相关论文: Hardware-Friendly Input Expansion for Accelerating…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
This EM review article focuses on parameter expansion, a simple technique introduced in the PX-EM algorithm to make EM converge faster while maintaining its simplicity and stability. The primary objective concerns the connection between…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
In this paper, we consider the fundamental problem of approximation of functions on a low-dimensional manifold embedded in a high-dimensional space, with noise affecting both in the data and values of the functions. Due to the curse of…
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…
With ever-increasing application of machine learning models in various domains such as image classification, speech recognition and synthesis, and health care, designing efficient hardware for these models has gained a lot of popularity.…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
The objective of this paper is to design an embedding method that maps local features describing an image (e.g. SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
Approximate computing is being considered as a promising design paradigm to overcome the energy and performance challenges in computationally demanding applications. If the case where the accuracy can be configured, the quality level versus…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Recent work has shown that parameterizing and optimizing coordinate transformations using normalizing flows, i.e., invertible neural networks, can significantly accelerate the convergence of spectral approximations. We present the first…