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Deep neural networks have revolutionized machine learning, yet their training dynamics remain theoretically unclear-we develop a continuous-time, matrix-valued stochastic differential equation (SDE) framework that rigorously connects the…

机器学习 · 计算机科学 2026-02-10 Brian Richard Olsen , Sam Fatehmanesh , Frank Xiao , Adarsh Kumarappan , Anirudh Gajula

Recent works (e.g., (Li and Arora, 2020)) suggest that the use of popular normalization schemes (including Batch Normalization) in today's deep learning can move it far from a traditional optimization viewpoint, e.g., use of exponentially…

机器学习 · 计算机科学 2020-10-07 Zhiyuan Li , Kaifeng Lyu , Sanjeev Arora

The recently proposed Temporal Ensembling has achieved state-of-the-art results in several semi-supervised learning benchmarks. It maintains an exponential moving average of label predictions on each training example, and penalizes…

神经与进化计算 · 计算机科学 2018-04-17 Antti Tarvainen , Harri Valpola

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

机器学习 · 计算机科学 2017-11-23 Haiping Huang , Taro Toyoizumi

In this work, we offer a theoretical analysis of two modern optimization techniques for training large and complex models: (i) adaptive optimization algorithms, such as Adam, and (ii) the model exponential moving average (EMA).…

机器学习 · 计算机科学 2024-10-31 Kwangjun Ahn , Ashok Cutkosky

Averaging checkpoints along the training trajectory is a simple yet powerful approach to improve the generalization performance of Machine Learning models and reduce training time. Motivated by these potential gains, and in an effort to…

机器学习 · 计算机科学 2025-11-25 Niccolò Ajroldi , Antonio Orvieto , Jonas Geiping

Stochastic gradient descent (SGD) and adaptive gradient methods, such as Adam and RMSProp, have been widely used in training deep neural networks. We empirically show that while the difference between the standard generalization performance…

机器学习 · 计算机科学 2023-11-30 Avery Ma , Yangchen Pan , Amir-massoud Farahmand

We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained…

机器学习 · 计算机科学 2025-12-15 Sotirios Nikoloutsopoulos , Iordanis Koutsopoulos , Michalis K. Titsias

Decentralized Stochastic Gradient Descent (SGD) is an emerging neural network training approach that enables multiple agents to train a model collaboratively and simultaneously. Rather than using a central parameter server to collect…

机器学习 · 计算机科学 2023-06-02 Lisang Ding , Kexin Jin , Bicheng Ying , Kun Yuan , Wotao Yin

Explaining the generalization characteristics of deep learning is an emerging topic in advanced machine learning. There are several unanswered questions about how learning under stochastic optimization really works and why certain…

机器学习 · 计算机科学 2022-04-01 Mahdi S. Hosseini , Mathieu Tuli , Konstantinos N. Plataniotis

Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…

计算与语言 · 计算机科学 2018-11-05 Deren Lei , Zichen Sun , Yijun Xiao , William Yang Wang

We show that stochastic gradient descent (SGD) escapes from sharp minima exponentially fast even before SGD reaches stationary distribution. SGD has been a de-facto standard training algorithm for various machine learning tasks. However,…

机器学习 · 计算机科学 2022-03-22 Hikaru Ibayashi , Masaaki Imaizumi

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the…

机器学习 · 计算机科学 2023-05-31 Antonio Sclocchi , Mario Geiger , Matthieu Wyart

Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average…

机器学习 · 计算机科学 2018-01-17 Pratik Chaudhari , Stefano Soatto

This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best…

机器学习 · 统计学 2020-12-02 Vatsal Shah , Anastasios Kyrillidis , Sujay Sanghavi

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT…

机器学习 · 计算机科学 2025-12-15 Jingyang Qiao , Zhizhong Zhang , Xin Tan , Yanyun Qu , Shouhong Ding , Yuan Xie

In this work, we study robust deep learning against abnormal training data from the perspective of example weighting built in empirical loss functions, i.e., gradient magnitude with respect to logits, an angle that is not thoroughly studied…

机器学习 · 计算机科学 2023-05-02 Xinshao Wang , Yang Hua , Elyor Kodirov , David A. Clifton , Neil M. Robertson

We study the problem of transfer learning and fine-tuning in linear models for both regression and binary classification. In particular, we consider the use of stochastic gradient descent (SGD) on a linear model initialized with pretrained…

机器学习 · 计算机科学 2025-02-25 Reza Ghane , Danil Akhtiamov , Babak Hassibi

Generalized Advantage Estimation (GAE) has been used to mitigate the computational complexity of reinforcement learning (RL) by employing an exponentially weighted estimation of the advantage function to reduce the variance in policy…

机器学习 · 计算机科学 2025-07-24 Shahil Shaik , Jonathon M. Smereka , Yue Wang

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

机器学习 · 计算机科学 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich