Related papers: TSFC: a structure-preserving form compiler

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant…

Feature generation is a critical step in machine learning, aiming to enhance model performance by capturing complex relationships within the data and generating meaningful new features. Traditional feature generation methods heavily rely on…

We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…

As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…

We present TTC, an open-source parallel compiler for multidimensional tensor transpositions. In order to generate high-performance C++ code, TTC explores a number of optimizations, including software prefetching, blocking, loop-reordering,…

This paper shows how to build a sparse tensor algebra compiler that is agnostic to tensor formats (data layouts). We develop an interface that describes formats in terms of their capabilities and properties, and show how to build a modular…

We present a new table structure recognition (TSR) approach, called TSRFormer, to robustly recognizing the structures of complex tables with geometrical distortions from various table images. Unlike previous methods, we formulate table…

Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra…

The paper introduces the development of a modular compiler for a subset of a C-like language, which addresses the challenges in constructing a compiler for high-level languages. This modular approach will allow developers to modify a…

Despite significant investment in software infrastructure, machine learning systems, runtimes and compilers do not compose properly. We propose a new design aiming at providing unprecedented degrees of modularity, composability and…

There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…

In this paper, we present a novel compression framework, TFZ, that preserves the topology of 2D symmetric and asymmetric second-order tensor fields defined on flat triangular meshes. A tensor field assigns a tensor - a multi-dimensional…

Symmetric and sparse tensors arise naturally in many domains including linear algebra, statistics, physics, chemistry, and graph theory. Symmetric tensors are equal to their transposes, so in the $n$-dimensional case we can save up to a…

We develop a tool that enables domain experts to quickly generate numerical solvers for emerging multi-physics phenomena starting from a high-level description based on ordinary/partial differential equations and their initial and boundary…

Conformal prediction offers finite-sample coverage guarantees under minimal assumptions. However, existing methods treat the entire modeling process as a black box, overlooking opportunities to exploit and understand modular structure. We…

Text semantic segmentation involves partitioning a document into multiple paragraphs with continuous semantics based on the subject matter, contextual information, and document structure. Traditional approaches have typically relied on…

When writing programs involving matrices or tensors in general, it is desirable to rule out the inconsistency of tensor shapes (i.e., the generalization of matrix sizes) before actual computation. For this purpose, some languages provide…

This paper shows how to generate code that efficiently converts sparse tensors between disparate storage formats (data layouts) such as CSR, DIA, ELL, and many others. We decompose sparse tensor conversion into three logical phases:…

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…