What can be expressed while allowing physical learning?

Equilibrium propagation allows us to tune parameters of some physical system to achieve a desired input-to-output map. Its local update rule for these parameters relies on using physics to propagate information through the system, and this information must flow in both directions. The simplest examples are linear resistor networks, although many nonlinear systems have also been studied. Here we explore what is required for complex nonlinear circuits to still allow this bidirectional flow of information.