[szvsw]

I’ve also used the sigmoid approximation to relax some problems (specifically for step changes in field properties in PINN problems) into continuous variables, cool to see this discussion here from a different perspective! Slightly off topic but the only other things I’m aware of that are vaguely related are things like the gumbel-softmax trick for making sampling from categorical distributions differentials or the Gaussian reparam trick (eg as used in VAEs). I’m curious if this is at least somewhat related to the approach taken in your work, in spirit if not in technical implementation?

[frankling_]

Yeah, those tricks are highly related to what we do, the main difference being that we don't require a priori information about the distributions involved in the program. Instead, we compute a density estimation of the distribution of branch conditions at runtime, which makes things quite general and fully automatic, at the cost of some accuracy.

As an aside, the combination "known distributions + automation" is covered in the Julia world by stochasticAD (https://github.com/gaurav-arya/StochasticAD.jl).