Related papers: Flexible Infinite-Width Graph Convolutional Neural…

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

In practice, multi-task learning (through learning features shared among tasks) is an essential property of deep neural networks (NNs). While infinite-width limits of NNs can provide good intuition for their generalization behavior, the…

Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

We study wide Bayesian neural networks focusing on the rare but statistically dominant fluctuations that govern posterior concentration, beyond Gaussian-process limits. Large-deviation theory provides explicit variational objectives-rate…

We present the Topology Transformation Equivariant Representation learning, a general paradigm of self-supervised learning for node representations of graph data to enable the wide applicability of Graph Convolutional Neural Networks…

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex nonlinear…

Kernels representing limiting cases of neural network architectures have recently gained popularity. However, the application and performance of these new kernels compared to existing options, such as the Matern kernel, is not well studied.…

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…

This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels…

Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…

Graph Convolutional Networks (GCNs) are powerful models for node representation learning tasks. However, the node representation in existing GCN models is usually generated by performing recursive neighborhood aggregation across multiple…

This paper presents a study of the effectiveness of Neural Network (NN) techniques for deconvolution inverse problems relevant for applications in Quantum Field Theory, but also in more general contexts. We consider NN's asymptotic limits,…

Deep neural networks (DNNs) in the infinite width/channel limit have received much attention recently, as they provide a clear analytical window to deep learning via mappings to Gaussian Processes (GPs). Despite its theoretical appeal, this…

Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or…

Graph Neural Networks (GNNs) show strong expressive power on graph data mining, by aggregating information from neighbors and using the integrated representation in the downstream tasks. The same aggregation methods and parameters for each…

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…