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We conjecture that the inherent difference in generalisation between adaptive and non-adaptive gradient methods in deep learning stems from the increased estimation noise in the flattest directions of the true loss surface. We demonstrate…

Machine Learning · Statistics 2022-03-17 Diego Granziol , Nicholas Baskerville

Differentially private (DP) release of multidimensional statistics typically considers an aggregate sensitivity, e.g. the vector norm of a high-dimensional vector. However, different dimensions of that vector might have widely different…

Machine Learning · Statistics 2022-10-31 Joonas Jälkö , Lukas Prediger , Antti Honkela , Samuel Kaski

Training large language models (LLMs) relies on adaptive optimizers such as Adam, which introduce extra operations and require significantly more memory to maintain first- and second-order moments than SGD. While recent works such as…

Machine Learning · Computer Science 2026-05-22 Athanasios Glentis , Jiaxiang Li , Andi Han , Mingyi Hong

Differential privacy is a widely accepted measure of privacy in the context of deep learning algorithms, and achieving it relies on a noisy training approach known as differentially private stochastic gradient descent (DP-SGD). DP-SGD…

Machine Learning · Computer Science 2023-07-26 Ce Feng , Nuo Xu , Wujie Wen , Parv Venkitasubramaniam , Caiwen Ding

Data privacy is an important concern in machine learning, and is fundamentally at odds with the task of training useful learning models, which typically require the acquisition of large amounts of private user data. One possible way of…

Machine Learning · Computer Science 2019-02-14 Mehrdad Showkatbakhsh , Can Karakus , Suhas Diggavi

The training of neural networks with Differentially Private Stochastic Gradient Descent offers formal Differential Privacy guarantees but introduces accuracy trade-offs. In this work, we propose to alleviate these trade-offs in residual…

Machine Learning · Computer Science 2022-05-09 Helena Klause , Alexander Ziller , Daniel Rueckert , Kerstin Hammernik , Georgios Kaissis

While modern machine learning models rely on increasingly large training datasets, data is often limited in privacy-sensitive domains. Generative models trained with differential privacy (DP) on sensitive data can sidestep this challenge,…

Machine Learning · Statistics 2024-01-02 Tim Dockhorn , Tianshi Cao , Arash Vahdat , Karsten Kreis

While preserving the privacy of federated learning (FL), differential privacy (DP) inevitably degrades the utility (i.e., accuracy) of FL due to model perturbations caused by DP noise added to model updates. Existing studies have considered…

Machine Learning · Computer Science 2023-03-09 Xin Yuan , Wei Ni , Ming Ding , Kang Wei , Jun Li , H. Vincent Poor

Differentially private SGD (DP-SGD) is one of the most popular methods for solving differentially private empirical risk minimization (ERM). Due to its noisy perturbation on each gradient update, the error rate of DP-SGD scales with the…

Machine Learning · Computer Science 2021-04-27 Yingxue Zhou , Zhiwei Steven Wu , Arindam Banerjee

Differentially private stochastic gradient descent (DPSGD) is a variation of stochastic gradient descent based on the Differential Privacy (DP) paradigm, which can mitigate privacy threats that arise from the presence of sensitive…

Machine Learning · Computer Science 2021-12-09 Ali Davody , David Ifeoluwa Adelani , Thomas Kleinbauer , Dietrich Klakow

We study a pitfall in the typical workflow for differentially private machine learning. The use of differentially private learning algorithms in a "drop-in" fashion -- without accounting for the impact of differential privacy (DP) noise…

Cryptography and Security · Computer Science 2022-05-16 Wenxuan Bao , Luke A. Bauer , Vincent Bindschaedler

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

Machine Learning · Computer Science 2024-10-08 Gus Kristiansen , Mark Sandler , Andrey Zhmoginov , Nolan Miller , Anirudh Goyal , Jihwan Lee , Max Vladymyrov

In this paper, we try to uncover the second-order essence of several first-order optimization methods. For Nesterov Accelerated Gradient, we rigorously prove that the algorithm makes use of the difference between past and current gradients,…

Machine Learning · Computer Science 2019-12-23 Yuzheng Hu , Licong Lin , Shange Tang

Despite advances in the use of large language models (LLMs) in downstream tasks, their ability to memorize information has raised privacy concerns. Therefore, protecting personally identifiable information (PII) during LLM training remains…

Machine Learning · Computer Science 2025-12-02 Stella Etuk , Ashraf Matrawy

Differentially private federated learning (DP-FL) often suffers from slow convergence under tight privacy budgets because the noise required for privacy preservation degrades gradient quality. Although second-order optimization can…

Machine Learning · Computer Science 2026-03-25 Sidhant Nair , Tanmay Sen , Mrinmay Sen , Sayantan Banerjee

Privacy-preserving distributed processing has received considerable attention recently. The main purpose of these algorithms is to solve certain signal processing tasks over a network in a decentralised fashion without revealing…

Signal Processing · Electrical Eng. & Systems 2023-12-14 Sebastian O. Jordan , Qiongxiu Li , Richard Heusdens

The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion…

Statistics Theory · Mathematics 2019-06-10 Mark Bun , Thomas Steinke

The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it…

Machine Learning · Computer Science 2025-03-04 Bingrui Li , Wei Huang , Andi Han , Zhanpeng Zhou , Taiji Suzuki , Jun Zhu , Jianfei Chen

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

Machine Learning · Computer Science 2022-10-14 Philipp Holl , Vladlen Koltun , Nils Thuerey

We consider the problem of minimizing a non-convex objective while preserving the privacy of the examples in the training data. Building upon the previous variance-reduced algorithm SpiderBoost, we introduce a new framework that utilizes…

Machine Learning · Computer Science 2023-02-21 Arun Ganesh , Daogao Liu , Sewoong Oh , Abhradeep Thakurta