Manifold curvature and intrinsic dimension predict layerwise SAE width exponents and asymptotic floors across Gemma models, with cross-model transfer of the geometric regression, establishing a transferable geometric law instead of a universal scaling law.
The geometry of categorical and hierarchical concepts in large language models
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
background 1
citation-polarity summary
fields
cs.LG 1years
2026 1verdicts
UNVERDICTED 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws
Manifold curvature and intrinsic dimension predict layerwise SAE width exponents and asymptotic floors across Gemma models, with cross-model transfer of the geometric regression, establishing a transferable geometric law instead of a universal scaling law.