Sequential Bayesian Inference and Monte-Carlo Sampling Using Memristor Stochasticity

In this paper, we study the stochastic state trajectory and conductance distributions of memristors under periodic pulse excitation. Our results, backed by experimental evidence, reveal that practical memristors exhibit a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1/f^{2}$ </tex-math></inline-formula> Brownian noise power spectrum. Based on this, we develop a Memristive Distribution Generator (MDG) circuit that produces tunable analog distributions by exploiting the physical stochasticity of memristors. By encoding the prior distributions of Bayesian problems in the physical output samples of these circuits, we demonstrate that Monte-Carlo sampling can be devised without knowledge of the analytical output distribution of the memristor. Using examples of 1-D Bayesian linear regression and a dynamic 2-D nonlinear localisation problem, we show how MDG circuits can act as a tunable source of randomness, efficiently representing distributions of interest. Our results, obtained using Pt/TiO2/Pt memristors, validate the use of memristor-based MDGs for implementing probabilistic algorithms.