Alper Nebi Kanlı

@alpernkanli.bsky.social

AI search engineer in London. Vectors, retrieval, and how models represent meaning. Also language, etymology, and movies.

In addition to being a good movie, Nolan’s the Odyssey became a great litmus test for me. I’m not talking about liking or not liking it, I’m talking about actually trying to understand what Nolan did or not.

Two language models can grow the same periodic signature for numbers, and one can use it while the other can't read it at all. Same structure, opposite usefulness. That gap is what my new essay is about: Representational Convergence, Part 2, now live.

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I have been talking about what shape a concept takes inside a language model: lines, circles or helix. I also talked about “present”/“used” distinction. This next paper also emphasises the question "is the shape actually used?"

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Recently I covered a model that adds by turning a clock: it computes directly on a number-circle/helix. Obvious next question: if a model stores "months" as a circle, does it guarantee that it computes with that circle? New work by Feucht et al., "Arithmetic in the Wild," says no.

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How does a language model actually add two numbers? A recent paper, "Language Models Use Trigonometry to Do Addition" (Kantamneni & Tegmark), reverse-engineered it in three LLMs. The answer fuses the two shapes from my last two threads into one object.

A number is a point on helix. Around a loop is the units digit, up the axis is magnitude. Same digit stacks vertically.On the units circle, addition is rotation. 7+8 lands on 5

Suppose Monday is 1, Sunday is 7. So Sunday plus one should be Monday. On a number line, those two sit at opposite ends. Inside a language model, some concepts fix this by not being lines at all. They are circles.

A line breaks at the wrap, a circle doesn't. Sunday and Monday are neighbours on a circle, but they are maximally far apart on a line.

Language models look like they just predict the next word. So it's surprising how much structure they build inside. They actually represent concepts: ideas like gender, sentiment, even truthfulness show up as geometry you can find and manipulate. A thread on how that works.