Legal-reasoning trajectories collapse ~45% in effective dimension with scale
measured in 1 paper- Recording chain-of-thought hidden-state trajectories during legal reasoning, PCA effective dimensionality d95 (components for 95% variance) falls from 501 to 274 (a 45% collapse) from Llama-3-8B-Instruct to Llama-3.1-70B-Instruct. [anderson-2026-geometry-of-thought] - The paper frames legal reasoning as "Crystallization" - a global-dimensionality collapse, distinct from the discrete-cluster ("Lattice") pattern found in code reasoning. [anderson-2026-geometry-of-thought] - Observational only (a covariance-spectrum statistic on two real checkpoints); no causal intervention. [anderson-2026-geometry-of-thought]
Structure
Context
effective dimension, chain-of-thought, scale, legal reasoning, PCA
Confirmed in models
Method
Papers
The Geometry of Thought: How Scale Restructures Reasoning in Large Language Models — Anderson, Samuel Cyrenius