Related papers: Data-driven Construction of Hierarchical Matrices …

Hierarchical Reinforcement Learning (HRL) is a promising approach for managing task complexity across multiple levels of abstraction and accelerating long-horizon agent exploration. However, the effectiveness of hierarchical policies…

Empty space skipping can be efficiently implemented with hierarchical data structures such as k-d trees and bounding volume hierarchies. This paper compares several recently published hierarchical data structures with regard to construction…

Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…

In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…

Datacenters are increasingly becoming heterogeneous, and are starting to include specialized hardware for networking, video processing, and especially deep learning. To leverage the heterogeneous compute capability of modern datacenters, we…

The cost involved in training deep neural networks (DNNs) on von-Neumann architectures has motivated the development of novel solutions for efficient DNN training accelerators. We propose a hybrid in-memory computing (HIC) architecture for…

In this thesis, we describe a new, practical approach to integrating hardware-based data compression within the memory hierarchy, including on-chip caches, main memory, and both on-chip and off-chip interconnects. This new approach is fast,…

Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and…

Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…

At present, attention mechanism has been widely applied to the fields of deep learning models. Structural models that based on attention mechanism can not only record the relationships between features position, but also can measure the…

This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…

The Hierarchical Inference (HI) paradigm employs a tiered processing: the inference from simple data samples are accepted at the end device, while complex data samples are offloaded to the central servers. HI has recently emerged as an…

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…

The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operators, the HIF achieves…

Dimensionality reduction (DR) techniques help analysts to understand patterns in high-dimensional spaces. These techniques, often represented by scatter plots, are employed in diverse science domains and facilitate similarity analysis among…

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…

In this paper, we propose and investigate a novel memory architecture for neural networks called Hierarchical Attentive Memory (HAM). It is based on a binary tree with leaves corresponding to memory cells. This allows HAM to perform memory…

This paper describes an effective and efficient image classification framework nominated distributed deep representation learning model (DDRL). The aim is to strike the balance between the computational intensive deep learning approaches…

This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…