arXiv:2607. 10869v1 Announce Type: new Abstract: We study the population gradient flow of an infinitely wide two-layer neural network learning a misspecified single-index model in high dimension.
arXiv:2606. 04327v1 Announce Type: cross Abstract: We investigate the geometric structure of stationary plateaus that arise in the loss landscape of two-layer neural networks with smooth activation functions.
arXiv:2608. 13335v1 Announce Type: new Abstract: Neural networks trained by gradient descent on a smooth cost function can nevertheless learn in steps: the cost holds on long plateaus and then drops abruptly.
arXiv:2607. 23397v1 Announce Type: new Abstract: Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood.
arXiv:2608. 06766v1 Announce Type: cross Abstract: Training changes a network's predictions while allocating task-relevant structure across its internal units.
arXiv:2511. 01938v3 Announce Type: replace-cross Abstract: Grokking is a puzzling phenomenon in neural networks where full generalization occurs only after a substantial delay following the complete memorization of the training data.
arXiv:2607. 12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
arXiv:2607. 03613v1 Announce Type: new Abstract: We study the implicit bias of noisy stochastic gradient descent in training wide two-layer ReLU networks for multivariate regression.
arXiv:2507. 14177v2 Announce Type: replace-cross Abstract: This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid type most commonly used before the advent of ReLUs.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
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.
arXiv:2606. 28464v1 Announce Type: new Abstract: In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture.