[bstx]

It doesn't make sense for speculatively executed code to throw architecturally visible exceptions. The appropriate behavior would be to not perform speculative loads across protection domains (i.e. the behavior of AMD implementations).

[j_coder]

It would make sense if it was the only alternative as the kernel can handle it. The appropriate behavior is to remove all traces of the speculative execution including cache hits.

[GrayShade]

Is that even possible? The data that would need to be removed from the cache has already evicted other cache lines, and that re-fetching those might have observable effects, like the timing.