Related papers: On the Generalization Behavior of Deep Residual Ne…
The utilization of residual learning has become widespread in deep and scalable neural nets. However, the fundamental principles that contribute to the success of residual learning remain elusive, thus hindering effective training of plain…
This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…
While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…
Deep learning (DL) has driven broad advances across scientific and engineering domains. Despite its success, DL models often exhibit limited interpretability and generalization, which can undermine trust, especially in safety-critical…
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evolution of the unknown system. Training a DNN with low…
We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear…
Deep neural networks (DNNs) must cater to a variety of users with different performance needs and budgets, leading to the costly practice of training, storing, and maintaining numerous user/task-specific models. There are solutions in the…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…
Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…
In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…
This paper proposes a straightforward and cost-effective approach to assess whether a deep neural network (DNN) relies on the primary concepts of training samples or simply learns discriminative, yet simple and irrelevant features that can…
We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…
Residual networks (ResNets) represent a powerful type of convolutional neural network (CNN) architecture, widely adopted and used in various tasks. In this work we propose an improved version of ResNets. Our proposed improvements address…
The robust generalization of models to rare, in-distribution (ID) samples drawn from the long tail of the training distribution and to out-of-training-distribution (OOD) samples is one of the major challenges of current deep learning…
Convolutional Neural Networks (CNNs) has revolutionized computer vision, but training very deep networks has been challenging due to the vanishing gradient problem. This paper explores Residual Networks (ResNet), introduced by He et al.…
The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory…
This paper follows up on a recent work of Neu et al. (2021) and presents some new information-theoretic upper bounds for the generalization error of machine learning models, such as neural networks, trained with SGD. We apply these bounds…
Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural…
We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations…