Ah so taking the Fourier transform of this function[0]? The summation of the fizz and buzz frequencies don't lead to perfect peaks for the fizz and buzz locations. I need to revisit Fourier cause I would have thought the transform would have just recovered the two fizz and buzz peaks not the fizzbuzz spot.

[0]: https://www.desmos.com/calculator/wgr3zvhazp

I'm new to this sort of inquiry. What do you do to see if questions can be recognized? Do you just ask/prompt "do you recognize this puzzle?"

What does it mean for it to "be surfaced without relying on reasoning"?

> Do you just ask/prompt "do you recognize this puzzle?"

In essence, yes, but with a bit more methodology (though as I mentioned it was all ad-hoc).

We've tried to extract pre-existing questions as well through a variety of "You are a contestant on the british TV show Only Connect" and see if it can recognize questions - couldn't find anything that reliably reproduced preexisting knowledge. It's absolutely possible we missed something.

The tricky thing is you get to define the state. So if the "state" is the current word _and_ the previous 10 it is still "memoryless". So an LLM's context window is the state. It doesn't matter whether _we_ see parts of the state as called history, the markov chain doesn't care (they are all just different features).

Edit: I could be missing important nuance that other people are pointing out in this thread!