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The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Machine Learning · Computer Science 2024-04-10 Kaloyan Danovski , Miguel C. Soriano , Lucas Lacasa

In this work, we investigate the mechanism underlying loss spikes observed during neural network training. When the training enters a region with a lower-loss-as-sharper (LLAS) structure, the training becomes unstable, and the loss…

Machine Learning · Computer Science 2024-10-08 Xiaolong Li , Zhi-Qin John Xu , Zhongwang Zhang

Sharpness-Aware Minimization (SAM) improves generalization by minimizing the worst-case loss within a fixed parameter-space radius neighborhood. SAM and its variants mainly rely on a first-order linearized surrogate, while flat minima are…

Machine Learning · Computer Science 2026-05-12 Jinping Wang , Qinhan Liu , Zhiwu Xie , Zhiqiang Gao

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

Machine Learning · Computer Science 2025-10-30 Blaise Delattre

In this paper, we provide a theoretical study of noise geometry for minibatch stochastic gradient descent (SGD), a phenomenon where noise aligns favorably with the geometry of local landscape. We propose two metrics, derived from analyzing…

Machine Learning · Computer Science 2024-02-02 Mingze Wang , Lei Wu

The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…

Machine Learning · Statistics 2022-10-18 Masaaki Imaizumi , Johannes Schmidt-Hieber

The largest eigenvalue of the Hessian, or sharpness, of neural networks is a key quantity to understand their optimization dynamics. In this paper, we study the sharpness of deep linear networks for univariate regression. Minimizers can…

Machine Learning · Statistics 2024-10-29 Pierre Marion , Lénaïc Chizat

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing - where synchronization between agents is induced through communication with…

Optimization and Control · Mathematics 2020-12-18 Nicholas M. Boffi , Jean-Jacques E. Slotine

Modern deep learning models are over-parameterized, where different optima can result in widely varying generalization performance. The Sharpness-Aware Minimization (SAM) technique modifies the fundamental loss function that steers gradient…

Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…

Dynamical Systems · Mathematics 2025-06-30 Liam Blake , John Maclean , Sanjeeva Balasuriya

We investigate the inherent bias of Stochastic Gradient Descent (SGD) toward learning low-rank weight matrices during the training of deep neural networks. Our results demonstrate that training with mini-batch SGD and weight decay induces a…

Machine Learning · Computer Science 2024-10-22 Tomer Galanti , Zachary S. Siegel , Aparna Gupte , Tomaso Poggio

Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for…

Machine Learning · Statistics 2020-06-15 Yiping Lu , Chao Ma , Yulong Lu , Jianfeng Lu , Lexing Ying

We theoretically characterize gradient descent dynamics in deep linear networks trained at large width from random initialization and on large quantities of random data. Our theory captures the ``wider is better" effect of…

Machine Learning · Computer Science 2025-06-17 Blake Bordelon , Cengiz Pehlevan

Obtaining versions of deep neural networks that are both highly-accurate and highly-sparse is one of the main challenges in the area of model compression, and several high-performance pruning techniques have been investigated by the…

Machine Learning · Computer Science 2023-09-11 Denis Kuznedelev , Eldar Kurtic , Eugenia Iofinova , Elias Frantar , Alexandra Peste , Dan Alistarh

Recently many first and second order variants of SGD have been proposed to facilitate training of Deep Neural Networks (DNNs). A common limitation of these works stem from the fact that they use the same learning rate across all instances…

Machine Learning · Computer Science 2021-05-31 Shreyas Saxena , Nidhi Vyas , Dennis DeCoste

Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through…

Machine Learning · Statistics 2019-02-19 Kirill Neklyudov , Dmitry Molchanov , Arsenii Ashukha , Dmitry Vetrov

Trace-wise noise is a type of noise often seen in seismic data, which is characterized by vertical coherency and horizontal incoherency. Using self-supervised deep learning to attenuate this type of noise, the conventional blind-trace deep…

Geophysics · Physics 2024-04-04 Mohammad Mahdi Abedi , David Pardo , Tariq Alkhalifah

Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…

Adaptation and Self-Organizing Systems · Physics 2019-05-14 Alexandra Pinto Castellanos

Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are…

Geophysics · Physics 2019-07-23 Siwei Yu , Jianwei Ma , Wenlong Wang

We introduce "AnnealSGD", a regularized stochastic gradient descent algorithm motivated by an analysis of the energy landscape of a particular class of deep networks with sparse random weights. The loss function of such networks can be…

Machine Learning · Computer Science 2017-04-25 Pratik Chaudhari , Stefano Soatto