Related papers: SySTeC: A Symmetric Sparse Tensor Compiler

Sparse matrix vector multiplication (SpMV) is an important kernel in scientific and engineering applications. The previous optimizations are sparse matrix format specific and expose the choice of the best format to application programmers.…

From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying…

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…

Sparse tensors appear frequently in distributed deep learning, either as a direct artifact of the deep neural network's gradients, or as a result of an explicit sparsification process. Existing communication primitives are agnostic to the…

This paper presents a meta-compilation framework, the MCompiler. The main idea is that different segments of a program can be compiled with different compilers/optimizers and combined into a single executable. The MCompiler can be used in a…

Sparse matrix-vector and matrix-matrix multiplication (SpMV and SpMM) are fundamental in both conventional (graph analytics, scientific computing) and emerging (sparse DNN, GNN) domains. Workload-balancing and parallel-reduction are…

Sparse tiling is a technique to fuse loops that access common data, thus increasing data locality. Unlike traditional loop fusion or blocking, the loops may have different iteration spaces and access shared datasets through indirect memory…

Recent research has focused on accelerating stencil computations by exploiting emerging hardware like Tensor Cores. To leverage these accelerators, the stencil operation must be transformed to matrix multiplications. However, this…

Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that…

Hardware architectures and machine learning (ML) libraries evolve rapidly. Traditional compilers often fail to generate high-performance code across the spectrum of new hardware offerings. To mitigate, engineers develop hand-tuned kernels…

Sparse fusion is a compile-time loop transformation and runtime scheduling implemented as a domain-specific code generator. Sparse fusion generates efficient parallel code for the combination of two sparse matrix kernels where at least one…

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…

A recurring theme in attempts to break the curse of dimensionality in the numerical approximations of solutions to high-dimensional partial differential equations (PDEs) is to employ some form of sparse tensor approximation. Unfortunately,…

This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…

Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from…

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

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…

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse…

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…