Related papers: MOM: Matrix Operations in MLIR
Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…
The new generation of machine learning processors have evolved from multi-core and parallel architectures that were designed to efficiently implement matrix-vector-multiplications (MVMs). This is because at the fundamental level, neural…
Recent developments in Multimodal Large Language Models (MLLMs) have shown rapid progress, moving towards the goal of creating versatile MLLMs that understand inputs from various modalities. However, existing methods typically rely on joint…
We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
Mojo is an emerging programming language built on MLIR (Multi-Level Intermediate Representation) and supports JIT (Just-in-Time) compilation. It enables transparent hardware-specific optimizations (e.g., for CPUs and GPUs), while allowing…
Linear algebra routines are basic building blocks for the statistical software. In this paper we analyzed how can we can improve R performance for matrix computations. We benchmarked few matrix operations using the standard linear algebra…
We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP…
A compiler processes the code written in a high level language and produces machine executable code. The compiler writers often face the challenge of keeping the compilation times reasonable. That is because aggressive optimization passes…
Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is…
Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
General Matrix Multiplication (GEMM) is a critical kernel in high-performance computing and deep learning. While modern architectures like ARM's Scalable Matrix Extension (SME) introduce dedicated hardware for matrix operations, existing…
The devices designed for the Internet-of-Things encompass a large variety of distinct processor architectures, forming a highly heterogeneous zoo. In order to tackle this, we employ a simulator to estimate the performance of the…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…
Modern data analytics pipelines increasingly combine relational queries, graph processing, and tensor computation within a single application, but existing systems remain fragmented across paradigms, execution models, and research…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
Language models (LMs) excel at tasks across diverse domains, yet require substantial computational resources during inference. Compression techniques such as pruning and quantization offer a practical path towards efficient LM deployment,…
Previous computation models either have equivalent abilities in representing all computations but fail to provide primitive operators for programming complex algorithms or lack generalized expression ability to represent newly-added…