Related papers: Practical Tera-scale Walsh-Hadamard Transform
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log…
This study investigates the integration of signal processing transformations -- Fast Fourier Transform (FFT), Walsh-Hadamard Transform (WHT), and Discrete Cosine Transform (DCT) -- within the ResNet50 convolutional neural network (CNN)…
Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a…
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing…
Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our TWD is specifically…
We present HadaCore, a modified Fast Walsh-Hadamard Transform (FWHT) algorithm optimized for the Tensor Cores present in modern GPU hardware. HadaCore follows the recursive structure of the original FWHT algorithm, achieving the same…
In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In ``Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang and A. Christlieb (2013), an efficient algorithm with…
Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy…
In this paper, we propose the Hierarchical Document Transformer (HDT), a novel sparse Transformer architecture tailored for structured hierarchical documents. Such documents are extremely important in numerous domains, including science,…
In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…
Transformer models encounter challenges in scaling hidden dimensions efficiently, as uniformly increasing them inflates computational and memory costs while failing to emphasize the most relevant features for each token. For further…
New efficient source feature compression solutions are proposed based on a two-stage Walsh-Hadamard Transform (WHT) for Convolutional Neural Network (CNN)-based object classification in underwater robotics. The object images are firstly…
Long-term time series forecasting is critical in domains such as finance, economics, and energy, where accurate and reliable predictions over extended horizons drive strategic decision-making. Despite the progress in machine learning-based…
Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations.…
We propose a novel hybrid classical-quantum approach for image processing based on polar Walsh basis functions. Using this approach, we present an algorithm for the removal of the circular banding noise (including Airy pattern noise) and…
Nowadays computational complexity of fast walsh hadamard transform and nonlinearity for Boolean functions and large substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear…
Transformers (Vaswani et al., 2017) have brought a remarkable improvement in the performance of neural machine translation (NMT) systems but they could be surprisingly vulnerable to noise. In this work, we try to investigate how noise…
Orthogonal frequency division multiplexing (OFDM) is a modulation technique susceptible to source, channel and amplifier nonlinearities because of its high peak-to-average ratio (PAPR). The distortion gets worse by increasing the average…
Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…