相关论文: Predicting the outputs of finite deep neural netwo…

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…

In suitably initialized wide networks, small learning rates transform deep neural networks (DNNs) into neural tangent kernel (NTK) machines, whose training dynamics is well-approximated by a linear weight expansion of the network at…

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…

We define deep kernel processes in which positive definite Gram matrices are progressively transformed by nonlinear kernel functions and by sampling from (inverse) Wishart distributions. Remarkably, we find that deep Gaussian processes…

Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications.…

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…

The output prediction of quantum circuits is a formidably challenging task imperative in developing quantum devices. Motivated by the natural graph representation of quantum circuits, this paper proposes a Graph Neural Networks (GNNs)-based…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…

In this paper, we study the data-dependent convergence and generalization behavior of gradient methods for neural networks with smooth activation. Our first result is a novel bound on the excess risk of deep networks trained by the logistic…

Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad…

Recently, quantum neural networks or quantum-classical neural networks (qcNN) have been actively studied, as a possible alternative to the conventional classical neural network (cNN), but their practical and theoretically-guaranteed…

Deep kernel learning (DKL) leverages the connection between Gaussian process (GP) and neural networks (NN) to build an end-to-end, hybrid model. It combines the capability of NN to learn rich representations under massive data and the…

A rising trend in theoretical deep learning is to understand why deep learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method that is equivalent to using gradient descent to train a multi-layer infinitely-wide neural…

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

This paper investigates the approximation power of three types of random neural networks: (a) infinite width networks, with weights following an arbitrary distribution; (b) finite width networks obtained by subsampling the preceding…

Deep Gaussian processes (DGPs), a hierarchical composition of GP models, have successfully boosted the expressive power of their single-layer counterpart. However, it is impossible to perform exact inference in DGPs, which has motivated the…

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success in adopting a deep network for feature extraction followed by a GP…

Following early work on Hessian-free methods for deep learning, we study a stochastic generalized Gauss-Newton method (SGN) for training DNNs. SGN is a second-order optimization method, with efficient iterations, that we demonstrate to…

Deep neural networks (DNNs) have excellent representative power and are state of the art classifiers on many tasks. However, they often do not capture their own uncertainties well making them less robust in the real world as they…