A fully piecewise linear Hopfield neural network with simplified mixed-mode activation function: dynamic analysis and analog implementation

Abstract The circuit realization of neural models is a well-known and essential approach in neuromorphic computing. However, Hopfield neural networks (HNN) depend on complex activation functions that produce bulky and cumbersome hardware implementations, which may limit HNN-based applications. Therefore, we introduce a four-neuron Hopfield neural network that uses just three-segment PWL descriptions as activation functions instead of complicated hyperbolic-type functions. Then, we propose two novel architectures of those PWL activation functions. The first one with voltage output requires just one operational amplifier and two resistors, while the other architecture produces multiple activations as current outputs. As a consequence of such PWL circuits, we obtain the most simplified circuit implementation of a PWL-type activation function. Next, the nonlinear dynamics and mechanism of chaos generation of the proposed PWL Hopfield neural network are studied by the stability of equilibrium points, bifurcation diagrams, and Lyapunov exponents computed according to the slope and plateaus of the PWL activation function. We also found that the proposed PWL activation circuit is robust against statistical variations of the element values and manufacturing tolerances using sensitivity and Monte Carlo analyses. As a result, the chaotic attractors of the PWL HNN observed in the hardware experiments confirm the feasibility of the proposed mixed-mode piecewise-linear activation function in replicating the chaos behavior of the original neuron model but with the lowest hardware requirements.