When updating a preprint on arXiv, should I update my affiliation? I have a preprint on the arXiv, a couple of years old, and will shortly be re-submitting an updated version.  The changes are fairly limited — more than just typos, but not so much as to change the section numbering, let’s say.

I and a co-author are postdocs, and have moved institutions since the original version.  Should we update the author affiliations as given in the article, or leave them as they are?

The article hasn’t been published and probably won’t be any time soon (it’s expository, and a bit difficult to find a suitable venue for).  However, it’s been fairly widely read and cited as a preprint.

The field is pure mathematics.
Your affiliation as far as the work goes is where the work was done. You should perhaps add a footnote giving your current location, and (obviously) update any contact information given.

Or do it the the other way around: give current affiliation, and in acknowledgements or at least a footnote state where the work was done.

I've seen both.