Hi all, I'm trying to get a research internship at a small research lab. I'm currently doing my undergrad in data science.

This is the research guideline document:

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1. [Research direction 1] AI that adapts to a domain

Topics: continual learning, memory, test time adaptation, active learning, sample efficiency, efficient training or inference, personalization, curiosity, exploration, agency, autonomy, OOD generalization, curriculum learning, meta-learning, uncertainty modeling

Some example questions:

What does it mean to "understand" a domain, and how does that differ from pattern matching over training data?

What kind of memory should an adapting AI have? What should be baked in weights or assembled during inference (via files or context)?

What techniques could enable minimal catastrophic forgetting as the AI learns something new in a domain?

What’s the right way to model a domain? What should the world model look like? What should be parametric or non-parametric?

How can training/learning happen locally in a constrained compute environment?

[Research direction 2] Creativity in artificial systems

Topics: novelty, creativity, representations, data manifold, extrapolation, surprise, world models, recombination, concept modeling, scientific theory building, innovation, abstractions, program synthesis, knowledge representation, taste

Some example questions:

How should novelty be modeled, detected and measured? What differentiates it from mere noise or surprising but irrelevant detail?

What role do world models and imagination play in creativity?

What process do most creative people in different domains follow and how can we encode that into AI?

What is “good taste” in a domain? What contribution does mere popularity/luck have in it v/s genuinely better process/output?

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My current level:

I've already studied these math courses:

1. Linear Algebra: MIT 18.06
2. Multivariable Calculus: MIT 18.02
3. Probability: Harvard Stat110
4. Statistics: MIT 18.650
5. Matrix methods for ML: MIT 18.650 (currently doing)

I've also studied these ML textbooks:

1. ISLP (Intro to Stat Learning with Py)
2. D2L (dive into deep learning) - Currently doing
3. Andrej Karpathy: Zero to Hero Neural Nets - Will do soon
4. MIT 6.7960 Deep Learning - Will do soon

I need some advice and guidance on:

1. Should I do a math course in proof-based linear algebra (such as MIT 18.700 or something like Linear Algebra Done Right (Axler)) before getting into ML research in one of those research directions listed above?
2. Should I do a math course in Real Analysis before getting into ML research in one of those research directions listed above?
3. Please provide some advice on what machine learning textbooks & courses should I refer to after doing the above in order to pursue research in the above research directions.

Thanks in advance!