How to combine deep learning and management to publish papers

First of all, the subject's question is what basic knowledge is needed to understand the mathematical derivation of the paper in deep learning theory.

The answer to this question is actually very broad. Here, I have mastered the theoretical basis of several points by default, high generation, probability theory, necessary statistical knowledge, Bayes. In addition, in recent years, some papers about ICLR and ICML have used more and more mathematical knowledge, including but not limited to real variables, functionals, point set topology, differential geometry and abstract algebra. If you are an engineering student, looking at a bunch of Greek letters and a bunch of flowers to write the definition of letters, you will often have a big head. I want to make up some math foundation, but I don't know where to start.

My personal experience is that it is unrealistic and a waste of time for engineering students in the direction of deep learning to finish all these courses. However, even engineering students are advised to study the following:

Real variable function (this is the part that appears most frequently in the paper. At least know what measurable set is, what measurable set is, what integrable, further Riemann integrable, Lebesgue integrable; Understand the concept of measurement)

Functional, variational method (this course is really difficult, I only learned part of it, but for machine learning, I must know the Euler-Lagrange equation of variational method)

Basic topological concept (everyone likes to use the word manifold in current papers, as long as it involves high-dimensional data, it is a manifold, and the source is here. Another example is the proof of perfect classifier in WGAN, which is actually a very basic proof of metric space and Hausdorff space in textbooks)

A little basic knowledge of measurement (there are many papers, but I feel familiar with metric tensor, exponential mapping, geodesic equation, and some deep geometric concepts rarely appear)

I didn't study math further. For example, ICLR's articles on spherical CNN this year are also very confusing, but the above are basically enough for you to look at most in-depth theoretical articles from a strategic point of view.