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I have read the GPT-1 paper, and my understanding is that it works as follows: $U$ is input tokens, $h_0=UW_e+W_p$, $h_i=\text{transformer_block}(h_{i-1})$ and the output is a probability vector $P(u)=\text{softmax}(h_nW_e^T)$, and the hidden states are the final latent layer before softmax, so the hidden states are $h_n(U)$? I do not really understand, how to formalise this as a hidden Markov chain similar to the definition in Wikipedia?

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The statement that GPT is a higher order hidden Markov model should not be taken too seriously. It is intended as a slogan or intuition, not something that is intended to be be rigorously proven.

Let $x_1,x_2,\dots,x_k$ denote the words of the text, in order ($x_1$ is the first word, etc.).

GPT is a model for predicting the next word, given all prior words. In other words, it estimates $p(x_i | x_1,x_2,\dots,x_{i-1})$. Hopefully you can see how this resembles the formulation of a Markov model.

It is higher-order, because it uses all prior words to predict the next word, not just the previous few words.

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  • $\begingroup$ Thank you. It is about my summer research, so I think is should be taken seriously. I can see the higher order Markov model structure, but I do not understand the hidden state. $\endgroup$
    – 123
    Jun 28, 2023 at 19:58
  • $\begingroup$ @123, I am not convinced that there is any hidden state, and I am not convinced that you should take the "hidden" part of that statement that seriously. Without any context about where you have encountered that statement, I find it hard to say any more. $\endgroup$
    – D.W.
    Jun 28, 2023 at 22:16

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