  Physical networks, such as biological neural networks, can learn desired
functions without a central processor, using local learning rules in space and
time to learn in a fully distributed manner. Learning approaches such as
equilibrium propagation, directed aging, and coupled learning similarly exploit
local rules to accomplish learning in physical networks such as mechanical,
flow, or electrical networks. In contrast to certain natural neural networks,
however, such approaches have so far been restricted to the quasistatic limit,
where they learn on time scales slow compared to their physical relaxation.
This quasistatic constraint slows down learning, limiting the use of these
methods as machine learning algorithms, and potentially restricting physical
networks that could be used as learning platforms. Here we explore learning in
an electrical resistor network that implements coupled learning, both in the
lab and on the computer, at rates that range from slow to far above the
quasistatic limit. We find that up to a critical threshold in the ratio of the
learning rate to the physical rate of relaxation, learning speeds up without
much change of behavior or error. Beyond the critical threshold, the error
exhibits oscillatory dynamics but the networks still learn successfully.
