But I agree there is much we neuroscientists can learn from the machine learning research that provide insight into the biological system. Trust me- we are paying close attention.
Can you give me rough time scale for how quick neurons learn (synaptic plasticity)? I have a recollection that the time scale is in order of tens of milliseconds but I might be wrong.
To specifically address your question about how quickly learning happens in neurons... it's fast. Is it ~10ms? mmm, that seems incredibly fast, and I'm not sure I can provide any definitive answer. I think it heavily depends on what you're willing to interpret as 'learning' when examining events on the molecular level. There are events that engender near-immediate alterations to ongoing transmission; and other events that support lasting electrical changes (necessarily?) develop across longer timescales. You might think of this distinction as the difference between being able to hold a phone number in consciousness via repeating it over and over, and then actually being able to recall that phone number 5 minutes later. In the former certainly something internally must have changed because a moment ago you weren't repeating this number in your head, and now you are. On the other hand, can we really say it was learning if the number is immediately lost the moment it leaves consciousness. Anyway, I"m not going to wax philosophical on that. I'll just show you some data for timescales we think are sufficient to produce lasting increases in synaptic efficacies...
Here is a video showing a single spine just after 2-photon 'glutamate uncaging':
(as I mentioned above, glutamate receptors are the primary receptors involved in fast-excitatory transmission; so uncaging tons of glutamate right next to a spine is going to evoke immediate plasticity changes - particularly under these experimental conditions)
Note that in just a few seconds the spine has doubled in size. Morphological change in the spine are probably not the first events that alter synaptic transmission, but morphological changes to the spine are a reliable sign of a lasting memory trace.
Here is a whole cell recording of the electrical response in a neuron to incoming signals, before and after stimulation like that above ('EPSC' stands for 'excitatory post synaptic currents'):
If you are interested in seeing how the postsynaptic neuron manages its synaptic receptor numbers (and the intricate process the backprop algo is cheating), you might like to check out a 3D simulation I've made to model this process.
Animation: https://www.youtube.com/embed/6ZNnBGgea0Y Code on github: https://github.com/subroutines/plasticity
(note the animation is not too exciting, so you might want to skip forward a few times)
But basically you will see that neurons rely on stochastic surface diffusion of receptors to deliver new receptors to synapses. The takeaway is that during rest (or whatever you want to call it... baseline, non-learning, etc) synapses will reach some steady-state number of receptors. If the synapse undergoes some learning event, it needs to 'capture' more receptors to increase the steady-state amount. It does this by modifications to proteins just below the surface of the postsynaptic membrane that act as velcro to surface receptors floating by. Thus synapses take control of their synaptic weights by managing the surface diffusion rate of excitatory receptors.