A universal approximation theorem for nonlinear resistive networks
Benjamin Scellier Siddhartha Mishra
Resistor networks have recently had a surge of interest as substrates for
energy-efficient self-learning machines. This work studies the computational
capabilities of these resistor networks. We show that electrical networks
composed of voltage sources, linear resistors, diodes and voltage-controlled
voltage sources (VCVS) can implement any continuous functions. To prove it, we
assume that the circuit elements are ideal and that the conductances of
variable resistors and the amplification factors of the VCVS's can take
arbitrary values -- arbitrarily small or arbitrarily large. The constructive
nature of our proof could also inform the design of such self-learning
electrical networks.