It's difficult to do because LLMs immediately consume all available corpus, so there is no telling if the algorithm improved, or if it just wrote one more post-it note and stuck it on its monitor. This is an agency vs replay problem.

Preventing replay attacks in data processing is simple: encrypt, use a one time pad, similarly to TLS. How can one make problems which are at the same time natural-language, but where at the same time the contents, still explained in plain English, are "encrypted" such that every time an LLM reads them, they are novel to the LLM?

Perhaps a generative language model could help. Not a large language model, but something that understands grammar enough to create problems that LLMs will be able to solve - and where the actual encoding of the puzzle is generative, kind of like a random string of balanced left and right parentheses can be used to encode a computer program.

Maybe it would make sense to use a program generator that generates a random program in a simple, sandboxed language - say, I don't know, LUA - and then translates that to plain English for the LLM, and asks it what the outcome should be, and then compares it with the LUA program, which can be quickly executed for comparison.

Either way we are dealing with an "information war" scenario, which reminds me of the relevant passages in Neal Stephenson's The Diamond Age about faking statistical distributions by moving units to weird locations in Africa. Maybe there's something there.

I'm sure I'm missing something here, so please let me know if so.