A Fast Algorithm to Simulate Nonlinear Resistive Networks

In the quest for energy-efficient artificial intelligence systems, resistor networks are attracting interest as an alternative to conventional GPU-based neural networks. These networks leverage the physics of electrical circuits for inference and can be optimized with local training techniques such as equilibrium propagation. Despite their potential advantage in terms of power consumption, the challenge of efficiently simulating these resistor networks has been a significant bottleneck to assess their scalability, with current methods either being limited to linear networks or relying on realistic, yet slow circuit simulators like SPICE. Assuming ideal circuit elements, we introduce a novel approach for the simulation of nonlinear resistive networks, which we frame as a quadratic programming problem with linear inequality constraints, and which we solve using a fast, exact coordinate descent algorithm. Our simulation methodology significantly outperforms existing SPICE-based simulations, enabling the training of networks up to 325 times larger at speeds 150 times faster, resulting in a 50,000-fold improvement in the ratio of network size to epoch duration. Our approach, adaptable to other electrical components, can foster more rapid progress in the simulations of nonlinear electrical networks.