Remove constant_function for AutoEnzyme

[gdalle]

Warning

This PR and the associated release are breaking wrt 1.6.1, but we will yank 1.6.1 and 1.6.0 right after

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Following a long discussion with @ChrisRackauckas and @wsmoses, we decided to remove the constant_function setting for now, and reinsert it later with different defaults (once Enzyme implements a few changes on their side). This PR does the removal and bumps ADTypes to v1.6.2, after which we will need to yank v1.6.0 and v1.6.1.

• Duplicating closures EnzymeAD/Enzyme.jl#1669

[gdalle]

Let's wait for a review from Billy and Chris before merging (I added Billy as "read" contributor to the repo so that I can request reviews in the future, if that's ok)

[ChrisRackauckas]

Let's just go straight to the nothing default then?

[gdalle]

I wanted to wait until the implementation exists on the Enzyme and DI side before reintroducing this kwarg. Our mistake last time was to introduce it before it actually did anything, and as a result we got the design wrong.

[gdalle]

But if @wsmoses is confident that constant_function=nothing is the right third option I can modify this PR to just change the default instead of removing the kwarg

[wsmoses]

I would probably do the yank now then design when ready.

Being even more forward looking this should likely actually be a Union{Nothing, Enzyme.Annotation}, since the function could be nothing, constant, duplicated, or even active

[wsmoses]

This constant function is not the appropriate name

[ChrisRackauckas]

function_activity

[wsmoses]

I mean that sounds like a good name to me, but it also might be wise to wait til things are settled before choosing

…

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[gdalle]

Okay then removing everything first is the right move. In this spirit, do you approve this PR?

[wsmoses]

Spiritually and actually approved