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.
arXiv:2503. 11891v2 Announce Type: replace Abstract: We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by isotropic normal noise during training.
arXiv:2603. 04895v2 Announce Type: replace-cross Abstract: Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima.
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
arXiv:2607. 12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization.
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
arXiv:2601. 19791v4 Announce Type: replace Abstract: We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting.
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
arXiv:2606. 28242v1 Announce Type: cross Abstract: Understanding how performance scales jointly with model size and data is a central problem in modern machine learning.
We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class of two-layer diagonal linear networks (as defined in Definition 4.
Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear. In particular, the perturbation radius $ρ$ is typically treated as an isolated tuning parameter, despite defining the neighborhood in which SAM measures sharpness.
arXiv:2608. 13171v1 Announce Type: cross Abstract: To avoid missing important variables and their connections in networks, more and more variables are included in network analysis.
arXiv:2602. 04078v2 Announce Type: replace-cross Abstract: Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence.