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We revisit the well-studied problem of differentially private empirical risk minimization (ERM). We show that for unconstrained convex generalized linear models (GLMs), one can obtain an excess empirical risk of $\tilde…

Cryptography and Security · Computer Science 2021-03-04 Shuang Song , Thomas Steinke , Om Thakkar , Abhradeep Thakurta

We analyze multi-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations. We rigorously establish the limiting behavior of the…

Probability · Mathematics 2021-04-06 Justin Sirignano , Konstantinos Spiliopoulos

Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In…

Machine Learning · Computer Science 2022-01-14 Tolga Ergen , Mert Pilanci

Differentially private (DP) mechanisms face the challenge of providing accurate results while protecting their inputs: the privacy-utility trade-off. A simple but powerful technique for DP adds noise to sensitivity-bounded query outputs to…

Cryptography and Security · Computer Science 2021-07-28 David M. Sommer , Lukas Abfalterer , Sheila Zingg , Esfandiar Mohammadi

Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via SGD for…

Machine Learning · Computer Science 2022-05-02 Alexander Shevchenko , Vyacheslav Kungurtsev , Marco Mondelli

Differential privacy (DP) ensures that training a machine learning model does not leak private data. In practice, we may have access to auxiliary public data that is free of privacy concerns. In this work, we assume access to a given amount…

Machine Learning · Computer Science 2024-09-11 Andrew Lowy , Zeman Li , Tianjian Huang , Meisam Razaviyayn

We study private prediction where differential privacy is achieved by adding noise to the outputs of a non-private model. Existing methods rely on noise proportional to the global sensitivity of the model, often resulting in sub-optimal…

In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…

Machine Learning · Computer Science 2025-10-03 Jinshu Huang , Haibin Su , Xue-Cheng Tai , Chunlin Wu

Differentially Private Stochastic Gradient Descent (DP-SGD) is a standard method for enforcing privacy in deep learning, typically using the Gaussian mechanism to perturb gradient updates. However, conventional mechanisms such as Gaussian…

Cryptography and Security · Computer Science 2025-09-09 Qin Yang , Nicholas Stout , Meisam Mohammady , Han Wang , Ayesha Samreen , Christopher J Quinn , Yan Yan , Ashish Kundu , Yuan Hong

Kolmogorov--Arnold Networks (KANs) have recently emerged as a structured alternative to standard MLPs, yet a principled theory for their training dynamics, generalization, and privacy properties remains limited. In this paper, we analyze…

Machine Learning · Computer Science 2026-05-14 Puyu Wang , Junyu Zhou , Philipp Liznerski , Marius Kloft

Training even moderately-sized generative models with differentially-private stochastic gradient descent (DP-SGD) is difficult: the required level of noise for reasonable levels of privacy is simply too large. We advocate instead building…

Machine Learning · Statistics 2023-07-21 Fredrik Harder , Milad Jalali Asadabadi , Danica J. Sutherland , Mijung Park

Broad adoption of machine learning techniques has increased privacy concerns for models trained on sensitive data such as medical records. Existing techniques for training differentially private (DP) models give rigorous privacy guarantees,…

Machine Learning · Statistics 2019-10-04 Zhengli Zhao , Nicolas Papernot , Sameer Singh , Neoklis Polyzotis , Augustus Odena

Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the…

Data Structures and Algorithms · Computer Science 2024-06-05 Dung Nguyen , Anil Vullikanti

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

Machine Learning · Computer Science 2019-12-06 Gauthier Gidel , Francis Bach , Simon Lacoste-Julien

Deep learning techniques based on neural networks have shown significant success in a wide range of AI tasks. Large-scale training datasets are one of the critical factors for their success. However, when the training datasets are…

Cryptography and Security · Computer Science 2019-12-23 Lei Yu , Ling Liu , Calton Pu , Mehmet Emre Gursoy , Stacey Truex

Pairwise learning focuses on learning tasks with pairwise loss functions, depends on pairs of training instances, and naturally fits for modeling relationships between pairs of samples. In this paper, we focus on the privacy of pairwise…

Machine Learning · Computer Science 2021-06-02 Yilin Kang , Yong Liu , Jian Li , Weiping Wang

Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the…

Machine Learning · Computer Science 2019-10-16 Frederik Harder , Jonas Köhler , Max Welling , Mijung Park

Federated Learning (FL) allows for the training of Machine Learning models in a collaborative manner without the need to share sensitive data. However, it remains vulnerable to Gradient Leakage Attacks (GLAs), which can reveal private…

Machine Learning · Computer Science 2025-10-29 Miguel Fernandez-de-Retana , Unai Zulaika , Rubén Sánchez-Corcuera , Aitor Almeida

Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima. The implicit bias refers to the limiting global minimum that is attained by a common optimization…

Machine Learning · Statistics 2026-03-06 Kuo-Wei Lai , Guanghui Wang , Molei Tao , Vidya Muthukumar

Decentralized min-max optimization allows multi-agent systems to collaboratively solve global min-max optimization problems by facilitating the exchange of model updates among neighboring agents, eliminating the need for a central server.…

Machine Learning · Computer Science 2025-08-12 Yueyang Quan , Chang Wang , Shengjie Zhai , Minghong Fang , Zhuqing Liu