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While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural…

Batch normalization (BN) is a technique to normalize activations in intermediate layers of deep neural networks. Its tendency to improve accuracy and speed up training have established BN as a favorite technique in deep learning. Yet,…

Modern deep neural networks (DNNs) have achieved state-of-the-art performances but are typically over-parameterized. The over-parameterization may result in undesirably large generalization error in the absence of other customized training…

We consider Sharpness-Aware Minimization (SAM), a gradient-based optimization method for deep networks that has exhibited performance improvements on image and language prediction problems. We show that when SAM is applied with a convex…

The intuition that local flatness of the loss landscape is correlated with better generalization for deep neural networks (DNNs) has been explored for decades, spawning many different flatness measures. Recently, this link with…

Deep learning has transformed computer vision, natural language processing, and speech recognition\cite{badrinarayanan2017segnet, dong2016image, ren2017faster, ji20133d}. However, two critical questions remain obscure: (1) why do deep…

This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the…

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic…

We prove that Riemannian contraction in a supervised learning setting implies generalization. Specifically, we show that if an optimizer is contracting in some Riemannian metric with rate $\lambda > 0$, it is uniformly algorithmically…

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well…

Understanding the dynamics of optimization in deep learning is increasingly important as models scale. While stochastic gradient descent (SGD) and its variants reliably find solutions that generalize well, the mechanisms driving this…

This paper studies generalization capabilities of neural networks (NNs) using new and improved PyTorch library Loss Landscape Analysis (LLA). LLA facilitates visualization and analysis of loss landscapes along with the properties of NN…

Sharpness-Aware Minimization (SAM) has been demonstrated to improve the generalization performance of overparameterized models by seeking flat minima on the loss landscape through optimizing model parameters that incur the largest loss…

Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines…

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but…

Recent studies have demonstrated that noise in stochastic gradient descent (SGD) is closely related to generalization: A larger SGD noise, if not too large, results in better generalization. Since the covariance of the SGD noise is…

Sharpness-aware minimization (SAM) improves generalization of various deep learning tasks. Motivated by popular architectures such as LoRA, we explore the implicit regularization of SAM for scale-invariant problems involving two groups of…

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…

The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed…