arXiv:2504.16450v4 Announce Type: replace Abstract: We derive a differential equation that governs the evolution of the generalization gap when a model is trained by gradient descent-based methods. T...
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:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
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.
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:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2601. 19791v4 Announce Type: replace Abstract: We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting.
arXiv:2607. 23967v1 Announce Type: new Abstract: Delayed generalization, or grokking, remains poorly understood despite extensive empirical study.
arXiv:2606. 30388v1 Announce Type: cross Abstract: Delayed generalization (\ie~grokking) refers to the phenomenon in which a neural network fits its training data early in training but only begins to generalize after a prolonged delay, often through an abrupt transition.
arXiv:2608. 11479v1 Announce Type: new Abstract: We establish convergence guarantees of gradient descent for general feedforward neural networks of arbitrary width or depth, with no special requirements on the initialization or dataset.
arXiv:2501. 07400v2 Announce Type: replace-cross Abstract: We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations.
arXiv:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.