Related papers: Fast Linear Transformations in Python

Information-efficient approaches for extracting randomness from imperfect sources have been extensively studied, but simpler and faster ones are required in the high-speed applications of random number generation. In this paper, we focus on…

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…

Dataframes are a popular abstraction to represent, prepare, and analyze data. Despite the remarkable success of dataframe libraries in Rand Python, dataframes face performance issues even on moderately large datasets. Moreover, there is…

Dynamically typed languages such as Python have become very popular. Among other strengths, Python's dynamic nature and its straightforward linking to native code have made it the de-facto language for many research areas such as Artificial…

Large language models (LLMs) have shown impressive performance on general-purpose tasks, yet adapting them to specific domains remains challenging due to the scarcity of high-quality domain data. Existing data synthesis tools often struggle…

Freely Long-Thinking Transformer (FraiLT) is an improved transformer model designed to enhance processing capabilities without scaling up size. It utilizes a recursive approach, iterating over a subset of layers multiple times, and…

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense…

As transformer-based language models are trained on increasingly large datasets and with vast numbers of parameters, finding more efficient alternatives to the standard Transformer has become very valuable. While many efficient Transformers…

We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…

As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…

Feature Transformation is crucial for classic machine learning that aims to generate feature combinations to enhance the performance of downstream tasks from a data-centric perspective. Current methodologies, such as manual expert-driven…

The rapid development of tools for acquisition and storage of information has lead to the formation of enormous medical databases. The large quantity of data definitely surpasses the abilities of humans for efficient usage without…

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage…

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,…

Packrat parsing is a novel technique for implementing parsers in a lazy functional programming language. A packrat parser provides the power and flexibility of top-down parsing with backtracking and unlimited lookahead, but nevertheless…

In this paper, we present resolvent4py, a parallel Python package for the analysis, model reduction and control of large-scale linear systems with millions or billions of degrees of freedom. This package provides the user with a friendly…

In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…

Partial differential equations describing the dynamics of physical systems rarely have closed-form solutions. Fourier spectral methods, which use Fast Fourier Transforms (FFTs) to approximate solutions, are a common approach to solving…

Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…