相关论文: Efficient kernel surrogates for neural network-bas…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Recent theoretical work has shown that massively overparameterized neural networks are equivalent to kernel regressors that use Neural Tangent Kernels(NTK). Experiments show that these kernel methods perform similarly to real neural…

Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider…

We study nonparametric regression by an over-parameterized two-layer neural network trained by gradient descent (GD) in this paper. We show that, if the neural network is trained by GD with early stopping, then the trained network renders a…

Past decades have witnessed a great interest in the distinction and connection between neural network learning and kernel learning. Recent advancements have made theoretical progress in connecting infinite-wide neural networks and Gaussian…

Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incomplete for neural…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Recently, neural networks utilizing periodic activation functions have been proven to demonstrate superior performance in vision tasks compared to traditional ReLU-activated networks. However, there is still a limited understanding of the…

Little is known about the training dynamics of equivariant neural networks, in particular how it compares to data augmented training of their non-equivariant counterparts. Recently, neural tangent kernels (NTKs) have emerged as a powerful…

This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and…

Many deep learning tasks have to deal with graphs (e.g., protein structures, social networks, source code abstract syntax trees). Due to the importance of these tasks, people turned to Graph Neural Networks (GNNs) as the de facto method for…

The Neural Tangent Kernel (NTK) offers a powerful tool to study the functional dynamics of neural networks. In the so-called lazy, or kernel regime, the NTK remains static during training and the network function is linear in the static…

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based…

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable…

Deep residual network architectures have been shown to achieve superior accuracy over classical feed-forward networks, yet their success is still not fully understood. Focusing on massively over-parameterized, fully connected residual…

The rapid development of Internet technology has given rise to a vast amount of graph-structured data. Graph Neural Networks (GNNs), as an effective method for various graph mining tasks, incurs substantial computational resource costs when…

Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…

We introduce the neural tangent kernel (NTK) regime for two-layer neural operators and analyze their generalization properties. For early-stopped gradient descent (GD), we derive fast convergence rates that are known to be minimax optimal…

In wide neural networks, the Neural Tangent Kernel (NTK) remains approximately constant during training, providing a powerful theoretical tool for studying training dynamics, generalization, and connections to kernel methods. However, this…

Neural networks are known for their ability to approximate smooth functions, yet they fail to generalize perfectly to unseen inputs when trained on discrete operations. Such operations lie at the heart of algorithmic tasks such as…