Related papers: TRIOT: Faster tensor manipulation in C++11

In this work, we propose a framework to store and manage spatial data, which includes new efficient algorithms to perform operations accepting as input a raster dataset and a vector dataset. More concretely, we present algorithms for…

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…

This paper describes how 3D XPoint memory arrays can be used as in-memory computing accelerators. We first show that thresholded matrix-vector multiplication (TMVM), the fundamental computational kernel in many applications including…

In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…

The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…

Recent rapid advancements in deep pre-trained language models and the introductions of large datasets have powered research in embedding-based dense retrieval. While several good research papers have emerged, many of them come with their…

Vector search plays a crucial role in many real-world applications. In addition to single-vector search, multi-vector search becomes important for multi-modal and multi-feature scenarios today. In a multi-vector database, each row is an…

The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object…

Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Scientific computing requires handling large linear models, which are often composed of structured matrices. With increasing model size, dense representations quickly become infeasible to compute or store. Matrix-free implementations are…

This paper introduces the continuous tensor abstraction, allowing indices to take real-number values (for example, A[3.14]). It also presents continuous tensor algebra expressions, such as C(x,y) = A(x,y) * B(x,y), where indices are defined…

Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…

We consider the problem of transposing tensors of arbitrary dimension and describe TTC, an open source domain-specific parallel compiler. TTC generates optimized parallel C++/CUDA C code that achieves a significant fraction of the system's…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. The common theme amongst these views is the need to store and operate on data as…

Hashing has recently sparked a great revolution in cross-modal retrieval because of its low storage cost and high query speed. Recent cross-modal hashing methods often learn unified or equal-length hash codes to represent the multi-modal…

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically…

Tensor parallelism is an essential technique for distributed training of large neural networks. However, automatically determining an optimal tensor parallel strategy is challenging due to the gigantic search space, which grows…

Scanning and filtering over multi-dimensional tables are key operations in modern analytical database engines. To optimize the performance of these operations, databases often create clustered indexes over a single dimension or…