Previously in this series: Elementary Infra-Bayesianism

1. There's this paper

Earlier last week I got nerd-sniped by a paper called Condensation: a theory of concepts (Eisenstat 2025). It's the kind of paper where the abstract makes a claim so clean you assume you must be misreading it: roughly, there is a right answer to “what are the concepts in this data,” and any two agents who carve it up well enough will agree on what those concepts are.[1]

If that sounds like John Wentworth's natural abstractions hypothesis, yes, the family resemblance is strong. I wrote about something adjacent a while back. Condensation is a different formalization, but the punchline rhymes: structure in the data constrains what any good representation can look like. People on LessWrong seem to dig it, and I wanted to see what the fuss was about.

The paper is forty pages of math and gives you no algorithm; it tells you what a good carving looks like, not how to find one. I spent a slightly embarrassing amount of time trying to get the basic objects to do something on a computer. This post is how far I got.[2]

2. Concepts, scopes, and a score

Say [...]

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Outline:

(00:13) 1. Theres this paper

(01:21) 2. Concepts, scopes, and a score

(03:55) 3. The same three tokens, three representations

(06:54) 4. A model gives you concepts; scope is your problem

(08:44) 5. Does it work on real models?

(09:17) The pipeline

(10:55) The datasets

(13:11) Results

(14:23) Why PCA wins on induction

(15:26) 6. How far I got, and what worries me

The original text contained 22 footnotes which were omitted from this narration.

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First published:

Source:

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Narrated by TYPE III AUDIO.

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