[visarga]

> When I read the headline I imagined they had implemented back propagation in a physical system

They touch on that by observing you could train a second physical neural network to compute the gradients for the first. So it could all be physical.

> Improvements to PAT could extend the utility of PNNs. For example, PAT’s backward pass could be replaced by a neural network that directly estimates parameter updates for the physical system. Implementing this ‘teacher’ neural network with a PNN would allow subsequent training to be performed without digital assistance.

So you need to use in silico training a at first, but can get rid of it in deployment.