I am 3rd year Phd student. So far I have been doing systems research in top US university. I realized that I want to do theory (in particular machine learning (ML) theory), but unfortunately I do not have any publications in that area. I do not have good math background, I never majored in math, and I did only basic math classes back in undergrad more than 6 years ago. So you realize that my math skills are very-very weak. But I truly enjoy learning maths, read ML papers, read theory papers, even though I struggle. It makes me feel happy, intellectually inspired and motivated. Meantime I completely do not care about systems research. That said I am def much much much less qualified than most Phd students in theory who majored in math, have tons of experience and publications.
Do I even have a chance to switch to theory? Should I even talked to professors? I am completely fine to stretch my Phd for the next 5-6 years (since if I switch I will need to start from the beginning and have a long period of learning).
Do you think I should give it a shot? Is it even feasible?