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In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in given ranges of the frequency. In these decades, some useful formulas for the Fourier transform…
Many neural speech enhancement and source separation systems operate in the time-frequency domain. Such models often benefit from making their Short-Time Fourier Transform (STFT) front-ends trainable. In current literature, these are…
We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical…
We present a new method for performing global redistributions of multidimensional arrays essential to parallel fast Fourier (or similar) transforms. Traditional methods use standard all-to-all collective communication of contiguous memory…
The transformer model is known to be computationally demanding, and prohibitively costly for long sequences, as the self-attention module uses a quadratic time and space complexity with respect to sequence length. Many researchers have…
Communication efficiency is a widely recognised research problem in Federated Learning (FL), with recent work focused on developing techniques for efficient compression, distribution and aggregation of model parameters between clients and…
Adapting pretrained large language models (LLMs) to various downstream tasks in tens or hundreds of human languages is computationally expensive. Parameter-efficient fine-tuning (PEFT) significantly reduces the adaptation cost, by tuning…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
The amount of large-scale scientific computing software is dramatically increasing. In this work, we designed a new language, named feature query language (FQL), to collect and extract software features from a quick static code analysis. We…
The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a…
We demonstrate the utility of the Multi-Level Intermediate Representation (MLIR) for quantum computing. Specifically, we extend MLIR with a new quantum dialect that enables the expression and compilation of common quantum assembly…
Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with…
In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…
Optimizing compilers are essential for the efficient and correct execution of software across various scientific fields. Domain-specific languages (DSL) typically use higher level intermediate representations (IR) in their compiler…
Field Programmable Gate Arrays (FPGAs) have the potential to accelerate specific HPC codes. However even with the advent of High Level Synthesis (HLS), which enables FPGA programmers to write code in C or C++, programming such devices still…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
In this work, we present a software package in Python for high-throughput first-principles calculations of thermodynamic properties at finite temperatures, which we refer to as DFTTK (Density Functional Theory Tool Kit). DFTTK is based on…
The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application. However, the high-performance DSP processor is the important method of electrical harmonic analysis. Hence, in this research…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational…