A common heuristic used to explain the generalization of first-order gradient methods on non-convex neural networks is that "flat interpolators generalize well" (Hochreiter and Schmidhuber, 1994; Keskar et al. , 2017), where flatness can be measured by the trace of the Hessian of the empirical loss.
arXiv:2609.31101v1 Announce Type: cross
Abstract: The flatness of the loss landscape at a minimizer is a widely used heuristic for reasoning about neural-network generalization, yet evidence for this...
By Brandon Livio Annesi, Davide Straziota, Enrico Maria Malatesta
arXiv:2605. 05209v2 Announce Type: replace-cross Abstract: Flat minima are an account of why deep networks generalise.
By Michael Timothy Bennett
The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
By Hao Yu
arXiv:2606. 28662v1 Announce Type: cross Abstract: The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization.
By Yuto Omae, Kazuki Sakai, Yohei Kakimoto, Makoto Sasaki, Yusuke Sakai, Hirotaka Takahashi
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