The output is a probability distribution for all potential tokens. Then a "temperature" is applied to weight the sampling randomly (unless the temperature is zero in which case the stack can be deterministic and simply the highest probability token is selected).

They go through this rigamarole because a little bit of randomness gives better results from a Turing test kind of perspective.

They are weights for matrix operations, so in principle you'd think they would be deterministic. In practice it's more complicated than that.

Not to be snarky or dismissive, I mean this genuinely: ask an LLM about it. I currently have a headache so I'm not up to explaining the technical details, but they are interesting and worth reading about.

Achieving determinism with LLMs and other neural network models is actually a hard problem that people spend a lot of time on, when they need that. It doesn’t happen by accident.

Issues include accumulated floating point errors happening in different orders due to distributed and parallel computation, CUDA kernels that deliberately sacrifice determinism for speed, and several other such issues.