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Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

Machine Learning · Computer Science 2021-02-24 Shengchao Liu , Dimitris Papailiopoulos , Dimitris Achlioptas

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Machine Learning · Statistics 2026-05-15 Hubert Leroux , Jean Marcus , Julien Roger

Overparameterized deep networks that generalize well have been key to the dramatic success of deep learning in recent years. The reasons for their remarkable ability to generalize are not well understood yet. When class labels in the…

Machine Learning · Computer Science 2026-02-03 Simran Ketha , Venkatakrishnan Ramaswamy

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite…

Statistics Theory · Mathematics 2021-03-17 Peter L. Bartlett , Andrea Montanari , Alexander Rakhlin

Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success…

Machine Learning · Computer Science 2025-07-11 Andrew Gordon Wilson

Gradient-based meta-learning (GBML) with deep neural nets (DNNs) has become a popular approach for few-shot learning. However, due to the non-convexity of DNNs and the bi-level optimization in GBML, the theoretical properties of GBML with…

Machine Learning · Computer Science 2020-11-17 Haoxiang Wang , Ruoyu Sun , Bo Li

Adversarial training is a widely used method to improve the robustness of deep neural networks (DNNs) over adversarial perturbations. However, it is empirically observed that adversarial training on over-parameterized networks often suffers…

Machine Learning · Statistics 2024-01-25 Zhongjie Shi , Fanghui Liu , Yuan Cao , Johan A. K. Suykens

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the…

Machine Learning · Computer Science 2017-02-28 Chiyuan Zhang , Samy Bengio , Moritz Hardt , Benjamin Recht , Oriol Vinyals

Deep neural networks (DNNs) are typically optimized using various forms of mini-batch gradient descent algorithm. A major motivation for mini-batch gradient descent is that with a suitably chosen batch size, available computing resources…

Machine Learning · Computer Science 2022-10-25 Oyebade K. Oyedotun , Konstantinos Papadopoulos , Djamila Aouada

An open question in the Deep Learning community is why neural networks trained with Gradient Descent generalize well on real datasets even though they are capable of fitting random data. We propose an approach to answering this question…

Machine Learning · Computer Science 2020-02-26 Satrajit Chatterjee

Deep neural networks are often trained in the over-parametrized regime (i.e. with far more parameters than training examples), and understanding why the training converges to solutions that generalize remains an open problem. Several…

Machine Learning · Statistics 2018-03-23 Hartmut Maennel , Olivier Bousquet , Sylvain Gelly

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

Machine Learning · Computer Science 2025-05-09 Haiyun He , Ziv Goldfeld

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…

Machine Learning · Computer Science 2019-06-18 Zeyuan Allen-Zhu , Yuanzhi Li , Zhao Song

Reinforcement learning research obtained significant success and attention with the utilization of deep neural networks to solve problems in high dimensional state or action spaces. While deep reinforcement learning policies are currently…

Machine Learning · Computer Science 2024-10-31 Ezgi Korkmaz

This paper follows up on a recent work of Neu et al. (2021) and presents some new information-theoretic upper bounds for the generalization error of machine learning models, such as neural networks, trained with SGD. We apply these bounds…

Machine Learning · Computer Science 2022-03-22 Ziqiao Wang , Yongyi Mao

Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…

Machine Learning · Statistics 2026-01-06 Haoran Zhan , Yingcun Xia

The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…

Machine Learning · Computer Science 2021-11-10 Kaifeng Lyu , Zhiyuan Li , Runzhe Wang , Sanjeev Arora

In the context of neural network models, overparametrization refers to the phenomena whereby these models appear to generalize well on the unseen data, even though the number of parameters significantly exceeds the sample sizes, and the…

Machine Learning · Statistics 2020-03-25 Matt Emschwiller , David Gamarnik , Eren C. Kızıldağ , Ilias Zadik

One of the principal scientific challenges in deep learning is explaining generalization, i.e., why the particular way the community now trains networks to achieve small training error also leads to small error on held-out data from the…

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and…

Machine Learning · Computer Science 2022-03-24 Kulin Shah , Amit Deshpande , Navin Goyal