Allow OpenCL simplex to use softmax?

[SteveBronder]

Description

I'm in the process of writing out the deserializer for OpenCL so we can have models that run entirely on the GPU. We do not yet have a simplex_constrain/unconstrain function in OpenCL.

I could do the stick breaking scheme on the gpu, I think it would be a weighted prefix product. That's possible for me to write but will take me a minute. The other alternative is just to use softmax. Since that's just exp(x_i) / sum(exp(X)) that's much easier to write for the GPU.

The downside of the softmax is that the cpu/gpu versions will be different, but we could just add that to the user docs so people know.

Does anyone have thoughts on this?

Current Version:

v4.7.0

[WardBrian]

@mjhajharia @bob-carpenter

[spinkney]

For ease of writing on the gpu and stability I believe the softplus will be better. Retagging @bob-carpenter who has looked into this.