Related papers: Low-Rank GEMM: Efficient Matrix Multiplication via…

We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…

Large language models (LLMs) have grown beyond the memory capacity of single GPU devices, necessitating quantization techniques for practical deployment. While NF4 (4-bit NormalFloat) quantization enables 4$\times$ memory reduction,…

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method…

Despite their ubiquity in NLP tasks, Long Short-Term Memory (LSTM) networks suffer from computational inefficiencies caused by inherent unparallelizable recurrences, which further aggravates as LSTMs require more parameters for larger…

Sparse general matrix-matrix multiplication (SpGEMM) is a critical operation in many applications. Current multithreaded implementations are based on Gustavson's algorithm and often perform poorly on large matrices due to limited cache…

Retrieval-Augmented Generation (RAG) systems combine vector similarity search with large language models (LLMs) to deliver accurate, context-aware responses. However, co-locating the vector retriever and the LLM on shared GPU infrastructure…

Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…

This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level,…

General-purpose Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental kernel in scientific computing and deep learning. The emergence of new matrix computation units such as Tensor Cores (TCs) brings more opportunities for SpMM…

The matrix-free gather-batched-GEMM-scatter pattern eliminates global stiffness assembly for three-dimensional SIMP topology optimization, but the conventional three-stage implementation forces avoidable DRAM traffic between stages. We…

Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…

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…

Deep learning hardware achieves high throughput and low power consumption by reducing computing precision and specializing in matrix multiplication. For machine learning inference, fixed-point value computation is commonplace, where the…

The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…

We propose an implementation of an efficient fused matrix multiplication kernel for W4A16 quantized inference, where we perform dequantization and GEMM in a fused kernel using a SplitK work decomposition. Our implementation shows…

General-purpose processor vendors have integrated customized accelerator in their products due to the widespread use of General Matrix-Matrix Multiplication (GEMM) kernels. However, it remains a challenge to further improve the…

General matrix multiplication (GEMM) is a ubiquitous computing kernel/algorithm for data processing in diverse applications, including artificial intelligence (AI) and deep learning (DL). Recent shift towards edge computing has inspired…

Training Large Language Models (LLMs) presents significant memory challenges, predominantly due to the growing size of weights and optimizer states. Common memory-reduction approaches, such as low-rank adaptation (LoRA), add a trainable…

Deep neural networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. A common approach to implementing DNNs is to recast the most computationally expensive operations as…