When you say that the training process ends up with an API set, do you mean that instead of the usual order where you prescribe constraints for the training process to move around in, which you enforce e.g. by clipping the parameters to the nearest values that satisfy the constraints after each training step, you start with any training process and then use constraints to describe its behavior?
e.g. for n bodies with approximately-known initial positions and velocities, subject to gravity, we may be unable to predict precisely where the bodies end up, but we can potentially use energy conservation to put bounds on the coordinates they can ever reach, and if we keep listing out provable constraints, we are eventually left unable to predict any further details of the system?
When you say that the training process ends up with an API set, do you mean that instead of the usual order where you prescribe constraints for the training process to move around in, which you enforce e.g. by clipping the parameters to the nearest values that satisfy the constraints after each training step, you start with any training process and then use constraints to describe its behavior?
e.g. for n bodies with approximately-known initial positions and velocities, subject to gravity, we may be unable to predict precisely where the bodies end up, but we can potentially use energy conservation to put bounds on the coordinates they can ever reach, and if we keep listing out provable constraints, we are eventually left unable to predict any further details of the system?
Yes.