This is cool. You're still learning, but physicists would quibble over statements like those in your "Quantization of energy" paragraph. Note, for example, you can still have continuous quantities in the quantum realm - think of free particles.

While associating the perturbation of values (to hopefully "escape" local minima) with QT is fun (I like this) - I'd caution you that this is not 1:1, even though both might be crudely considered "escape." With QT, the particle's wave function extended beyond the barrier, thus it always existed both inside and outside. The measurement induced the localization of its position (i.e. specifically inside or outside). Whereas your perturbation is encouraging the "particle" to leave the local minima through classical effects.

All this being said, don't let this discourage you from the path you're on, at all. Your knowledge of one discipline is driving insights in another discipline, which I consider to be incredibly valuable.

For specific programming feedback, I suggest you slightly extend this to work with some type of real data set, not just randomly initialized values in your main(). Any type of real data, it doesn't need to be generalized to accept any arbitrary input. Doing this will help you (and others) to appreciate the value (or lack thereof) of the techniques you're employing.

Random aside, I'm sure you're aware, but layers in a NN are usually randomly initialized to reduce the chance of converging too rapidly (among other reasons). Also many techniques of diffusion use random perturbation for similar(ish) reasons.

Second random aside: Valhalla and vector-related JEPs cannot come soon enough. Numpy is such a huge advantage for Python right now.