Related papers: Convergence analysis of the Generalized Empirical …
We provide a unified framework that applies to a general family of convex losses across binary and multiclass settings in the overparameterized regime to approximately characterize the implicit bias of gradient descent in closed form.…
In this paper, we investigate the approximation properties of two types of multiscale finite element methods with oversampling as proposed in [Hou \& Wu, {\textit{J. Comput. Phys.}}, 1997] and [Efendiev, Hou \& Wu, \textit{SIAM J. Numer.…
We propose a method to interpolate Signed Distance Function (SDF) data from a discrete set of samples. Unlike prior work, our approach ensures that the new SDF data values are fully consistent with the input and each other, such that the…
We theoretically demonstrate that the generalization error of interpolators for machine learning models under teacher-student settings becomes 0 once the number of training samples exceeds a certain threshold. Understanding the high…
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…
Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast…
We consider the problem of recovering (that is, interpolating) and identity testing of a "hidden" monic polynomial $f$, given an oracle access to $f(x)^e$ for $x\in{\mathbb F_q}$ (extension fields access is not permitted). The naive…
Generative models based on normalizing flows are very successful in modeling complex data distributions using simpler ones. However, straightforward linear interpolations show unexpected side effects, as interpolation paths lie outside the…
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the…
Radio interferometry invariably suffers from an incomplete coverage of the spatial Fourier space, which leads to imaging artifacts. The current state-of-the-art technique is to create an image by Fourier-transforming the incomplete…
This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound…
We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…
An important linear algebra routine, GEneral Matrix Multiplication (GEMM), is a fundamental operator in deep learning. Compilers need to translate these routines into low-level code optimized for specific hardware. Compiler-level…
For an interpolation pair $(E_0,E_1)$ of Banach spaces with $E_1 \hookrightarrow E_0$ we use vectors $b_1,b_2,\ldots \in E_1$ that satisfy an extremal property with respect to the $J$- and $K$-functional to construct sub-spaces that are…
Greedy methods have recently been successfully applied to generalized kernel interpolation, or the recovery of a function from data stemming from the evaluation of linear functionals, including the approximation of solutions of linear PDEs…
We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…
Generative adversarial networks (GANs) are unsupervised learning methods for training a generator distribution to produce samples that approximate those drawn from a target distribution. Many such methods can be formulated as minimization…
Motivated by surprisingly good generalization properties of learned deep neural networks in overparameterized scenarios and by the related double descent phenomenon, this paper analyzes the relation between smoothness and low generalization…
Interpolations in the latent space of deep generative models is one of the standard tools to synthesize semantically meaningful mixtures of generated samples. As the generator function is non-linear, commonly used linear interpolations in…
General matrix/matrix multiplication (GEMM) is crucial for scientific computing and machine learning. However, the increased scale of the computing platforms raises concerns about hardware and software reliability. In this poster, we…