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The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

Modern deep learning models are over-parameterized, where different optima can result in widely varying generalization performance. The Sharpness-Aware Minimization (SAM) technique modifies the fundamental loss function that steers gradient…

Differentially Private Stochastic Gradient Descent (DPSGD) is widely used to train deep neural networks with formal privacy guarantees. However, the addition of differential privacy (DP) often degrades model accuracy by introducing both…

Deep neural networks have been shown to achieve state-of-the-art performance in several machine learning tasks. Stochastic Gradient Descent (SGD) is the preferred optimization algorithm for training these networks and asynchronous SGD…

Many modern learning tasks involve fitting nonlinear models to data which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training…

Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

In Theory IIb we characterize with a mix of theory and experiments the optimization of deep convolutional networks by Stochastic Gradient Descent. The main new result in this paper is theoretical and experimental evidence for the following…

The Lookahead optimizer enhances deep learning models by employing a dual-weight update mechanism, which has been shown to improve the performance of underlying optimizers such as SGD. However, most theoretical studies focus on its…

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

To reduce the long training time of large deep neural network (DNN) models, distributed synchronous stochastic gradient descent (S-SGD) is commonly used on a cluster of workers. However, the speedup brought by multiple workers is limited by…

Graph Neural Networks (GNNs) have achieved remarkable success across various graph-based tasks but remain highly sensitive to distribution shifts. In this work, we focus on a prevalent yet under-explored phenomenon in graph generalization,…

Distributed training algorithms of deep neural networks show impressive convergence speedup properties on very large problems. However, they inherently suffer from communication related slowdowns and communication topology becomes a crucial…

Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have…

Approximate second-order optimization methods often exhibit poorer generalization compared to first-order approaches. In this work, we look into this issue through the lens of the loss landscape and find that existing second-order methods…

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually…

Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad…

We study the population loss landscape of two-layer ReLU networks of the form $\sum_{k=1}^K \mathrm{ReLU}(w_k^\top x)$ in a realisable teacher-student setting with Gaussian covariates. We show that local minima admit an exact…

Software fault localization remains challenging due to limited feature diversity and low precision in traditional methods. This paper proposes a novel approach that integrates multi-objective optimization with deep learning models to…

Differentially Private Stochastic Gradient Descent (DP-SGD) has been widely used for solving optimization problems with privacy guarantees in machine learning and statistics. Despite this, a systematic non-asymptotic convergence analysis…