There isn’t really as much difference as it might seem.
This is true in a prosaic, boring sense: a steep continuous change may have exactly the same outcome as a discontinuous change on some process, even if technically there is some period during which the behaviour differs.
It is also true in a more interesting sense: the long term (technically: asymptotic) outcome of a completely continuous system can be actually discontinuous in the values of some parameter. This almost certainly does apply to things like values of hyperparameters in a model and to attractor basins following learning processes. It seems likely to apply to measures such as capabilities for self-awareness and self-improvement.
So really I’m not sure that the question of whether the best model is continuous or discontinuous is especially relevant. What matters more is along the lines of whether it will be faster than we can effectively respond.
There isn’t really as much difference as it might seem.
This is true in a prosaic, boring sense: a steep continuous change may have exactly the same outcome as a discontinuous change on some process, even if technically there is some period during which the behaviour differs.
It is also true in a more interesting sense: the long term (technically: asymptotic) outcome of a completely continuous system can be actually discontinuous in the values of some parameter. This almost certainly does apply to things like values of hyperparameters in a model and to attractor basins following learning processes. It seems likely to apply to measures such as capabilities for self-awareness and self-improvement.
So really I’m not sure that the question of whether the best model is continuous or discontinuous is especially relevant. What matters more is along the lines of whether it will be faster than we can effectively respond.