  We introduce frequency propagation, a learning algorithm for nonlinear
physical networks. In a resistive electrical circuit with variable resistors,
an activation current is applied at a set of input nodes at one frequency, and
an error current is applied at a set of output nodes at another frequency. The
voltage response of the circuit to these boundary currents is the superposition
of an `activation signal' and an `error signal' whose coefficients can be read
in different frequencies of the frequency domain. Each conductance is updated
proportionally to the product of the two coefficients. The learning rule is
local and proved to perform gradient descent on a loss function. We argue that
frequency propagation is an instance of a multi-mechanism learning strategy for
physical networks, be it resistive, elastic, or flow networks. Multi-mechanism
learning strategies incorporate at least two physical quantities, potentially
governed by independent physical mechanisms, to act as activation and error
signals in the training process. Locally available information about these two
signals is then used to update the trainable parameters to perform gradient
descent. We demonstrate how earlier work implementing learning via chemical
signaling in flow networks also falls under the rubric of multi-mechanism
learning.
