When the Preconditioning Exponent Turns Negative: Learning-Rate Coupling and Cross-Environment Generalization

arXiv:2609.30271 · cs.LG · Submitted 2026-07-25 · Read on arXiv

cs.LG

Submitted: 2026-07-25

Updated: 2026-07-25

Terminology

• Accuracy — 19× in this paper · explained in 1 episode
• Generalization — 15× in this paper · explained in 13 episodes
• Adam — 11× in this paper · explained in 2 episodes
• Adaptive Gradient Methods — 4× in this paper · explained in 1 episode
• Adaptivity — 4× in this paper · explained in 1 episode
• Robustness — 4× in this paper · explained in 5 episodes
• Distribution Shift — 3× in this paper · explained in 5 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes

Sources

• Invariant Risk Minimization
• Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization
• The Anatomy of Implicit Bias: Information Allocation in Neural Network Training

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