Disclaimer: I am not a Machine Learning Researcher, but I am planning to become one. This list mostly consists of stuff I found on the internet and advices from people I know who are.
To speedrun your path to an ML research career. Spoiler Alert: you can't (but you can try).
Necessary:
- Probability theory
- All optimization
- All statistics
- Complexity theory
- Functional analysis
Probably:
- All analysis
- information theory
- Measure theory
- numerical analysis
- Graph theory
- computational geometry
Book:
- Berner, J., Grohs, P., Kutyniok, G., & Petersen, P. (2021). The Modern Mathematics of Deep Learning. ArXiv, abs/2105.04026.