Related papers: Spectrum Dependent Learning Curves in Kernel Regre…
We construct and analyze a neural network two-sample test to determine whether two datasets came from the same distribution (null hypothesis) or not (alternative hypothesis). We perform time-analysis on a neural tangent kernel (NTK)…
Previous influential work showed that infinite width limits of neural networks in the lazy training regime are described by kernel machines. Here, we show that neural networks trained in the rich, feature learning infinite-width regime in…
Unlabeled data is a key component of modern machine learning. In general, the role of unlabeled data is to impose a form of smoothness, usually from the similarity information encoded in a base kernel, such as the $\epsilon$-neighbor kernel…
We propose a greedy strategy to spectrally train a deep network for multi-class classification. Each layer is defined as a composition of linear weights with the feature map of a Gaussian kernel acting as the activation function. At each…
As modern machine learning models continue to advance the computational frontier, it has become increasingly important to develop precise estimates for expected performance improvements under different model and data scaling regimes.…
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…
The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works…
As deep neural networks (DNNs) achieve tremendous success across many application domains, researchers tried to explore in many aspects on why they generalize well. In this paper, we provide a novel perspective on these issues using the…
Hybrid optical neural networks (HONNs) offload some electronic computation to optical preprocessors to achieve low-power and fast training and inference phases in machine learning tasks. Our contribution to the development of HONNs is a…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…
Recent research shows that for training with $\ell_2$ loss, convolutional neural networks (CNNs) whose width (number of channels in convolutional layers) goes to infinity correspond to regression with respect to the CNN Gaussian Process…
We develop a theory of transfer learning in infinitely wide neural networks under gradient flow that quantifies when pretraining on a source task improves generalization on a target task. We analyze both (i) fine-tuning, when the downstream…
The underlying mechanism of neural networks in capturing precise knowledge has been the subject of consistent research efforts. In this work, we propose a theoretical approach based on Neural Tangent Kernels (NTKs) to investigate such…
We perform a careful, thorough, and large scale empirical study of the correspondence between wide neural networks and kernel methods. By doing so, we resolve a variety of open questions related to the study of infinitely wide neural…
Recent work has shown that training wide neural networks with gradient descent is formally equivalent to computing the mean of the posterior distribution in a Gaussian Process (GP) with the Neural Tangent Kernel (NTK) as the prior…
We study the optimization of wide neural networks (NNs) via gradient flow (GF) in setups that allow feature learning while admitting non-asymptotic global convergence guarantees. First, for wide shallow NNs under the mean-field scaling and…
As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK…
The goal of this work is to shed light on the remarkable phenomenon of transition to linearity of certain neural networks as their width approaches infinity. We show that the transition to linearity of the model and, equivalently, constancy…
State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain…