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:2609.37787v1 Announce Type: new Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
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.
The paper establishes uniform a priori bounds for the Adam optimizer, enabling an unconditional error analysis for a broad class of strongly convex stochastic optimization problems. Prior analyses were conditional, assuming Adam remained bounded, whereas this work removes that assumption. The results provide a rigorous foundation for Adam’s performance in training deep neural networks and other convex optimization tasks.
arXiv:2602. 10204v2 Announce Type: replace Abstract: We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.
arXiv:2603. 09923v4 Announce Type: replace Abstract: Exponential moving averages (EMAs) are a central component of widely used adaptive optimizers such as Adam.
The paper presents a theoretical study of Adam in non‑stationary stochastic optimization, distinguishing two regimes: Euclidean tracking under adaptive strong monotonicity and high‑probability projected stationarity for general smooth objectives. It derives finite‑time bounds that decompose into initialization, objective drift, first‑moment tracking error (β₁), and preconditioner perturbation (β₂), and characterizes burn‑in times for constant and step‑decay schedules. The analysis reveals a noise–drift tradeoff, showing that in noise‑dominated settings Adam’s adaptive mechanisms can improve guarantees, while in drift‑dominated settings they may worsen tracking, potentially making vanilla SGD preferable.
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. 03519v1 Announce Type: new Abstract: We show that projected Adam for online optimization with arbitrary moment decay parameters $\beta_1,\beta_2\in[0,1)$ can have average regret bounded away from zero.
arXiv:2511. 13465v5 Announce Type: replace Abstract: This paper studies the exponential decay mechanism of the second-moment estimate in Adam.
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.
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:2609.36600v1 Announce Type: cross Abstract: Classical stochastic approximation methods rely on estimators of the first moment (mean) of a random regression function. We study methods that emplo...