[digikata]

There are large bodies of work for optimization of state space control theory that I strongly suspect as a lot of crossover for AI, and at least has very similar mathematical structure.

e.g. optimization of state space control coefficients looks something like training a LLM matrix...

[brosco]

There is indeed a lot of crossover, and a lot of neural networks can be written in a state space form. The optimal control problem should be equivalent to training the weights, as you mention.

However, from what I have seen, this isn't really a useful way of reframing the problem. The optimal control problem is at least as hard, if not harder, than the original problem of training the neural network, and the latter has mature and performant software for doing it efficiently. That's not to say there isn't good software for optimal control, but it's a more general problem and therefore off-the-shelf solvers can't leverage the network structure very well.

Some researchers have made interesting theoretical connections like in neural ODEs, but even there the practicality is limited.

[blt]

Yes, in most cases the reduction of supervised learning to optimal control is not interesting.

We can also reduce supervised learning to reinforcement learning, but that doesn't mean we should use RL algorithms to do supervised learning.

We can also reduce sorting a list of integers to SAT, but that doesn't mean we should use a SAT solver to sort lists of integers.