The paper investigates how many data samples per domain are needed for effective learning across multiple domains. It derives criteria from learning bounds that reveal an inverse linear relationship between the number of training domains and the required samples per domain, offering theoretical guidance for dataset adequacy and construction. The study also establishes a close link between in-domain learning and out-of-domain generalization through new generalization bounds.
By Hong Zheng
arXiv:2606. 16883v1 Announce Type: cross Abstract: Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications.
By Abdul-Rauf Nuhu, Parham M. Kebria, Vahid Hemmati, Mahmoud N. Mahmoud, Edward Tunstel, Abdollah Homaifar
arXiv:2606. 06855v1 Announce Type: cross Abstract: While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses.
By Qianqian Lei, Soham Bonnerjee, Yuefeng Han, Wei Biao Wu
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying
arXiv:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
By Diego Marcondes, Cl\'audia Peixoto
arXiv:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.
By Khoat Than, Dat Phan
arXiv:2602. 20971v3 Announce Type: replace-cross Abstract: Bubeck and Selke (2021) propose the connection between the Law of Robustness and robust generalization error as an open problem.
By Mihir More, Aritra Das, Jaee Ponde, Himadri Mandal, Vishnu Varadarajan, Debayan Gupta
arXiv:2602. 23128v2 Announce Type: replace Abstract: Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes.
By Mathieu Bazinet, Valentina Zantedeschi, Pascal Germain
arXiv:2606. 01002v1 Announce Type: cross Abstract: Engression is a recently proposed and effective framework for conditional distribution learning.
By Jiaqi Huang, Gongjun Xu, Ji Zhu
arXiv:2609.07755v1 Announce Type: new
Abstract: Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training d...
By Yuqing Wang, Ioannis G. Kevrekidis, Mikhail Belkin
arXiv:2608. 13133v1 Announce Type: cross Abstract: Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data.
By Zhiyi Li, Xiaojie Mao, Yunbei Xu, Ruohan Zhan
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
By Junyu Zhou, Puyu Wang, Yunwen Lei, Marius Kloft, Yiming Ying