arXiv:2509.13793v3 Announce Type: replace Abstract: It is shown that the port behavior of a resistor-diode network corresponds to the solution of a ReLU monotone operator equilibrium network (a neural network in the limit of infinite depth), giving a parsimonious construction of a neural network in analog hardware. We furthermore show that the gradient of such a circuit can be computed directly in hardware, using a procedure we call hardware linearization. This allows the network to be trained in hardware, which we demonstrate with a device-level circuit simulation. We extend the results to cascades of resistor-diode networks, which can be used to implement feedforward and other asymmetric networks. We finally show that different nonlinear elements give rise to different activation functions, and introduce the novel diode ReLU which is induced by a non-ideal diode model.