arXiv Machine Learning By Maria Matveev, Vit Fojtik, Hung-Hsu Chou, Gitta Kutyniok, Johannes Maly

Conflicting Biases at the Edge of Stability: Norm versus Sharpness Regularization

Read the original on arXiv Machine Learning →

arXiv:2505. 21423v3 Announce Type: replace Abstract: The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime.

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arXiv Statistics ML
3d ago

Grokking through the Lens of Minimum-Norm Interpolation

The paper develops a statistical theory for minimum‑norm interpolation in high‑dimensional regression, showing how regularization geometry and signal sparsity affect generalization. It identifies regimes where sparsity‑promoting regularizers yield exact interpolation that is far more accurate than approximate fitting, and proves a zero–one generalization law for strongly overparameterized noiseless problems. The authors also characterize training and generalization errors along ρ‑regularization paths when feature dimension and sample size are proportional, demonstrating that generalization improves with more sparsity‑promoting norms and sparser targets, and that small changes in regularization strength can cause large shifts in generalization. whyItMatters":"The work provides a quantitative understanding of delayed generalization (grokking) and reveals a statistical instability in minimum‑norm interpolation, offering insights that could guide the design of regularizers for better generalization in overparameterized models."

By Gil Kur, Ileana Rugina, Cl\'ementine Carla Juliette Domin\'e, Marco Mondelli