>Yes, you get the same predicted token every time for a given context. But why that token and not a different one? Too many factors to reliably abstract.

Fixed input-to-output mapping is determinism. Prompt instability is not determinism by any definition of this word. Too many people confuse the two for some reason. Also, determinism is a pretty niche thing that is only necessary for reproducibility, and prompt instability/unpredictability is irrelevant for practical usage, for the same reason as in humans - if the model or human misunderstands the input, you keep correcting the result until it's right by your criteria. You never need to reroll the result, so you never see the stochastic side of the LLMs.

It always feels like I just have to figure out and type the correct magical incantation, and that will finally make LLMs behave deterministically. Like, I have to get the right combination of IMPORTANT, ALWAYS, DON'T DEVIATE, CAREFUL, THOROUGH and suddenly this thing will behave like an actual computer program and not a distracted intern.

Like the brain

You are right that as commonly implemented, the evaluation of an LLM may be non deterministic even when explicit randomization is eliminated, due to various race conditions in a concurrent evaluation.

However, if you evaluate carefully the LLM core function, i.e. in a fixed order, you will obtain perfectly deterministic results (except on some consumer GPUs, where, due to memory overclocking, memory errors are frequent, which causes slightly erroneous results with non-deterministic errors).

So if you want deterministic LLM results, you must audit the programs that you are using and eliminate the causes of non-determinism, and you must use good hardware.

This may require some work, but it can be done, similarly to the work that must be done if you want to deterministically build a software package, instead of obtaining different executable files at each recompilation from the same sources.