Flatland: The Adventures of Gradient Descent with Large Step Sizes
arXiv:2606. 06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth.
arXiv:2604. 14669v2 Announce Type: replace Abstract: Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored.
arXiv:2606. 06722v1 Announce Type: new Abstract: The training of neural networks often entails objective functions that are not globally $L$-smooth.
arXiv:2601. 04710v2 Announce Type: replace-cross Abstract: Fine-tuning large language models (LLMs) achieves strong performance but is often limited by the memory overhead of backpropagation.
arXiv:2409. 03682v2 Announce Type: replace Abstract: Learning new tasks by leveraging prior experience is a fundamental trait of intelligent systems.
arXiv:2606. 02857v1 Announce Type: cross Abstract: Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation.
arXiv:2608. 03197v1 Announce Type: new Abstract: 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.
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv:2607. 21716v1 Announce Type: new Abstract: Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics.
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. 15665v1 Announce Type: new Abstract: Zeroth-order (ZO) optimization enables backpropagation-free fine-tuning of large language models, but existing ZO methods suffer from high-variance gradient estimators, making convergence unstable and highly sensitive to learning rates.
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:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
arXiv:2605. 29547v2 Announce Type: replace-cross Abstract: Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators.