Nitpick: The usual physical term for this kind of thing would be “symmetry”, not “conservation law”.
(Though by Noether’s theorem, symmetries imply conservation laws.)
I agree with the impression that symmetries seem super overpowered for inference. One of the favorite tricks for causal inference I’ve learned is that you can easily uniquely pin down causality from correlation if you’ve got symmetries across different contexts with sufficiently different distributions.
Nitpick: The usual physical term for this kind of thing would be “symmetry”, not “conservation law”.
(Though by Noether’s theorem, symmetries imply conservation laws.)
I agree with the impression that symmetries seem super overpowered for inference. One of the favorite tricks for causal inference I’ve learned is that you can easily uniquely pin down causality from correlation if you’ve got symmetries across different contexts with sufficiently different distributions.