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).
By Steffen Dereich, Arnulf Jentzen, Adrian Riekert
arXiv:2508. 03105v3 Announce Type: replace Abstract: We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function.
By Yuichi Kondo, Hideaki Iiduka
arXiv:2509. 23052v2 Announce Type: replace Abstract: We present a new meta-learning method to determine the optimal learning rate schedule for gradient descent.
By Matt L. Sampson, Peter Melchior
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.
By Yijiang Pang, Shuyang Yu, Bao Hoang, Jiayu Zhou
arXiv:2509. 11285v2 Announce Type: replace-cross Abstract: Class-Incremental Learning (CIL) in deep neural networks is conventionally framed as an iterative gradient-based optimization problem, incurring high computational cost, hyperparameter sensitivity, and risk of catastrophic forgetting.
By Alejandro Dopico-Castro, Oscar Fontenla-Romero, Bertha Guijarro-Berdi\~nas, Amparo Alonso-Betanzos
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.
By Tianjin Huang, Zhangyang Wang, Haotian Hu, Zhenyu Zhang, Gaojie Jin, Xiang Li, Li Shen, Jiaxing Shang, Tianlong Chen, Ke Li, Lu Liu, Qingsong Wen, Shiwei Liu
Deep neural networks can exhibit periodic loss spikes known as the "Slingshot Mechanism" during long‑term training. This paper shows that such spikes arise from finite‑precision floating‑point arithmetic: when the correct‑class logit becomes much larger than the others, the gradient for that class is rounded to zero while others remain nonzero, breaking the zero‑sum constraint and creating a positive feedback loop that inflates feature and classifier norms. The authors term this Numerical Feature Inflation (NFI) and demonstrate that it explains the rapid norm growth, reappearance of gradients, and loss spikes, while also showing that partial absorption can still cause hidden norm growth without visible spikes.
By Hanqing Liu, Jianjun Cao, Yuanze Li, Zijian Zhou
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.
By Foivos Alimisis, Rustem Islamov, Aurelien Lucchi
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.
By Yuanzhe Tao, Yifeng Liu, Huizhuo Yuan, Xun Zhou, Yuan Cao, Quanquan Gu
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.
By Pranav Vaidhyanathan, Lucas Schorling, Natalia Ares, Maike Osborne
The paper reports on the updated AlgoPerf V1 benchmark, evaluating new training algorithms on wall‑clock time‑to‑target across nine workloads on fixed hardware. Using a self‑tuning ruleset that requires a single configuration for all workloads, Schedule‑Free AdamW achieved the best overall performance among 13 PyTorch and JAX submissions. The study also examines trade‑offs between step efficiency and runtime, finding that matrix‑preconditioned and two‑loop methods are sample‑efficient but need aggressive computational optimizations, and highlights the high sensitivity of learning rate and momentum across domains, underscoring the need for more robust hyperparameter‑tuning‑resistant methods.
By Priya Kasimbeg (Alice), Ahmed Khaled (Alice), Aahlad Chandrabhatta (Alice), Yifan Wang (Alice), Andy Liu (Alice), Niccol\`o Ajroldi (Alice), David Tweedle (Alice), Xingyu (Alice), Yang, Isaac Patole, Frank Schneider, George E. Dahl
The paper systematically evaluates regression objectives for tabular deep learning across many datasets and neural backbones, finding that most alternatives to Mean Squared Error (MSE) offer limited or inconsistent gains, while quantile loss consistently improves performance. It identifies a limitation of global early stopping: different noise levels in target regions reach optimal performance at different epochs, causing a compromise. To address this, the authors propose a heteroskedasticity‑aware extension of quantile loss using input‑dependent label smoothing, which outperforms standard quantile loss on several backbones.
By Danil Rudenko, Georgii Bulgakov, Nikolay Kartashev, Ivan Rubachev, Daniil Krasylnikov, Artem Babenko