Related papers: Neurally-plausible radial basis kernels using dist…

We discuss computational procedures based on descriptor state-space realizations to compute proper range space bases of rational matrices. The main computation is the orthogonal reduction of the system matrix pencil to a special…

We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…

This paper shows how numerical methods on a regular grid in a box can be used to generate numerical schemes for problems in general smooth domains contained in the box with no need for a domain specific discretization. The focus is mainly…

We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…

This note proposes rapidly convergent computational formulae for evaluating scattering kernels from radiative transfer theory. The approach used here does not rely on Legendre expansions, but rather uses exponentially convergent numerical…

Recently, non-stationary spectral kernels have drawn much attention, owing to its powerful feature representation ability in revealing long-range correlations and input-dependent characteristics. However, non-stationary spectral kernels are…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…

To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…

We prove that a particular deep network architecture is more efficient at approximating radially symmetric functions than the best known 2 or 3 layer networks. We use this architecture to approximate Gaussian kernel SVMs, and subsequently…

Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data…

This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very…

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…

Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…

Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…

Neural networks have enabled applications in artificial intelligence through machine learning, and neuromorphic computing. Software implementations of neural networks on conventional computers that have separate memory and processor (and…

In this chapter we review the main literature related to the recent advancement of deep neural-kernel architecture, an approach that seek the synergy between two powerful class of models, i.e. kernel-based models and artificial neural…

In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The…

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source…

Neural fields, also known as implicit neural representations (INRs), offer a powerful framework for modeling continuous geometry, but their effectiveness in high-dimensional scientific settings is limited by slow convergence and scaling…