Related papers: SASSHA: Sharpness-aware Adaptive Second-order Opti…

Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of 'flat minima'…

Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…

Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years,…

In this work, we address the problem of Hessian inversion bias in distributed second-order optimization algorithms. We introduce a novel shrinkage-based estimator for the resolvent of gram matrices which is asymptotically unbiased, and…

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,…

Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood. In this work, we analyze SAM's…

This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{\xi=1}^N f(\mathbf{x};\xi) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch…

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…

While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of…

Deep Neural Networks (DNNs) generalization is known to be closely related to the flatness of minima, leading to the development of Sharpness-Aware Minimization (SAM) for seeking flatter minima and better generalization. In this paper, we…

We investigate the fundamental optimization question of minimizing a target function $f$, whose gradients are expensive to compute or have limited availability, given access to some auxiliary side function $h$ whose gradients are cheap or…

Second-order optimization methods have desirable convergence properties. However, the exact Newton method requires expensive computation for the Hessian and its inverse. In this paper, we propose SPAN, a novel approximate and fast Newton…

We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…

Energy-efficient deep neural network (DNN) accelerators are prone to non-idealities that degrade DNN performance at inference time. To mitigate such degradation, existing methods typically add perturbations to the DNN weights during…

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…

Recent experiments have shown that, often, when training a neural network with gradient descent (GD) with a step size $\eta$, the operator norm of the Hessian of the loss grows until it approximately reaches $2/\eta$, after which it…

Sharpness-Aware Minimization (SAM) is an effective method for improving generalization ability by regularizing loss sharpness. In this paper, we explore SAM in the context of adversarial robustness. We find that using only SAM can achieve…

In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…