Near-Floor Geometry Is Generic: Leverage Dispersion in Trained Overcomplete Codes

arXiv:2605.01192 · cs.LG, cs.IT, math.IT · Submitted 2026-05-02 · Read on arXiv

cs.LG, cs.IT, math.IT

Submitted: 2026-05-02

Updated: 2026-09-05

Comments: v2: 53 pages, 7 figures. Substantial revision and extension; title changed. Three formal statements in v1 were too strong and are corrected here (two need h_i <= 1/2; one is wrong at kappa_i = 1), and two empirical readings are withdrawn. See "Changes from version 1" in the manuscript. Code: github.com/hecboar/linear-readout-threshold-recovery

Code: https://github.com/hecboar/linear-readout-threshold-recovery

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sparsity — 16× in this paper · explained in 4 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Interpretability — 4× in this paper · explained in 15 episodes
• Pruning — 3× in this paper · explained in 4 episodes
• Transformer — 3× in this paper · explained in 2 episodes
• Distillation — 2× in this paper · explained in 2 episodes
• Knowledge Distillation — 2× in this paper · explained in 11 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes

Sources

• On the Complexity of Neural Computation in Superposition
• How Pruning Reshapes Features: Sparse Autoencoder Analysis of Weight-Pruned Language Models
• Sparse Autoencoders Find Highly Interpretable Features in Language Models
• Scaling and evaluating sparse autoencoders
• Mathematical Models of Computation in Superposition
• Spectral Superposition: A Theory of Feature Geometry
• Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2
• Superposition Yields Robust Neural Scaling
• Understanding sparse autoencoder scaling in the presence of feature manifolds
• From Data Statistics to Feature Geometry: How Correlations Shape Superposition
• Geometric Limits of Knowledge Distillation: A Minimum-Width Theorem via Superposition Theory
• Open Problems in Mechanistic Interpretability

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