A universal approximation theorem for nonlinear resistive networks

Abstract

Resistor networks have recently been studied as analog computing platforms for machine learning, particularly due to their compatibility with the Equilibrium Propagation training framework. In this work, we explore the computational capabilities of these networks. We prove that electrical networks consisting of voltage sources, linear resistors, diodes, and voltage-controlled voltage sources (VCVSs) can approximate any continuous function to arbitrary precision. Central to our proof is a method for translating a neural network with rectified linear units into an approximately equivalent electrical network comprising these four elements. Our proof relies on two assumptions: (a) that circuit elements are ideal, and (b) that variable resistor conductances and VCVS amplification factors can take any value (arbitrarily small or large). Our findings provide insights that could guide the development of universal self-learning electrical networks.

PRApplied (2025)

References in corpus (13)

• Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems
• Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons
• Learning without neurons in physical systems
• Nonlinear optical encoding enabled by recurrent linear scattering
• Demonstration of Decentralized, Physics-Driven Learning
• Trainable and Dynamic Computing: Error Backpropagation through Physical Media
• Supervised learning in physical networks: From machine learning to learning machines
• Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial
• Desynchronous Learning in a Physics-Driven Learning Network
• Self-learning Machines based on Hamiltonian Echo Backpropagation
• The Physical Effects of Learning
• Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagation
• Equilibrium Propagation: the Quantum and the Thermal Cases