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Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
The technologically-relevant task of feature extraction from data performed in deep-learning systems is routinely accomplished as repeated fast Fourier transforms (FFT) electronically in prevalent domain-specific architectures such as in…
Subgraph matching is a basic operation widely used in many applications. However, due to its NP-hardness and the explosive growth of graph data, it is challenging to compute subgraph matching, especially in large graphs. In this paper, we…
Two-dimensional Fourier transform plays a significant role in a variety of image processing problems, such as medical image processing, digital holography, correlation pattern recognition, hybrid digital optical processing, optical…
Extensive set of tests on different platforms indicated that there is a performance drop of current standard de facto software library for the Discrete Fourier Transform (DFT) in case of large 2D array sizes (larger than 16384x16384).…
Large Language Models (LLMs) have become indispensable in numerous real-world applications. However, fine-tuning these models at scale, especially in federated settings where data privacy and communication efficiency are critical, presents…
Fortran's prominence in scientific computing requires strategies to ensure both that legacy codes are efficient on high-performance computing systems, and that the language remains attractive for the development of new high-performance…
Convolutional Neural Networks (CNNs), one of the most representative algorithms of deep learning, are widely used in various artificial intelligence applications. Convolution operations often take most of the computational overhead of CNNs.…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists…
Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…
Convolutional neural networks are paramount in image and signal processing including the relevant classification and training tasks alike and constitute for the majority of machine learning compute demand today. With convolution operations…
We present a new implementation of the Fourier acceleration method for Landau gauge fixing. By means of a multigrid inversion we are able to avoid the use of the fast Fourier transform. This makes the method more flexible, and well suited…
Performant all-to-all collective operations in MPI are critical to fast Fourier transforms, transposition, and machine learning applications. There are many existing implementations for all-to-all exchanges on emerging systems, with the…
Fractional programming (FP) arises in various communications and signal processing problems because several key quantities in the field are fractionally structured, e.g., the Cram\'{e}r-Rao bound, the Fisher information, and the…
The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented…
The need for wireless communication has driven the communication systems to high performance. However, the main bottleneck that affects the communication capability is the Fast Fourier Transform (FFT), which is the core of most modulators.…
Modern high-performance computing and Internet-of-Things deployments increasingly generate large volumes of signal data that must be compressed efficiently on resource-constrained acquisition devices and decompressed at scale on centralized…