In physics, the conserved quantity isn't always time. Invariance over time translation is specifically conservation of energy. Invariance over spatial translation is conservation of momentum, invariance over spatial rotation is conservation of conservation of angular momentum, invariance of electromagnetic field is conservation of current, and invariance of wave function phase is conservation of charge.
I think the analogue in machine learning is conservation over changes in the training data. After all, the point of machine learning is to find general models that describe the training data given, and minimize the loss function. Assuming that a useful model can be trained, the whole point is that it generalizes to new, unseen instances with minimal losses, i.e. the model remains invariant under shifts in the instances seen.
The more interesting part to me is what this says about philosophy of physics. Noether's Theorem can be restated as "The laws of physics are invariant under X transformation", where X is the gauge symmetry associated with the conservation law. But maybe this is simply a consequence of how we do physics. After all, the point of science is to produce generalized laws from empirical observations. It's trivially easy to find a real-world situation where conservation of energy does not hold (any system with friction, which is basically all of them), but the math gets very messy if you try to actually model the real data, so we rely on approximations that are close enough most of the time. And if many people take empirical measurements at many different points in space, and time, and orientations, you get generalized laws that hold regardless of where/when/who takes the measurement.
Machine learning could be viewed as doing science on empirically measurable social quantities. It won't always be accurate, as individual machine-learning fails show. But it's accurate enough that it can provide useful models for civilization-scale quantities.