> I thought the problem is just that it isn't proven that neural nets are sufficiently smooth.
I think this is exactly what the GP was trying to say (at least, this is what I understand from it). The continuity bit is about the (non ML) controller, not about the neural network.
Nearly all neural networks generate continuous output. They do interpolate between their learned points. The problem is that it is very hard to verify (and impossible to predict) the interpolation function, so it may cross outside of the safety area on any point.
I think this is exactly what the GP was trying to say (at least, this is what I understand from it). The continuity bit is about the (non ML) controller, not about the neural network.
Nearly all neural networks generate continuous output. They do interpolate between their learned points. The problem is that it is very hard to verify (and impossible to predict) the interpolation function, so it may cross outside of the safety area on any point.