Goodfire's Neural Geometry series maps manifolds inside LLMs, from circular numbers to steering
burny_tech · x · 2026-11-10
Goodfire published "The Neural Geometry Series", a research series on the geometric structure of neural network activations.
Key entries:
- Opening essay (Geiger et al.): activations mirror the structure of training data — weekdays form circles, colors form an HSL manifold, the tree of life appears in genomic representations.
- Steering along manifolds (Wurgaft et al.): steering along curved manifolds yields cleaner, more targeted behavior changes than conventional linear steering vectors.
- A geometric calculator inside a network (Feucht et al.): a general-purpose addition module in Llama 3.1 8B operating over circular number representations.
- Can SAEs capture neural geometry? (Bhalla et al.): studying how sparse autoencoder features (straight lines) can reconstruct curved geometry, plus an unsupervised pipeline for discovering manifolds.
- Temporal dynamics: how LLM representations evolve over a prompt or conversation.
The series argues neural geometry is a crucial frontier for understanding, improving, and controlling AI models.
Related event: Goodfire Launches Neural Geometry Series to Map and Control Model Internals(2 posts)→
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