相关论文: Fixing the NTK: From Neural Network Linearizations…

We develop fast algorithms and robust software for convex optimization of two-layer neural networks with ReLU activation functions. Our work leverages a convex reformulation of the standard weight-decay penalized training problem as a set…

We study regularized deep neural networks (DNNs) and introduce a convex analytic framework to characterize the structure of the hidden layers. We show that a set of optimal hidden layer weights for a norm regularized DNN training problem…

We analyze the convergence of the averaged stochastic gradient descent for overparameterized two-layer neural networks for regression problems. It was recently found that a neural tangent kernel (NTK) plays an important role in showing the…

We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We first prove that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set, where simple…

We perform a study on the generalization ability of the wide two-layer ReLU neural network on $\mathbb{R}$. We first establish some spectral properties of the neural tangent kernel (NTK): $a)$ $K_{d}$, the NTK defined on $\mathbb{R}^{d}$,…

We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage…

We study training one-hidden-layer ReLU networks in the neural tangent kernel (NTK) regime, where the networks' biases are initialized to some constant rather than zero. We prove that under such initialization, the neural network will have…

We analyze the generalization properties of two-layer neural networks in the neural tangent kernel (NTK) regime, trained with gradient descent (GD). For early stopped GD we derive fast rates of convergence that are known to be minimax…

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…

We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation is exponential in the ratio of network depth to width.…

Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In…

While deep learning has achieved remarkable success across a wide range of applications, its theoretical understanding of representation learning remains limited. Deep neural kernels provide a principled framework to interpret…

The NTK is a widely used tool in the theoretical analysis of deep learning, allowing us to look at supervised deep neural networks through the lenses of kernel regression. Recently, several works have investigated kernel models for…

Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

A major factor in the success of deep neural networks is the use of sophisticated architectures rather than the classical multilayer perceptron (MLP). Residual networks (ResNets) stand out among these powerful modern architectures. Previous…

The Neural Tangent Kernel (NTK) has recently attracted intense study, as it describes the evolution of an over-parameterized Neural Network (NN) trained by gradient descent. However, it is now well-known that gradient descent is not always…

Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks. In the infinite-width limit, NTKs can easily be computed for most common architectures, yielding full analytic control over the training…