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Hi Wayne, I'm also an llm skeptic. I worked in a fang's ai group for a year.
I've got a different analogy, maybe a little closer to the truth but then also maybe less accessible.
There's a thing people do with data called 'interpolation'. If you have some points you can do a linear regression that draws a balanced straight line through the scattered points and then the best guess for values between the points is the value on that line. Yeah straight line is probably not a good match so there's all sorts of curved interpolation functions. The point here is that without knowledge of how the points came to be, we really don't know how well the interpolation is working. For example if we're graphing values of sine at 0, pi, 2 pi, ... x pi, then the scatter chart will show points all in a straight line, the interpolations will all be straight lines because the interpolation doesn't know the values came from the sine function. The guesses are only correct for multiples of pi. A knowledgable person could set up the interpolation to just use sine but an LLM starts without any knowledge so builds a big probability model to interpolate the values its trained with.
LLMs training creates an interpolation model for its input data. Instead of 2d scatter charts it creates vectors (list of numbers) and constructs a giant n-dimensional vector field. If you look into how to interpolate vector fields you'll see there's a ton of problems. As the number of dimensions increases the number of potential discontinuities grows exponentially. A general high dimension state spaces is very scary to interpolate because you find yourself making stuff up at every turn.
Anyway, llm creates a giant model to interpolate between data vectors. The amazing thing is that this approach does appear to work for things we didn't expect. Like human handwriting. Like human languages. Playing games of probability. Human emotional behavior. This is a real reason to be amazed at these new things we made - because they really can do some powerful stuff. The future of LLMs is whatever new uses we can find for them - they really can do some unexpectedly nifty stuff.
What llms can't 'do' is the discrete stuff that cannot be interpolated. Integer math. Bitwise math. Logic. Mathematics. Rationality. Writing code. A generated llm response is a tensor multiply. And a tensor multiply isn't turing complete. LLM cannot compute.
And when an llm can't 'do' something it still does its interpolation trick and generates an answer. The answer will read like its correct but the process that created the answer is strictly lexical and isn't based on any semantic.
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