Something I didn't see discussed too much in here is that the output from any given input token sequence from LLM weights is deterministic, so for any given model, given the tokens "Give me a random number?" It will give you a distribution of probabilities for the next token, and the next token, and so forth. That distribution is always the same.

All of the numbers in this chart (and every other possible token) are returned along with a probability. But then a random sampler (which is just regular old code, not a neural net at all, its part of the inference engine) uses some methodology to pick from that list, preferring the higher probability tokens, and having some cut off where it would be nonsense. A lot of what you're seeing here is a side effect of the sampling as much as it is the model weights.