Related papers: Mass Matrix Assembly on Tensor Cores for Implicit …
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
Tensor Core is a mixed-precision matrix-matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
Model merging aims to integrate multiple task-specific fine-tuned models derived from a shared pre-trained checkpoint into a single multi-task model without additional training. Despite extensive research, task interference remains a major…
Multi-dimensional non-Cartesian MRI encoding using the precomputed interpolator can encounter the curse of dimensionality, in which the interpolator size exceeds the available memory on the parallel accelerators. Here we reformulate the…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…
The advanced magnetic resonance (MR) image reconstructions such as the compressed sensing and subspace-based imaging are considered as large-scale, iterative, optimization problems. Given the large number of reconstructions required by the…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
The machine-part cell formation problem consists of creating machine cells and their corresponding part families with the objective of minimizing the inter-cell and intra-cell movement while maximizing the machine utilization. This article…
To alleviate the memory bandwidth bottleneck in Large Language Model (LLM) inference workloads, weight matrices are stored in memory in quantized and sparsified formats. Hence, before tiles of these matrices can be processed by in-core…
Modern ConvNets continue to achieve state-of-the-art results over a vast array of vision and image classification tasks, but at the cost of increasing parameters. One strategy for compactifying a network without sacrificing much expressive…
General Matrix Multiplication (GEMM) is the cornerstone of HPC workloads and Deep Learning. State-of-the-art vendor libraries tune tensor layouts, parallelization schemes, and cache blocking to minimize data movement across the memory…
The embedded atom method (EAM) is one of the most widely used many-body, short-range potentials in molecular dynamics simulations, particularly for metallic systems. To enhance the efficiency of calculating these short-range interactions,…
A commonly occurring computation idiom in neural networks is to perform some pointwise operations on the result of a matrix multiplication. Such a sequence of operations is typically represented as a computation graph in deep learning…
Sparse Ternary General Matrix-Matrix Multiplication (GEMM) remains under-optimized in existing libraries for Apple Silicon CPUs. We present a Sparse Ternary GEMM kernel optimized specifically for Apple's M-series processors. We propose a…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…