Some ways to invert a generator
Look inside the generator to see how it works (Williams et. al)
Too tedious. Not possible for the real motor system.
Define a prior over codes and generate lots of (code, image) pairs.
Then train a function approximator that does image code.
What about ambiguous images? The average code is bad.
Define a prior over codes and train a neural net to model code
image. Then backpropagate image residuals to iteratively find a
locally optimal code for each test image.
May be better than using a fixed linear mapping from image
residuals to code corrections (Cootes et al)
We need the prior over codes to avoid learning to invert the
generator in irrelevant parts of image space.