What's the function of the clean-up memory in SPA?
SPA is used (among other things) for combining (binding) and extracting (unbinding) knowledge representations for processing. This is a (purposely) lossy compression. In the "Learning Rule Generation for Induction" case, the clean-up memory is used to convert a general transformation that is being learned (lots of different transformations convolved together) into a transformation that is already known. So basically it's associating the in-progress transformation to a known transformation.

This is why the "clean-up memory" is also called the "associative memory" in other SPA models and in Nengo 2.0.