But it may be a bad mental model in other contexts, like debugging models. As an extreme example models is that collapse during training become strictly deterministic, eg a language model that always predicts the most common token and never takes into account it's context.
Across all runs, any sequence can be generated, and potentially scored highly.
Thus, any sequence can eventually be selected.
The probability that an ideal, continuous LLM would output a 0 for a particular token in it's distribution is itself 0. The probability that an LLM using real floating point math isn't terrifically higher than 0.
There is a piece of knowledge you seem to be missing. Yes, a transformer will output a distribution over all possible tokens at a given step. And none of these are indeed zero, but always at least larger than epsilon.
However, we usually don't sample from that distribution at inference time!
The common approach (called nucleus sampling or also known as top-p sampling) will look at the largest probabilities that make up 95% of the probability mass. It will set all other probabilities to zero, renormalize, and then sample from the resulting probability distribution. There is another parameter `top-k`, and if k is 50, it means that you zero out any token that is not in the 50 most likely tokens.
In effect, it means that for any token that is sampled, there is usually really only a handful of candidates out of the thousands of tokens that can be selected.
So during sampling, most trajectories for the agent are literally impossible.
So I want you to understand this. You are basically selling heroin to junkies and then acting like the consequences aren't in any way your fault. Management will far too often jump at false promises made by your execs. Your technology is inherently non-deterministic. Therefore your promises can't be true. Yet you are going to continue being part of a machine that destroys businesses and lives. Please at least act like you understand this.