[WCSTombs]

Mathematically, it is literally a probability distribution, because it fits the definition of a measure whose total mass is one, so I think the language is just imprecise. What they may be trying to say is that semantically it doesn't arise in a principled way from an uncertainty model, such as from Bayesian or frequentist statistics.

[jmalicki]

Hogwash. If you get into deriving maximum entropy distributions via the calculus of variations, the multinomial is the maximum entropy distribution among categorical distributions.

This is exactly the sense that it comes up for old school LMs and why it appears in thermodynamics.

Of course it is entirely possible that newfangled ML people use it without understanding that it is derived from first principles - i.e. see article.

[WCSTombs]

That definitely could be the case. I was also a bit surprised by what the article said, so I was simply trying to interpret it, but I'm not extremely well versed in ML so I could be missing some details. My main point was that contrary to what the article said, they do in fact have a probability distribution on their hands.

[jmalicki]

This is literally the probability distribution ML models are trained on.

https://docs.pytorch.org/docs/2.11/generated/torch.nn.CrossE...

You have a relatively small dictionary of tokens, each prediction has a neural network score that goes into the final token prediction layer, and they are trained based on a log-softmax (i.e. the above function) to predict their next token.

This is exactly how anyone in any field does conditional multinomial/categorical (i.e. one of a bunch of distinct tokens) distributions, and AFAIK what LLMs generally use as their loss functions on the output layer, though I have not deeply investigated all of them, since this has been how you do that since time immemorial.

I am extremely confused by all of the people screaming it's not a probability distribution?!?!?

I have seen computer vision tasks use binomial training objectives (one-vs-all) and then use the multinomial only at inference time, and that could be fair that that is not a probability distribution induced by training (while technically a probability distribution only in the sense it is \ge 0 and sums to 1).

But afaik token prediction LLMs that I am aware of use the softmax for the probability in their loss function, i.e. the maximize log softmax.