Convergent Waveform Relaxation Schemes for the Transient Analysis of Associative ReLU Arrays

Abstract

In this circuit-theoretic paper, we establish a new result for the global convergence of the waveform relaxation (WR) algorithm in the specific context of analog associative arrays having the Rectified Linear Unit (ReLU) as an activation function. The traditional methods for proving WR convergence on generic analog circuits rely on the use of exponentially weighted norms to control the behavior of the transient waveforms for large simulation intervals. The main contribution of this paper is to show that in the particular case of analog associative ReLU arrays, WR convergence for large simulation intervals does not require exponentially weighted norms and can instead be ascertained using the common norm of uniform convergence. Using the connectivity matrix of the associativity array, a practical criterion for guaranteeing WR convergence is provided.