We address efficient calculation of influence functions for tracking predictions back to the training data. propose and analyze a new approach speeding up inverse Hessian based on Arnoldi iteration. With this improvement, we achieve, best our knowledge, first successful implementation that scales full-size (language vision) Transformer models with several hundreds millions parameters. evaluate ...

Interpolating implicit surfaces using radial basis functions can directly specify surface points and surface normals with closed form solutions, so they are elegantly used in surface reconstruction and shape morphing. This paper presents subdivision interpolating implicit surfaces, a new progressive subdivision tessellation scheme for interpolating implicit surfaces controlled by a triangular m...

Universal constructions of univariate and bivariate Gaussian distributions, as transformations of diffuse probability distributions via, respectively, planeand space-filling fractal interpolating functions and the central limit theorems that they imply, are reviewed. It is illustrated that the construction of the bivariate Gaussian distribution yields exotic kaleidoscopic decompositions of the ...

Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator on G. The existence and uniqueness of interpolating variational spline on a graph is shown. As an application of variational splines the paper presents a reconstruction algorithm of PaleyWiener functions o...

The paper is concerned with the Chebyshev approximation of decay-type functions /(x) by interpolating rationals. The interpolating points are chosen to be the zeros of j(x). Existence, uniqueness and characterization of best approximations are first shown. An exchange algorithm is then described for computing the best approximation.

Many hydrological variables usually show the presence of spatial drifts. Most often they are accounted for by either universal or residual kriging and usually assuming low order polynomials. The Universal Kriging matrix ( M ), which includes in it the values of the polynomials at data locations (matrix F ), in some cases may have a too large condition number and can even be nearly singular due ...

this paper  considersthe problem of  aliasing in information processing. the cubic spline method of interpolating the uniformly sampled signals and its effects on the autocorrelation estimation as well as the resulting spectral density function are studied by simulating random signals with known autocorrelation functions. hence, by comparison of aliased and alias-free cases, indications are ded...

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...

in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...