I am 100% convinced that these kind of approaches will be what delivers ML research from the current resource-hungry and ungeneralizable status quo. Low-dimensi

I am 100% convinced that these kind of approaches will be what delivers ML research from the current resource-hungry and ungeneralizable status quo. Low-dimensional Euclidean geometry is special. Higher-dimensional Euclidean spaces are less special. Most real-life data is high-dimensional, not at all smooth, and possessing a structure you cannot call Euclidean with a straight face. Look at what works with tabular data (which is probably most of what practitioners work with in the wild). It's gradient boosted trees, not neural networks. There is a fundamental mismatch between the data we usually work with and the spaces we shove it into. Tools from algebraic topology and geometry are old hat in physics. If anything, they should be even more useful in ML.