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While loop reordering and fusion can make big impacts on the constant-factor performance of dense tensor programs, the effects on sparse tensor programs are asymptotic, often leading to orders of magnitude performance differences in…
Sparse tensor algebra computations have become important in many real-world applications like machine learning, scientific simulations, and data mining. Hence, automated code generation and performance optimizations for tensor algebra…
Recent years have seen considerable work on compiling sparse tensor algebra expressions. This paper addresses a shortcoming in that work, namely how to generate efficient code (in time and space) that scatters values into a sparse result…
Sparse tensor decomposition and completion are common in numerous applications, ranging from machine learning to computational quantum chemistry. Typically, the main bottleneck in optimization of these models are contractions of a single…
This paper shows how to generate efficient tensor algebra code that compute on dynamic sparse tensors, which have sparsity structures that evolve over time. We propose a language for precisely specifying recursive, pointer-based data…
Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…
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:…
This paper shows how to optimize sparse tensor algebraic expressions by introducing temporary tensors, called workspaces, into the resulting loop nests. We develop a new intermediate language for tensor operations called concrete index…
This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support…
We address the problem of optimizing mixed sparse and dense tensor algebra in a compiler. We show that standard loop transformations, such as strip-mining, tiling, collapsing, parallelization and vectorization, can be applied to irregular…
Sparse compiler is a promising solution for sparse tensor algebra optimization. In compiler implementation, reduction in sparse-dense hybrid algebra plays a key role in performance. Though GPU provides various reduction semantics that can…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
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…
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…
Sparse tensors are rapidly becoming critical components of modern deep learning workloads. However, developing high-performance sparse operators can be difficult and tedious, and existing vendor libraries cannot satisfy the escalating…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
Tensor algebra is widely used in many applications, such as scientific computing, machine learning, and data analytics. The tensors represented real-world data are usually large and sparse. There are tens of storage formats designed for…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
Sparse matrix operations involve a large number of zero operands which makes most of the operations redundant. The amount of redundancy magnifies when a matrix operation repeatedly executes on sparse data. Optimizing matrix operations for…