相关论文: Approximate Gaussianity Beyond Initialisation in N…

Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…

This paper presents a pioneering exploration of the mechanisms underlying large foundation models' (LFMs) weights, aiming to simplify AI research. Through extensive observation and analysis on prevailing LFMs, we find that regardless of…

With the proliferation of deep convolutional neural network (CNN) algorithms for mobile processing, limited precision quantization has become an essential tool for CNN efficiency. Consequently, various works have sought to design fixed…

Based on the concepts of Wasserstein barycenter (WB) and Gromov-Wasserstein barycenter (GWB), we propose a unified mathematical framework for neural network (NN) model fusion and utilize it to reveal new insights about the linear mode…

Given a cloud of $n$ data points in $\mathbb{R}^d$, consider all projections onto $m$-dimensional subspaces of $\mathbb{R}^d$ and, for each such projection, the empirical distribution of the projected points. What does this collection of…

We propose a new quantum neural network for image classification, which is able to classify the parity of the MNIST dataset with full resolution with a test accuracy of up to 97.5% without any classical pre-processing or post-processing.…

Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this…

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis…

Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian…

Inband full-duplex communication requires accurate modeling and cancellation of self-interference, specifically in the digital domain. Neural networks are presently candidate models for capturing nonlinearity of the self-interference path.…

We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…

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…

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances,…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Personalized recommender systems are playing an increasingly important role as more content and services become available and users struggle to identify what might interest them. Although matrix factorization and deep learning based methods…

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…