Review for NeurIPS paper: An implicit function learning approach for parametric modal regression

Summary and Contributions: Update: I've read this paper many times, and I have always had a lot of trouble understanding the mathematical development leading to the objective function. I now understand it better, so I'd like to suggest how I would present it, in case it gives you some ideas for your own presentation: eps(x,y) is the error between y and the "closest mode". Let's define m(x,y) to be a deterministic "mode function" that returns the mode of p(y x) that is closest to y. By modeling assumption, we assert that for fixed x and Y p(y x), we have eps(x,Y) N(0,sig 2). We want to approximate the function eps(x,y) with a function from the class f_theta(x,y).