Related papers: Infinite attention: NNGP and NTK for deep attentio…

It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian…

A recent line of works studied wide deep neural networks (DNNs) by approximating them as Gaussian Processes (GPs). A DNN trained with gradient flow was shown to map to a GP governed by the Neural Tangent Kernel (NTK), whereas earlier works…

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…

We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown…

Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that…

Performing gradient descent in a wide neural network is equivalent to computing the posterior mean of a Gaussian Process with the Neural Tangent Kernel (NTK-GP), for a specific prior mean and with zero observation noise. However, existing…

Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting.…

This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…

Graph Convolutional Networks (GCNs) have emerged as powerful tools for learning on network structured data. Although empirically successful, GCNs exhibit certain behaviour that has no rigorous explanation -- for instance, the performance of…

Recent developments in applications of artificial neural networks with over $n=10^{14}$ parameters make it extremely important to study the large $n$ behaviour of such networks. Most works studying wide neural networks have focused on the…

Study of neural networks with infinite width is important for better understanding of the neural network in practical application. In this work, we derive the equivalence of the deep, infinite-width maxout network and the Gaussian process…

Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to…

A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…

Artificial neural networks have revolutionized machine learning in recent years, but a complete theoretical framework for their learning process is still lacking. Substantial advances were achieved for wide networks, within two disparate…

There is a previously identified equivalence between wide fully connected neural networks (FCNs) and Gaussian processes (GPs). This equivalence enables, for instance, test set predictions that would have resulted from a fully Bayesian,…

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…

Combining Gaussian processes with the expressive power of deep neural networks is commonly done nowadays through deep kernel learning (DKL). Unfortunately, due to the kernel optimization process, this often results in losing their Bayesian…

Recent work has established the equivalence between deep neural networks and Gaussian processes (GPs), resulting in so-called neural network Gaussian processes (NNGPs). The behaviour of these models depends on the initialisation of the…

Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called…

How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its width --- namely, number of channels in convolutional layers, and number of nodes in fully-connected internal…