Very, very simple form of AI exists in CPUs themselves, since quite some time. Branch predictors decide which execution path to follow based on previous 'experience'. Usually there are only few bits of information per branch instruction, but this is still a form of learning.

As for the kernel itself… cache optimization (whatever type of cache it may be) comes to mind.

1) Branch prediction is not AI. AI has nothing to do with branch prediction.
2) Training a AI model can be expensive (which is why you use GPUs), but you wouldn't have your kernel train an AI model. You would have your kernel use a pre-trained model (which is called inference).
3) Optimizing how parameters are passed to the kernel during system calls is NOT a good / possible use of AI.
4) Optimizing a caching algorithm based on workload seems like a more reasonable use of AI. More generically, AI could potentially be used for resource management (scheduling, memory / cache / swap file management, etc). But the AI model would have to be trained off-line, not at run-time in the kernel. Coming up with a model that works on all combination of hardware seems a rather non-trivial amount of work.

Not really sure how you'd accomplish this. Most AIs (from what I know anyway) operate using SSE/AVX or GPUs, and training an aI is not exactly a fast process.

Inference? So kernels actually use pre-trained models? How, for what and who does it?