic variability due to fabrication mismatch, cycle-to-cycle fluctuations, and conductance drift, which introduce stochasticity in the reservoir dynamics. In this work we develop a probabilistic formulation of memristive reservoir computing that explicitly models conductance variability in the crossbar array. Analytical expressions are derived to describe how device uncertainty propagates through the reservoir states and determines the predictive distribution at the readout layer. This framework enables the analysis of dynamical regimes in which hardware variability either degrades performance or can instead enhance the diversity of the reservoir dynamics. The theoretical results are validated through numerical experiments on chaotic time-series prediction tasks, including the Mackey–Glass benchmark, showing how device variability affects both prediction accuracy and predictive uncertainty. These results provide theoretical insight into uncertainty propagation in memristive reservoirs and establish connections between variability-aware reservoir computing and stochastic random feature methods.