I seem to recall there were clever but well-known techniques in analog to get higher accuracy than that of your actual components, through negative feedback IIRC. So why is it correct to say that the precision of the components is what limits output precision? Wouldn't the technique potentially make a difference? (and yeah I know accuracy != precision but I'm using them loosely... the distinction doesn't seem relevant here)
I haven't thought it through, but feedback lets you do a few (perhaps connected?) things: 1. explore a trade-off between gain and bandwidth, 2. Reject disturbances and nonlinearities.
So you could have a high gain but "low precision" (in the sense of deviating from an ideal, not in the sense of not being noisy) component, and through feedback you can make a low gain, high precision (having desired properties, not low noise) component.
I don't know the math of such things but did take a stab at it. My idea was doing something similar as we do for high or unlimited precision on digital computers. They usually emulate the higher precision using a series of lower-precision, primitive operations. My thought was that you could probably implement higher precision in analog if you could do a similar emulator with operations acting within the precision common in analog components. All I could guess at, though, since I'm in over my head here.
One other thing I always note is the brain seems to be mostly analog. Look what all it can do which includes memory and high-precision math. So, there's almost certainly some tricks we can use to do something similar with analog. Maybe an analog/digital hybrid. The wafer-scale project on NN's shows the potential esp if it was made 3D w/ a cooling system:
