Related papers: Training Without Orthogonalization, Inference With…

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

Low-precision training has become crucial for reducing the computational and memory costs of large-scale deep learning. However, quantizing gradients introduces magnitude shrinkage, which can change how stochastic gradient descent (SGD)…

Safety post-training can improve the harmfulness and policy compliance of Large Language Models (LLMs), but it may also reduce general utility, a phenomenon often described as the \emph{alignment tax}. We study this trade-off through the…

Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…

Determining the 3D orientations of an object in an image, known as single-image pose estimation, is a crucial task in 3D vision applications. Existing methods typically learn 3D rotations parametrized in the spatial domain using Euler…

In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss…

Differentially Private Stochastic Gradient Descent (DP-SGD) limits the amount of private information deep learning models can memorize during training. This is achieved by clipping and adding noise to the model's gradients, and thus…

Deep Neural Networks are powerful tools for understanding complex patterns and making decisions. However, their black-box nature impedes a complete understanding of their inner workings. Saliency-Guided Training (SGT) methods try to…

Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both…

The selection of initial parameter values for gradient-based optimization of deep neural networks is one of the most impactful hyperparameter choices in deep learning systems, affecting both convergence times and model performance. Yet…

Convex optimization over the spectrahedron, i.e., the set of all real $n\times n$ positive semidefinite matrices with unit trace, has important applications in machine learning, signal processing and statistics, mainly as a convex…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

Stochastic Gradient Descent (SGD) based training of neural networks with a large learning rate or a small batch-size typically ends in well-generalizing, flat regions of the weight space, as indicated by small eigenvalues of the Hessian of…

Recent advances in 3D perception have shown impressive progress in understanding geometric structures of 3Dshapes and even scenes. Inspired by these advances in geometric understanding, we aim to imbue image-based perception with…

In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors…

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

Recent works have demonstrated that the sample complexity of gradient-based learning of single index models, i.e. functions that depend on a 1-dimensional projection of the input data, is governed by their information exponent. However,…

Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected…

Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…