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I don't quite understand how it can produce rhyming poetry if it's building the output one word at a time.

Previously generated words are added to the input token window.

At the point it’s generating the next word, it knows what its preceding words were. With a conceptual representation of various rhyme schemes, subsequent words will (probably) fit that form.

So once it's done one line, when it's writing the next line, it will be stuck with being force to rhyme with whatever it came up with on the first line? Curious what happens when the first line ends in the word 'orange' (or maybe it tries to pick end-of-line-words based on rhyme-ability?)

If certain words (like “orange”) are statistically unlikely to be used in that context in that rhyme scheme, then they’re unlikely to be picked to begin with.

You can specifically ask it to end the first line in "orange" or whatever.

In my experience, when it can't come up with a good rhyme, it tends to fib it. But also keep in mind that, as it operates on token representation of words internally, its notion of what rhymes and what does not is far from perfect. This is more noticeable in languages other than English.

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