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Stochastic Gradient Descent (SGD) methods are prominent for training machine learning and deep learning models. The performance of these techniques depends on their hyperparameter tuning over time and varies for different models and…
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…
The stochastic gradient descent (SGD) method is most widely used for deep neural network (DNN) training. However, the method does not always converge to a flat minimum of the loss surface that can demonstrate high generalization capability.…
Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…
We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
Data loss in Structural Health Monitoring (SHM) networks has recently become one of the main challenges for engineers. Therefore, a data recovery method for SHM, generally an expensive procedure, is essential. Lately, some techniques…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
The support vector machines (SVM) is a powerful classifier used for binary classification to improve the prediction accuracy. However, the non-differentiability of the SVM hinge loss function can lead to computational difficulties in high…
Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…
We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then…
Learning accurate low-dimensional embeddings for a network is a crucial task as it facilitates many downstream network analytics tasks. For large networks, the trained embeddings often require a significant amount of space to store, making…
While classical forms of stochastic gradient descent algorithm treat the different coordinates in the same way, a framework allowing for adaptive (non uniform) coordinate sampling is developed to leverage structure in data. In a non-convex…
We develop a quantum-classical hybrid algorithm for function optimization that is particularly useful in the training of neural networks since it makes use of particular aspects of high-dimensional energy landscapes. Due to a recent…
Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…
State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…
The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and…
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…
We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…