相关论文: HODLR3D: Hierarchical matrices for $N$-body proble…

Many fundamental problems in computational geometry admit no algorithm running in $o(n \log n)$ time for $n$ planar input points, via classical reductions from sorting. Prominent examples include the computation of convex hulls, quadtrees,…

Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount of input data vectors,…

Hyperdimensional computing (HDC) has emerged as a new light-weight learning algorithm with smaller computation and energy requirements compared to conventional techniques. In HDC, data points are represented by high-dimensional vectors…

Both humans and deep learning models can recognize objects from 3D shapes depicted with sparse visual information, such as a set of points randomly sampled from the surfaces of 3D objects (termed a point cloud). Although deep learning…

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

3D integration offers key advantages in improving system performance and efficiency for the End-of-Scaling era. It enables the incorporation of heterogeneous system components and disparate technologies, eliminates off-chip communication…

In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…

Advancements in 3D vision have increased the impact of blood vessel modeling on medical applications. However, accurately representing the complex geometry and topology of blood vessels remains a challenge due to their intricate branching…

This paper proposes a Kolmogorov high order deep neural network (K-HOrderDNN) for solving high-dimensional partial differential equations (PDEs), which improves the high order deep neural networks (HOrderDNNs). HOrderDNNs have been…

Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…

Huge amount of applications in various fields, such as gene expression analysis or computer vision, undergo data sets with high-dimensional low-sample-size (HDLSS), which has putted forward great challenges for standard statistical and…

Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied,…

Autoregressive models have proven to be very powerful in NLP text generation tasks and lately have gained popularity for image generation as well. However, they have seen limited use for the synthesis of 3D shapes so far. This is mainly due…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

We discuss an implementation of our 3D radiative transfer (3DRT) framework with the OpenCL paradigm for general GPU computing. We implement the kernel for solving the 3DRT problem in Cartesian coordinates with periodic boundary conditions…

Outlier recognition is a fundamental problem in data analysis and has attracted a great deal of attention in the past decades. However, most existing methods still suffer from several issues such as high time and space complexities or…

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

We construct the effective Hamiltonian for hadronic parity violation in strangeness-nonchanging ($\Delta S=0$) processes in next-to-leading order (NLO) in QCD, for all isosectors, and at a renormalization scale of 2 GeV, thus extending our…

Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…