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Epicycles All the Way Down

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Why This Matters

This article highlights the limitations of relying solely on models and heuristics, whether in human cognition or AI, emphasizing that understanding and success often require complex, layered approaches. It underscores the importance of combining intuition with explicit calculations, especially in fields like AI development, where simplistic assumptions can lead to failures. For consumers and the tech industry, this serves as a reminder that progress often involves iterative refinement and acknowledging the inherent imperfections of models.

Key Takeaways

“All models are wrong, but some are useful.” — George E. P. Box

“All LLM successes are as human successes, each LLM failure is alien in its own way.”

I. Two ways to “know”

I was convinced I had a terrible memory throughout my schooling. As a consequence pretty much for every exam in math or science I would re-derive any formula that was needed. Kind of a waste, but what could I do. Easier than trying to remember them, I thought. It worked until I think second year of college, when it didn’t.

But because of this belief, I did other dumb things too beyond not study. For example I used to play poker. And I was convinced, and this was back in the day when neural nets were tiny things, that my brain was similar and I could train it using inputs and outputs and not actually bother doing the complex calculations that would be needed to measure pot odds and things like that. I mean, I can’t know the counterfactual but I’m reasonably sure this was a worse way to play poker that just actually doing the math, but it definitely was a more fun way to do it, especially when combined with reasonable quantities of beer. I was convinced that just from the outcomes I would be able to somehow back out a playing strategy that would be superior.

It didn’t work very well. I mean, I didn’t lose much money, but I definitely didn’t make much money either. Somehow the knowledge I got from the outcomes didn’t translate into telling me when to bet, how much to bet, when to raise, how much to raise, when to fold, how to analyse others, how to bluff, you know all those things that if you want to play poker properly you should have a theory about.

Instead what I had were some decent heuristics on betting and a sense of how others would bet. The times I managed to get a bit better were the times I could convert those ideas of how my “somewhat trained neural net” said I should and then calculated the pot odds and explicitly tried to figure out what others had and tried to use those as inputs alongside my vibes. I tried to bootstrap understanding from outcomes alone, and I failed.

II. Patterns and generators

“What I cannot create, I do not understand.” — Richard Feynman

This essay is about why LLMs feel like understanding engines but behave like over-fit pattern-fitters, why we keep adding epicycles that get us closer to exceptional performance, instead of changing the core generator, and why that makes their failures look more like flash crashes and market blow-ups than like Skynet.

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