arXiv:2606. 32000v1 Announce Type: cross Abstract: Why do neural networks memorize algorithmic training data long before they generalize?
arXiv:2607. 11666v1 Announce Type: new Abstract: Grokking is a phenomenon in which neural networks initially memorize training data and only later exhibit strong generalization after prolonged optimization.
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. 22444v1 Announce Type: new Abstract: For scale-invariant deep networks, Hyperball-style optimizers have shown strong performance in large-scale training by fixing the norms of matrix-valued parameters and normalizing updates.
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.
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:2510. 03164v2 Announce Type: replace Abstract: Learning rate warm-up -- increasing the learning rate at the beginning of training -- has become a ubiquitous heuristic in modern deep learning, yet its theoretical foundations remain poorly understood.
arXiv:2610.00446v1 Announce Type: cross Abstract: As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its v...
arXiv:2601. 22450v2 Announce Type: replace-cross Abstract: Masked Diffusion Language Models have recently emerged as a powerful generative paradigm, yet their generalization properties remain understudied compared to their auto-regressive counterparts.
arXiv:2606. 15669v1 Announce Type: cross Abstract: Modern deep neural networks rely on Euclidean scalar activations (e.
arXiv:2609.07755v1 Announce Type: new Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...