Related papers: Practical Tera-scale Walsh-Hadamard Transform
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
Hyperdimensional Computing (HDC) is an emerging computational framework that mimics important brain functions by operating over high-dimensional vectors, called hypervectors (HVs). In-memory computing implementations of HDC are desirable…
The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard $L_0$ constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard…
This paper introduces the $w$-product, a novel wavelet-based tensor multiplication scheme leveraging second-generation wavelet transforms to achieve linear transformation complexity while preserving essential algebraic properties. The…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
Transformer architectures have achieved state-of-the-art performance across natural language tasks, yet they fundamentally misrepresent the hierarchical nature of human language by processing text as flat token sequences. This results in…
Wireless Power Transfer (WPT) is expected to be a technology reshaping the landscape of low-power applications such as the Internet of Things, Radio Frequency identification (RFID) networks, etc. Although there has been some progress…
Token-based text-to-speech (TTS) models have emerged as a promising avenue for generating natural and realistic speech, yet they grapple with low pronunciation accuracy, speaking style and timbre inconsistency, and a substantial need for…
This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the…
We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
Learning sparse linear models with two-way interactions is desirable in many application domains such as genomics. l1-regularised linear models are popular to estimate sparse models, yet standard implementations fail to address specifically…
Despite the capacity of neural nets to learn arbitrary functions, models trained through gradient descent often exhibit a bias towards ``simpler'' functions. Various notions of simplicity have been introduced to characterize this behavior.…
We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the…
Two-dimensional terahertz spectroscopy (2DTS) is a low-frequency analogue of two-dimensional optical spectroscopy that is rapidly maturing as a probe of a wide variety of condensed matter systems. However, a persistent problem of 2DTS is…
Although certain vision transformer (ViT) and CNN architectures generalize well on vision tasks, it is often impractical to use them on green, edge, or desktop computing due to their computational requirements for training and even testing.…
In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…