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Deep learning using neural networks is an effective technique for generating models of complex data. However, training such models can be expensive when networks have large model capacity resulting from a large number of layers and nodes.…
This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner…
Purpose: Previously-developed Voxel Spread Function (VSF) method (Yablonskiy, et al, MRM, 2013;70:1283) provides means to correct artifacts induced by macroscopic magnetic field inhomogeneities in the images obtained by…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand…
When implementing functionality which requires sparse matrices, there are numerous storage formats to choose from, each with advantages and disadvantages. To achieve good performance, several formats may need to be used in one program,…
To handle vast amounts of data, it is natural and popular to compress vectors and matrices. When we compress a vector from size $N$ down to size $n \ll N$, it certainly makes it easier to store and transmit efficiently, but does it also…
Neural networks are often challenging to work with due to their large size and complexity. To address this, various methods aim to reduce model size by sparsifying or decomposing weight matrices, such as magnitude pruning and low-rank or…
We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve…
With the announcement that the Aurora Supercomputer will be composed of general purpose Intel CPUs complemented by discrete high performance Intel GPUs, and the deployment of the oneAPI ecosystem, Intel has committed to enter the arena of…
Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank,…
We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…
We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
General matrix multiplication (GEMM) is a fundamental operation in deep learning (DL). With DL moving increasingly toward low precision, recent works have proposed novel unary GEMM designs as an alternative to conventional binary GEMM…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
This paper presents an efficient method for implementing the Gaussian elimination technique for an nxm (m>=n) matrix, using a 2D SIMD array of nxm processors. The described algorithm consists of 2xn-1=O(n) iterations, which provides an…
In chemistry tabulations and Flamelet combustion models, the Flamelet Generated Manifold (FGM) is recognized for its precision and physical representation. The practical implementation of FGM requires a significant allocation of memory…