Related papers: Compiling Structured Tensor Algebra
We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…
Axon is a language that enables shape and rank inference for tensors in a Deep Learning graphs. It aims to make shapes implicit and inferred, in a similar manner to how types are implicit and inferred in many functional programming…
Semantic sparsity is a common challenge in structured visual classification problems; when the output space is complex, the vast majority of the possible predictions are rarely, if ever, seen in the training set. This paper studies semantic…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
Existing methods for Table Structure Recognition (TSR) from camera-captured or scanned documents perform poorly on complex tables consisting of nested rows / columns, multi-line texts and missing cell data. This is because current…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
Table structure recognition (TSR) aims to convert tabular images into a machine-readable format, where a visual encoder extracts image features and a textual decoder generates table-representing tokens. Existing approaches use classic…
We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists…
Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…
Deep learning models with convolutional and recurrent networks are now ubiquitous and analyze massive amounts of audio, image, video, text and graph data, with applications in automatic translation, speech-to-text, scene understanding,…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
Sparse Tensor Cores offer exceptional performance gains for AI workloads by exploiting structured 2:4 sparsity. However, their potential remains untapped for core scientific workloads such as stencil computations, which exhibit irregular…
Tabular data is common yet typically incomplete, small in volume, and access-restricted due to privacy concerns. Synthetic data generation offers potential solutions. Many metrics exist for evaluating the quality of synthetic tabular data;…
Sparse tensors arise in problems in science, engineering, machine learning, and data analytics. Programs that operate on such tensors can exploit sparsity to reduce storage requirements and computational time. Developing and maintaining…
Tabular data in digital documents is widely used to express compact and important information for readers. However, it is challenging to parse tables from unstructured digital documents, such as PDFs and images, into machine-readable format…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…