Related papers: Implicit Bias in Noisy-SGD: With Applications to D…
Privacy preservation in machine learning, particularly through Differentially Private Stochastic Gradient Descent (DP-SGD), is critical for sensitive data analysis. However, existing statistical inference methods for SGD predominantly focus…
Recently, due to the popularity of deep neural networks and other methods whose training typically relies on the optimization of an objective function, and due to concerns for data privacy, there is a lot of interest in differentially…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
Distributed methods are essential for handling machine learning pipelines comprising large-scale models and datasets. However, their benefits often come at the cost of increased communication overhead between the central server and agents,…
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…
State-of-the-art approaches for training Differentially Private (DP) Deep Neural Networks (DNN) face difficulties to estimate tight bounds on the sensitivity of the network's layers, and instead rely on a process of per-sample gradient…
A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries. In this work, we study the implicit bias of mini-batch stochastic steepest…
Neural networks are usually trained by some form of stochastic gradient descent (SGD)). A number of strategies are in common use intended to improve SGD optimization, such as learning rate schedules, momentum, and batching. These are…
Differential Privacy (DP) provides a formal framework for training machine learning models with individual example level privacy. In the field of deep learning, Differentially Private Stochastic Gradient Descent (DP-SGD) has emerged as a…
This paper presents a holistic approach to gradient leakage resilient distributed Stochastic Gradient Descent (SGD). First, we analyze two types of strategies for privacy-enhanced federated learning: (i) gradient pruning with random…
Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate…
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,…
Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…
We investigate the ability of deep neural networks to identify the support of the target function. Our findings reveal that mini-batch SGD effectively learns the support in the first layer of the network by shrinking to zero the weights…
Stochastic Gradient Descent (SGD) has become a cornerstone of neural network optimization due to its computational efficiency and generalization capabilities. However, the gradient noise introduced by SGD is often assumed to be uncorrelated…
We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…
Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a non-convex high-dimensional…
Differentially private stochastic gradient descent (DP-SGD) is the canonical approach to private deep learning. While the current privacy analysis of DP-SGD is known to be tight in some settings, several empirical results suggest that…
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…
When we enforce differential privacy in machine learning, the utility-privacy trade-off is different w.r.t. each group. Gradient clipping and random noise addition disproportionately affect underrepresented and complex classes and…