Happy to answer them!

1. Because we only have blackbox access to the LLM and the evaluation function might not be differentiable.

2. We're trying to search over the space of all programs in a programming language. To cover enough of this huge search space, we need to instantiate (1) a large number of programs in each population and (2) a large number of populations themselves (3) A large number of update steps for each population.

3. I have a couple of graphics motivating, conceptually, what an island/population looks like: https://trishullab.github.io/lasr-web/ . This whitesheet might also be useful: https://arxiv.org/abs/2305.01582

4. This is an interesting question. I believe so. However, my observations were derived from a non turing complete language (mathematical equations). There might be other ways of enforcing a succinctness pressure.