In theory, temperature 0 does make the LLM deterministic.

Well, in theory theory, temperature 0 doesn't really exist. Mathematically, as lim temperature->0, the distribution gets spikier and spikier, the most likely sample goes to almost-but-not-quite infinity and the rest go to almost-but-not-quite 0. In practice, temperature=0 is literally a separate branch of an if statement that just picks the most common sample (using the actual formula that works for non-zero values would cause a zero division).

However, due to things such as batching and even different kinds of floating point imprecisions for different algorithm implementations, the probability distribution itself often differs run-by-run, so what you sample from it also differs.

>in theory theory, temperature 0 doesn't really exist.

It does exist very much, even if you go to pure math. Look at the softmax function and take the limit as T->0. It becomes a dirac-delta function. I.e. in a discrete setting (like for LLMs with a finite set of output tokens), probability P becomes one for argmax and 0 for everything else. Only in coding practice it is easer to implement T=0 as a simple if check that directly chooses argmax instead of calculating the limit of some function that includes 1/T quotients. But setting T to zero is in both, theory and practice, turning the usual probability function into greedy sampling.

If you make an exact integer implementation and run with temp=0 it's deterministic.

You don't even need temperature 0, just make a random seed for the sampler part of the input and then its deterministic as a function of the input.

But running autoregressive models at temp=0 tends to expose pathological behavior, because the training process produces a function with a lot of gain so its prone to feedback on its own noise.

> However, due to things such as batching and even different kinds of floating point imprecisions for different algorithm implementations, the probability distribution itself often differs run-by-run

The implementation does not often differ run by run.

As I understood it, the "randomness" affecting what is selected at any temperature still comes from a PRNG or CSPRNG (or whatever RNG you want, maybe a hardware one), and if you where to swap out that with something deterministic you'd get the same results every time (barring non-determinism in other parts of the OS/drivers/maybe even hardware).

But theoretically, the output of every LLM is seed-driven (or could be if you wrote the software to isolate it) just like any computer software. It's just none of the software written (even llama.cpp AFAIK) chooses to support stable-seeding due to the changes in stuff like CPU/Vulkan/CUDA/Metal differences making it difficult to make consistent.

They could though! Hopefully one day someone implements it into the mainstream LLM-engine software and it gets exposed in the APIs serving the models. It'd do a lot to show folks the "internals" of these models.