What level of math is required for machine learning research There are several levels of math understanding:


Know the math
Know the intuitions behind math concepts
Know the intuitions and proofs of math concepts
Know the intuitions, proofs of math concepts and be able to apply them to deduce new results


My question is what level of understanding is required for machine learning research? Especially for publishing papers in conferences like CVPR or NeurIPS.
There can be no objective answer to this question. Obviously the more one understands the better, but the field of ML is vast, quite specialized and ranges from very theoretical to very applied research, so it's perfectly reasonable to publish in ML without a strong background in maths. 

A better way to estimate your own ability to publish papers in a particular area or journal is to study recent papers published in this area/journal. You should be able not only to understand them but to redo the reasoning: 


Understand the problem and the solution proposed by the authors
starting from the initial problem, how would you solve it? Can you think of alternatives to the authors' solution? 
Can you find limitations to their approach and improve on it?


If you reach step 3 then congratulations: you are ready to publish your own research!