physical symmetries and machine learning

Soledad Villar (JHU) and I spent time today discussing symmetries and machine-learning methods. Like many astronomers, I'm interested in imposing deep physical symmetries on methods, figuring that if the methods respect the symmetries, they will learn much more relevant and useful things from their training data (and not spend their training information on learning the symmetries). An easy symmetry is the convolutional symmetry, but physics has far more: The laws of physics are permutation-equivariant (which in the ML business is graph symmetry), they are unitary (which in the ML business is (sometimes) normalizing), and they have rotation and translation and boost symmetries. We looked at papers on gauge invariant networks, graph networks, and hamiltonian networks. All extremely relevant! It seems like all the tools are in place to do something interesting in cosmology.