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The generic matrix-matrix multiplication (GEMM) is arguably the most popular computational kernel of the 20th century. Yet, surprisingly, no common methodology for evaluating GEMM performance has been established over the many decades of…
Meeting growing demands for low latency and cost efficiency in production-grade large language model (LLM) serving systems requires integrating advanced optimization techniques. However, dynamic and unpredictable input-output lengths of…
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…
General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
The integration of large language models (LLMs) into automated algorithm design has shown promising potential. A prevalent approach embeds LLMs within search routines to iteratively generate and refine candidate algorithms. However, most…
The performance of modern AI systems is fundamentally constrained by the quality of their underlying kernels, which translate high-level algorithmic semantics into low-level hardware operations. Achieving near-optimal kernels requires…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
Emerging deep learning workloads urgently need fast general matrix multiplication (GEMM). To meet such demand, one of the critical features of machine-learning-specific accelerators such as NVIDIA Tensor Cores, AMD Matrix Cores, and Google…
Generative AI technology based on Large Language Models (LLM) has been developed and applied to assist or automatically generate program codes. In this paper, we evaluate the capability of existing general LLMs for Basic Linear Algebra…
This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the…
Language models such as GPT and Llama have shown remarkable ability on diverse natural language tasks, yet their performance on complex table tasks (e.g., NL-to-Code and data cleaning) remains suboptimal. Improving performance typically…
This dissertation introduces measurement-based performance modeling and prediction techniques for dense linear algebra algorithms. As a core principle, these techniques avoid executions of such algorithms entirely, and instead predict their…
Implementing Deep Neural Networks (DNNs) on resource-constrained edge devices is a challenging task that requires tailored hardware accelerator architectures and a clear understanding of their performance characteristics when executing the…
The rapidly evolving landscape of AI and machine learning workloads has widened the gap between high-level domain operations and efficient hardware utilization. Achieving near-peak performance still demands deep hardware expertise-experts…
Large Language Models (LLMs) have revolutionized automated program repair (APR) but current benchmarks like SWE-Bench predominantly focus on userspace applications and overlook the complexities of kernel-space debugging and repair. The…
Optimizing GPU kernels for high performance is a complex task, often demanding deep architectural knowledge, extensive profiling, and iterative experimentation. This challenge is amplified when targeting newer or less-documented GPU…
3D Gaussian splatting (3DGS) is a transformative technique with profound implications on novel view synthesis and real-time rendering. Given its importance, there have been many attempts to improve its performance. However, with the…
General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic…
There is a lot of interest today in building autonomous (or, self-driving) data processing systems. An emerging school of thought is to leverage AI-driven "black box" algorithms for this purpose. In this paper, we present a contrarian view.…