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these sort-of-lies might help:

think of the latent space inside the model like a topological map, and when you give it a prompt, you're dropping a ball at a certain point above the ground, and gravity pulls it along the surface until it settles.

caveat though, thats nice per-token, but the signal gets messed up by picking a token from a distribution, so each token you're regenerating and re-distorting the signal. leaning on language that places that ball deep in a region that you want to be makes it less likely that those distortions will kick it out of the basin or valley you may want to end up in.

if the response you get is 1000 tokens long, the initial trajectory needed to survive 1000 probabilistic filters to get there.

or maybe none of that is right lol but thinking that it is has worked for me, which has been good enough

[noduerme]

Hah! Reading this, my mind inverted it a bit, and I realized ... it's like the claw machine theory of gradient descent. Do you drop the claw into the deepest part of the pile, or where there's the thinnest layer, the best chance of grabbing something specific? Everyone in everu bar has a theory about claw machines. But the really funny thing that unites LLMs with claw machines is that the biggest question is always whether they dropped the ball on purpose.

The claw machine is also a sort-of-lie, of course. Its main appeal is that it offers the illusion of control. As a former designer and coder of online slot machines... totally spin off into pages on this analogy, about how that illusion gets you to keep pulling the lever... but the geographic rendition you gave is sort of priceless when you start making the comparison.

[basch]

My mental model for them is plinko boards. Your prompt changes the spacing between the nails to increase the probability in certain directions as your chip falls down.

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i literally suggested this metaphor earlier yesterday to someone trying to get agents to do stuff they wanted, that they had to set up their guardrails in a way that you can let the agents do what they're good at, and you'll get better results because you're not sitting there looking at them.

i think probably once you start seeing that the behavior falls right out of the geometry, you just start looking at stuff like that. still funny though.