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Is there a study or anything that that is guaranteed adding an incomplete assistant: response as the input and the API taking off exactly the same way on the same position?

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It’s how LLMs work - they are effectively recursive at inference time, after each token is sampled, you feed it back in. You will end up with the same model state (not including noise) as if that had been the original input prompt.

LLMs sure. My question is whether it is the same in practice for LLMs behind said API. I found no official documentation that we will get exactly the same result as far as I can tell.

And no one here touched how high a multiple the cost is, so I assume its pretty high.

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