Related papers: Closed-Form Last Layer Optimization
Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…
We analyze the training dynamics for deep linear networks using a new metric - layer imbalance - which defines the flatness of a solution. We demonstrate that different regularization methods, such as weight decay or noise data…
Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification,…
This work focuses on the behavior of stochastic gradient descent (SGD) in solving least-squares regression with physics-informed neural networks (PINNs). Past work on this topic has been based on the over-parameterization regime, whose…
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and…
Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate…
Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We…
Gradient descent algorithm is the most utilized method when optimizing machine learning issues. However, there exists many local minimums and saddle points in the loss function, especially for high dimensional non-convex optimization…
We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…
Kolmogorov--Arnold Networks (KANs), a recently proposed neural network architecture, have gained significant attention in the deep learning community, due to their potential as a viable alternative to multi-layer perceptrons (MLPs) and…
Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…
In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient…
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…
Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to…