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We introduce FFN Fusion, an architectural optimization technique that reduces sequential computation in large language models by identifying and exploiting natural opportunities for parallelization. Our key insight is that sequences of…
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 Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
The matrix expressions for every parts of a transformer are firstly described. Based on semi-tensor product (STP) of matrices the hypervectors are reconsidered and the linear transformation over hypervectors is constructed by using…
Factorization Machines (FM) are powerful class of models that incorporate higher-order interaction among features to add more expressive power to linear models. They have been used successfully in several real-world tasks such as…
We present a new algorithm for the 2D Sliding Window Discrete Fourier Transform (SWDFT). Our algorithm avoids repeating calculations in overlapping windows by storing them in a tree data-structure based on the ideas of the Cooley- Tukey…
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping…
This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU…
Machine-intelligence has become a driving factor in modern society. However, its demand outpaces the underlying electronic technology due to limitations given by fundamental physics such as capacitive charging of wires, but also by system…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. There are mainly two stages in the sFFT: frequency bucketization and spectrum reconstruction. Frequency…
Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
The continuous wavelet transform (CWT) is very useful for processing signals with intricate and irregular structures in astrophysics and cosmology. It is crucial to propose precise and fast algorithms for the CWT. In this work, we review…
The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…
This paper describes a low-power processor tailored for fast Fourier transform computations where transport triggering template is exploited. The processor is software-programmable while retaining an energy-efficiency comparable to existing…
The whole computer hardware industry embraced multicores. For these machines, the extreme optimisation of sequential algorithms is no longer sufficient to squeeze the real machine power, which can be only exploited via thread-level…
We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…