Epistemic Status: Written with my Simulator Worlds framing. E.g I ran simulated scenarios with claude in order to generate good cognitive basins and then directed those to output this. This post is Internally Verified (e.g I think most of the claims are correct with an average of 60-75% certainty) and a mixture of an exploratory and analytical world.[1]

This post also has a more technical companion piece pointing out the connections to Singular Learning Theory and Geometric Deep Learning for the more technically inclined of you called Crystals in NNs: Technical Companion Piece.

Have You Tried Thinking About It As Crystals?

Scene: A house party somewhere in the Bay Area. The kind where half the conversations are about AI timelines and the other half are about whether you can get good pho in Berkeley. Someone corners an interpretability researcher near the kombucha. (Original story concept by yours truly.)

CRYSTAL GUY: So I've been thinking about shard theory.

INTERP RESEARCHER: Oh yeah? What about it?

CRYSTAL GUY: Well, it describes what trained networks look like, right? The structure. Multiple shards, contextual activation, grain boundaries between—

INTERP RESEARCHER: Sure. Pope, Turner, the whole thing. What about it?

CRYSTAL GUY: But it [...]

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Outline:

(00:47) Have You Tried Thinking About It As Crystals?

(03:42) RLHF as Reheating

(04:51) The Formation Problem

(06:41) The Empirical Starting Point

(09:35) Path Dependence

(10:31) Why This Is Actually Crystallization: The Fixed-Point Thing

(12:41) What Crystallization Actually Is

(15:52) Interlude: On Smells and Other Frozen Things

(21:35) Relating it to Neural Networks

(21:47) Abstractions as Crystallized Compressions

(22:31) Shards as Crystal Domains

(23:29) Nucleation and Growth

(24:23) Defects and Failure Modes

(26:22) Appendix: Glossary of Correspondences

The original text contained 2 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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