Related papers: Tensor Computation of Euler Characteristic Functio…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
We write the Euler characteristic X(G) of a four dimensional finite simple geometric graph G=(V,E) in terms of the Euler characteristic X(G(w)) of two-dimensional geometric subgraphs G(w). The Euler curvature K(x) of a four dimensional…
In this paper, we propose a novel feature weighting method to address the limitation of existing feature processing methods for tabular data. Typically the existing methods assume equal importance across all samples and features in one…
In the field of data-driven 3D shape analysis and generation, the estimation of global topological features from localized representations such as point clouds, voxels, and neural implicit fields is a longstanding challenge. This paper…
The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model that combines the concepts of extreme machine learning with quantum reservoir computation. Key to QERC is the generation of a complex quantum…
Accurate hardware performance models are critical to efficient code generation. They can be used by compilers to make heuristic decisions, by superoptimizers as a minimization objective, or by autotuners to find an optimal configuration for…
We present an algorithm that computes Friedl and L\"uck's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonn\'e determinant. The algorithm…
Parameter-efficient finetuning (PEFT) has become ubiquitous to adapt foundation models to downstream task requirements while retaining their generalization ability. However, the amount of additionally introduced parameters and compute for…
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this…
Heterogeneous computing integrates diverse processing elements, such as CPUs, GPUs, and FPGAs, within a single system, aiming to leverage the strengths of each architecture to optimize performance and energy consumption. In this context,…
Domain-specific, fixed-function units are becoming increasingly common in modern processors. As the computational demands of applications evolve, the capabilities and programming interfaces of these fixed-function units continue to change.…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
We present an algorithm for the symbolic and numerical computation of the degrees of the Chern-Schwartz-MacPherson classes of a closed subvariety of projective space P^n. As the degree of the top Chern-Schwartz-MacPherson class is the…
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
This work details a highly efficient implementation of the 3D scale-invariant feature transform (SIFT) algorithm, for the purpose of machine learning from large sets of volumetric medical image data. The primary operations of the 3D SIFT…
We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…
In this short note we present a generating function computing the compactly supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible…
Graph convolutional neural networks have been instrumental in machine learning of material properties. When representing tensorial properties, weights and descriptors of a physics-informed network must obey certain transformation rules to…
This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the…
In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…