My understanding is that this doesn’t work for back propagation because it needs to know the forward pass computation exactly to adjust the weights. Analog computation introduces error in the form of noise (thermal, environmental, etc) which makes training on analog a non starter. It probably works for inference if the error is low enough, but training is where most of the power is spent unless it’s massively deployed.

I have an analog weight evaluation neural net in my own skull. It runs fine on a few Snickers bars.