A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks

arXiv:2607.23397 · cs.LG, math.ST, stat.ML · Submitted 2026-07-26 · Read on arXiv

Sumio Watanabe

cs.LG, math.ST, stat.ML

Submitted: 2026-07-26

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

Terminology

• Generalization — 18× in this paper · explained in 14 episodes
• Phase Transition — 4× in this paper · explained in 3 episodes
• Hierarchical Structure — 3× in this paper · explained in 3 episodes
• Phase Transitions — 3× in this paper · explained in 2 episodes
• AI Alignment — 1× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Fisher Information — 1× in this paper · explained in 4 episodes
• In-Context Learning — 1× in this paper · explained in 7 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 3 episodes

Sources

• Singular Learning Theory for Factor Analysis
• Loss Landscape Degeneracy and Stagewise Development in Transformers
• Deep Neural Networks as Gaussian Processes

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