相关论文: Gaussian RBF Centered Kernel Alignment (CKA) in th…

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…

Motivated by the growing application of wireless multi-access networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum…

Feature learning, or the ability of deep neural networks to automatically learn relevant features from raw data, underlies their exceptional capability to solve complex tasks. However, feature learning seems to be realized in different ways…

Understanding whether attention mechanisms converge to the kernel regime is foundational to the validity of influence functions for transformer accountability. Exact NTK characterization of softmax attention is precluded by its exponential…

We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting…

The study of Neural Tangent Kernels (NTKs) has provided much needed insight into convergence and generalization properties of neural networks in the over-parametrized (wide) limit by approximating the network using a first-order Taylor…

Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of the heat kernel on abelian coverings of M with mixed Dirichlet and Neumann boundary conditions. As an application, we study…

Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…

The architecture of the brain is too complex to be intuitively surveyable without the use of compressed representations that project its variation into a compact, navigable space. The task is especially challenging with high-dimensional…

We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…

In this paper, we study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit. While previous work has established qualitative convergence…

This paper proposes the paradigm of large convolutional kernels in designing modern Convolutional Neural Networks (ConvNets). We establish that employing a few large kernels, instead of stacking multiple smaller ones, can be a superior…

Deep convolutional neural networks (CNNs) are commonly analyzed through geometric and linear-algebraic perspectives, yet the statistical distribution of their internal feature activations remains poorly understood. In many applications,…

Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is…

We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…

This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less…

This paper establishes error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem posed in a reproducing kernel Hilbert space (RKHS). This problem can be reformulated as a Bayesian…

We apply the discrepancy method and a chaining approach to give improved bounds on the coreset complexity of a wide class of kernel functions. Our results give randomized polynomial time algorithms to produce coresets of size…

Cross-correlating the lensing signals of galaxies and comic microwave background (CMB) fluctuations is expected to provide valuable cosmological information. In particular it may help tighten constraints on parameters describing the…

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…