Hamiltonian Neural Networks from a Differential Geometry Perspective [D]

This is a write-up on our company blog that I wrote, sharing our perspective into Hamiltonian Neural Networks (Greydanus et al., 2019) from a differential-geometry angle rather than the usual "here's the loss function" treatment. I've been working on HNN and LNN adjacent topics for years now and I found this particular lens made the *why* click in a way the standard framing never did for me, and I've been meaning to put everything in writing for a while now. I just feel like the Noether's Theorem which shows conservations can be mapped to symmetries (and in ML context, generalization) is not g