Rewrite `argmax(f(x)` -> argmax(x)` for monotonic f

[ricardoV94]

Description

Similarly max(f(x)) -> f(max(x))

We can also convert (arg)max to (arg)min for monotonic decreasing functions

[jessegrabowski]

More use cases for algebraic property tags

[ricardoV94]

Why tags? It's about functions not variables?

[jessegrabowski]

We're a static graph library, what's the difference

[ricardoV94]

knowing that in y = f(x), f is monotonic doesn't require us to know anything about x or y. For this rewrite we only need to know about properties of f.

Tags are things we attach to variables like x and y. You wouldn't say y is monotonic, that doesn't make sense. It's just a list of values.

So I don't understand what do tags have to do with this suggestion

[jessegrabowski]

if y = fn(x) and fn is a monotonic function, y is a valid target for this rewrite, and can carry that information. If you prefer, y.owner can carry that information, but that is hair splitting.

I don't see what tags don't have to do with this. The alternative is to maintain a big list of monotonic functions, which is probably what we will end up doing, but that sucks.

[ricardoV94]

The op can have a property is_monotonic if that's what you mean. When you mention tags I think of the things we attach to variables, but this info is about the Op not the variables?

[Jasjeet-Singh-S]

Could you clarify if the rewrite is for argmax or for max (and consecutively min or argmin for monotonically decreasing function)?

because f(argmax(x)) wouldnt make sense as argmax returns index not value so the rewrite would actually be argmax(f(x)) -> argmax(x)

[ricardoV94]

Yes those are different cases, the one in the title and then the one in the description was meant as a "as well as". So it's two kind of rewrites we can do