Physics likes optimization! Subject to its boundary conditions, the time evolution of a physical system is a critical point for a quantity called an action. This point of view sets the stage for Noether's principle, a remarkable correspondence between continuous invariances of the action and conservation laws of the system.
In machine learning, we often deal with discrete "processes" whose control parameters are chosen to minimize some quantity. For example, we can see a deep residual network as a process where the role of "time" is played by depth. We may ask:
- Does Noether's theorem apply to these processes?
- Can we find meaningful conserved quantities?
Our answers: "yes," and "not sure!"