I do deep learning research focused on pharma applications. My personal background is a MS in chemical engineering. From my experience it's easier to get into the industry if you work on applications you have a specific background for (ie when I was new and less experienced I could still run circles around CS grads who don't understand SAR). If you want to do research at a major lab and don't want to spend 5+ years on a PhD, it's easier to get a data science or machine learning engineering job and then move into research.
For doing stuff on the job, the most important thing is being good at practical applications. You should be able to read a paper and implement it from scratch with good quality code. There's also a lot to be said for knowing how to architect good ML systems (the whole infra/serving system, not just the model algorithm which on its own is rather useless) and choose the right ML projects based on business strategy.
For theoretical background, you need to know linear algebra, calculus and statistics as applied to ML. The key here is you don't need to know everything about all those fields. Some people get sidetracked trying to master everything in linear algebra. A good reference is the first section of the Goodfellow book (
www.deeplearningbook.org/) which is basically a review of linear algebra, calculus and statistics applied to ML. You want to have enough foundational knowledge that you understand why you're doing certain things. For example when you use Kaiming initialization to initialize your weights, understanding why that's a good thing to do.
Overall though the most important thing is being able to put ideas to code. If you're serious about pursuing this, you should spend more time coding up examples than studying theory. Don't start trying to code everything from scratch, you just get lost in the weeds. Start with high level libraries and peel back the layers until you get to a from-scratch implementation.
