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Crystals in NNs: Technical Companion Piece — LessWrong

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Epistemic Status: This is me writing out the more technical connections and trying to mathematize the undelying dynamics to make it actually useful. I've spent a bunch of time on Spectral Graph Theory & GDL over the last year so I'm confident in that part but uncertain in the rest. From the perspective of my Simulator Worlds framing this post is Exploratory (e.g I'm uncertain whether the claims are correct and it hasn't been externally verified) and it is based on an analytical world. Therefore, take it with a grain of salt and explore the claims as they come, it is meant more for inspiration for future work than anything else, especially the physics and SLT part. When we watch a neural network train, we witness something that looks remarkably like a physical process. Loss decreases in fits and starts. Capabilities emerge suddenly after long plateaus. The system seems to "find" structure in the data, organizing its parameters into configurations that capture regularities invisible to r

x Crystals in NNs: Technical Companion Piece — LessWrong AI World Modeling Frontpage 24 Crystals in NNs: Technical Companion Piece by Jonas Hallgren 28th Dec 2025 18 min read 5 24 This is the technical companion piece for Have You Tried Thinking About It As Crystals . Epistemic Status: This is me writing out the more technical connections and trying to mathematize the undelying dynamics to make it actually useful. I've spent a bunch of time on Spectral Graph Theory & GDL over the last year so I'm confident in that part but uncertain in the rest. From the perspective of my Simulator Worlds fram

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