arXiv:2606. 28879v1 Announce Type: new Abstract: The adaptive moment estimation algorithm, known as Adam, is widely used in modern machine learning, owing to its low per-iteration complexity and strong empirical performance.
arXiv:2603. 09923v4 Announce Type: replace Abstract: Exponential moving averages (EMAs) are a central component of widely used adaptive optimizers such as Adam.
arXiv:2607. 27383v1 Announce Type: new Abstract: We establish the first convergence guarantees for the plain vector-form \emph{Adam} optimizer under heavy-tailed stochastic noise.
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:2608. 04026v1 Announce Type: cross Abstract: In this paper, we develop a trust-region framework for understanding the behavior of adaptive moment estimation mechanisms, such as \textsc{Adam}, in stochastic gradient optimization.
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.
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:2505. 13196v3 Announce Type: replace-cross Abstract: We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics.
arXiv:2604. 08742v2 Announce Type: replace-cross Abstract: Adam is widely used, but its convergence theory remains incomplete even in the deterministic full-batch setting because momentum and adaptive preconditioning are tightly coupled.
arXiv:2602. 00329v4 Announce Type: replace-cross Abstract: Reliable data attribution is essential for mitigating bias and reducing computational waste in modern machine learning, with the Shapley value serving as the theoretical gold standard.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2608. 15824v1 Announce Type: new Abstract: Adam retains a moving average of past squared gradients in its denominator, but the optimization cost of this memory is not well understood.
arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.