arXiv:2607. 06151v1 Announce Type: new Abstract: Generalization remains a pivotal challenge in deep learning, where traditional optimizers like Stochastic Gradient Descent (SGD) often converge to sharp minima, leading to overfitting and reduced performance on unseen data.
arXiv:2606. 30813v1 Announce Type: cross Abstract: Deep neural networks with repeated architectural blocks, such as transformers, often exhibit structured relationships across layers that emerge during training.
arXiv:2607. 18306v1 Announce Type: cross Abstract: Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss in a local parameter neighborhood.
arXiv:2608. 15105v1 Announce Type: new Abstract: Recent progress in optimization research has highlighted the sharpness of the loss landscape as a key factor in narrowing the generalization gap.
arXiv:2607. 16261v1 Announce Type: cross Abstract: Modern optimizers combine gradients from the current mini-batch with historical optimization state, such as momentum or adaptive moments.
arXiv:2405. 04376v4 Announce Type: replace Abstract: Hyperparameter tuning, particularly the selection of an appropriate learning rate in adaptive gradient training methods, remains a challenge.
arXiv:2505. 23866v2 Announce Type: replace Abstract: Deep neural networks have been increasingly used in safety-critical applications such as medical diagnosis and autonomous driving.
arXiv:2606. 16112v1 Announce Type: cross Abstract: Residual architectures are ubiquitous in deep learning, but they suffer from a subtle structural limitation: the norm of the residual stream can grow rapidly with depth.
arXiv:2606. 13894v1 Announce Type: cross Abstract: AdamW is a default optimizer for modern deep learning, but its first and second moment states add roughly two parameter-sized buffers to training memory.
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:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).
arXiv:2412. 19444v2 Announce Type: replace Abstract: Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process.
arXiv:2502. 17055v5 Announce Type: replace Abstract: Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence.