Is a token’s probability the model’s confidence that a claim is true?
No. It is a probability for a continuation under the model and decoding setup. That quantity is different from a calibrated assessment of factual correctness.
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A standard autoregressive language model produces next-token scores repeatedly. Some decoding methods explore alternatives, but the basic prediction is conditioned on the sequence available at each step.
Yes. The output vocabulary can contain punctuation, whitespace-related pieces, word fragments, and special markers in addition to complete words, so any permitted item may be selected.
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