相关论文: Data-driven Construction of Hierarchical Matrices …

We present a fast and memory-efficient algorithm for transient, space-time-domain, and elastodynamic boundary-integral analysis. Associated data-sparse approximations and operations are named fast domain partitioning hierarchical matrices…

We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a…

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding,…

Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…

The ability to generalize under distributional shifts is essential to reliable machine learning, while models optimized with empirical risk minimization usually fail on non-$i.i.d$ testing data. Recently, invariant learning methods for…

Over the past few years, silicon photonics-based computing has emerged as a promising alternative to CMOS-based computing for Deep Neural Networks (DNN). Unfortunately, the non-linear operations and the high-precision requirements of DNNs…

Text classification is a primary task in natural language processing (NLP). Recently, graph neural networks (GNNs) have developed rapidly and been applied to text classification tasks. As a special kind of graph data, the tree has a simpler…

Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…

Hierarchical clustering is an effective, interpretable method for analyzing structure in data. It reveals insights at multiple scales without requiring a predefined number of clusters and captures nested patterns and subtle relationships,…

We tackle the problem of generalization to unseen configurations for dynamic tasks in the real world while learning from high-dimensional image input. The family of nonlinear dynamical system-based methods have successfully demonstrated…

We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model…

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…

The hierarchical structure inherent in many real-world datasets makes the modeling of such hierarchies a crucial objective in both unsupervised and supervised machine learning. While recent advancements have introduced deep architectures…

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 present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…

Despite many modern applications of Deep Neural Networks (DNNs), the large number of parameters in the hidden layers makes them unattractive for deployment on devices with storage capacity constraints. In this paper we propose a Data-Driven…

We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…

Nonprehensile manipulation, such as pushing objects across cluttered environments, presents a challenging control problem due to complex contact dynamics and long-horizon planning requirements. In this work, we propose HeRD, a hierarchical…