> Read research publications and try to implement them.
In my opinion, jump straight into this! Learn prerequisites as you need them.
I found Goodfellow's book [1] to be helpful to learn some basics.
But don't think you need to read the whole book before you start reading and implementing research papers.
If you try and build up all the fundamentals thorougly, you run the risk of going down a very deep rabbit hole e.g. learning real analysis so you can learn measure theory so you can learn measure theoretic probability theory so you can learn stats properly etc.
You can be a productive researcher and patch up the fundamentals over time.
In my opinion, jump straight into this! Learn prerequisites as you need them.
I found Goodfellow's book [1] to be helpful to learn some basics.
But don't think you need to read the whole book before you start reading and implementing research papers.
If you try and build up all the fundamentals thorougly, you run the risk of going down a very deep rabbit hole e.g. learning real analysis so you can learn measure theory so you can learn measure theoretic probability theory so you can learn stats properly etc.
You can be a productive researcher and patch up the fundamentals over time.
[1] https://www.deeplearningbook.org/