Does verbatim completion of a bible passage look different from generation of a novel sequence in interesting ways? How many sequences of this length do they memorize? Do the memorized ones roughly correspond to things humans would find important enough to memorize, or do LLMs memorize just as much SEO garbage as they do bible passages?
They take the input context and generate the next token, then feed that whole thing back in as context and predict the next token, and repeat until the most likely next token is their stop word.
If they produce anything like a retrieved sequence, that's because they just happened to pick that set of tokens based on their training data. Regenerating the output from exactly the same input has a non-zero chance of generating different output.
The point is, though – somehow the model has memorized these passages, in a way that allows reliable reproduction. No doubt in a super amorphous and diffuse way, as minute adjustments to the nth sigbits of myriads of floating-point numbers, but it cannot be denied that it absolutely has encoded the strings in some manner. Or otherwise you have to accept that humans can't memorize things either. Indeed given how much our memory works by association, and how it's considerably more difficult to recount some memorized sequence from an arbitrary starting point, it's easy to argue that in some relevant way human brains are next-token predictors too.
Yes, if you reduce temperature to zero and set the same random seed, you should get the same output tokens for a given set of input tokens.
However, there is no guarantee the output for a given seed will be the correct expected output.
For example, there logically must be a model and seed where providing the lord's prayer as input for completion produces a Metallica song as output, because that's a viable set of input tokens: https://genius.com/Metallica-enter-sandman-lyrics
That seed is no more or less valid than any other seed which completes the actual lord's prayer or which provides something completely different. All those seeds are just predicting their next token.
If people want that sort of exact reliable retrieval of sequences, and for the sequences to be "correct", then an LLM is the wrong tool for the job.
The question I’m asking is, how is this working in an LLM? How exactly do their weights encode (seemingly) the entire bible such that they can recreate long passages verbatim from a prompt that likely doesn’t appear anywhere in the training data (e.g. some vague description of a particular passage).