LLMs Learn to Be "Generative"

• nanoGPT

  69 31,914 5.4 Python

  The simplest, fastest repository for training/finetuning medium-sized GPTs.

where x1 denotes the 1st token, x2 denotes the 2nd token and so on, respectively.

I understand the conditional terms p(x_n|...) where we use cross-entropy to calculate their losses. However, I'm unsure about the probability of the very first token p(x1). How is it calculated? Is it in some configurations of the training process, or in the model architecture, or in the loss function?

IMHO, if the model doesn't learn p(x1) properly, the entire formula for Bayes' rule cannot be completed, and we can't refer to LLMs as "truly generative". Am I missing something here?

I asked the same question on nanoGPT repo: https://github.com/karpathy/nanoGPT/issues/432, but I haven't found the answer I'm looking for yet. Could someone please enlighten me.

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