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Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…
We consider a decentralized learning problem, where a set of computing nodes aim at solving a non-convex optimization problem collaboratively. It is well-known that decentralized optimization schemes face two major system bottlenecks:…
Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…
In this paper, we present CT-AGD (Curvature-Tuned Accelerated Gradient Descent), an optimization method for non-convex optimization problems in deep learning training tasks. CT-AGD is a general boosting procedure that accelerates…
In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
Deep neural networks are usually trained with stochastic gradient descent (SGD), which minimizes objective function using very rough approximations of gradient, only averaging to the real gradient. Standard approaches like momentum or ADAM…
We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying assumptions, while…
We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on $\mathcal{M}_k^{m\times n}$ -- the set of $m\times n$ real matrices with a fixed rank $k$. Our analysis is…
Deep neural networks (DNNs) have been proven to have many redundancies. Hence, many efforts have been made to compress DNNs. However, the existing model compression methods treat all the input samples equally while ignoring the fact that…
One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…
Gradient descent (GD) and stochastic gradient descent (SGD) are the workhorses of large-scale machine learning. While classical theory focused on analyzing the performance of these methods in convex optimization problems, the most notable…
Robustness evaluation against adversarial examples has become increasingly important to unveil the trustworthiness of the prevailing deep models in natural language processing (NLP). However, in contrast to the computer vision domain where…
We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the…
Fixed-point optimization of deep neural networks plays an important role in hardware based design and low-power implementations. Many deep neural networks show fairly good performance even with 2- or 3-bit precision when quantized weights…
Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…
In deep learning, optimization plays a vital role. By focusing on image classification, this work investigates the pros and cons of the widely used optimizers, and proposes a new optimizer: Perturbated Unit Gradient Descent (PUGD) algorithm…
This paper investigates a novel finite-time gradient descent-based adaptive neural network finite-time control strategy for the attitude tracking of a 3-DOF lab helicopter platform subject to composite disturbances. First, the radial basis…
Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…
The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…