Coupled dynamical systems, especially those comprised of hysteretic elements, possess remarkable behavioral similarities to some aspects of neural activity in living systems. While some features of this similarity have been explored, the results have not yet been leveraged to improve machine learning techniques or artificial neural networks. In this work, a dynamical system of coupled overdamped bistable elements subject to a noise floor assists in information transfer. With the noise allowing the system elements to switch randomly between their stable states, the system response is quantified via a steady state probability distribution. A simple five element realization of this network is used to produce the analog equivalent of an XOR gate, an “XOR transform”, through the proper choice of coupling coefficients and controllable external biases. The demonstration of the XOR transform indicates the ability of the system to synthesize more general functions, a necessary prerequisite for machine learning and computing applications. Finally, a silicon implementation is proposed and simulated using a verified process model that could be fabricated to generate a working analog computing system.