It depends on your interest, since even though it is a subfield it is diverse. Relevant to this work here is a general overview: https://arxiv.org/abs/2603.10090

Also check out Tracr: https://deepmind.google/research/publications/22295/ Here they attempt to compile static programs into weights.

This is less of an overview but I remember reading this before, from the larger collection of posts: https://sidn.baulab.info/david_atkinson_project/