This makes a lot of sense, Thanks for highlighting the need to define value more explicitly. I'll have a look into this stuff!

on the math point - I don't think that IV would be continuous is the problem, but in general this would mean the noise is present in both frameworks! The case of x^2 sin(1/x) shows the integral of a function with a discontinuity is not necessarily discontinuous but in general discontinuous functions would have a discontinuous integral so the noise doesn't distinguish the frameworks.

Thank you!

Not sure of this at all but I’m under the impression commercial use tends to find loopholes for malicious use of AI systems that regulators/safety teams are unable to predict. 

Could we get a parallel with misaligned behaviour, where we start to notice misalignment with high volume of use in ways not rigorously testable or present under regulator testing? Would it be useful to consider a commercial incubation period with certain compute limits for example, or would we be able to definitely trust regulators?