相关论文: Long Polynomial Modular Multiplication using Low-C…

The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…

Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…

Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the…

The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…

Fully homomorphic encryption (FHE) enables private inference by evaluating neural networks on encrypted data. In this way, we can delegate the computation to a third party server without ever revealing the user's data. Currently, the CKKS…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

In this paper, we present a simple yet effective padding scheme that can be used as a drop-in module for existing convolutional neural networks. We call it partial convolution based padding, with the intuition that the padded region can be…

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…

This paper explores the novel deep learning Transformers architectures for high-frequency Bitcoin-USDT log-return forecasting and compares them to the traditional Long Short-Term Memory models. A hybrid Transformer model, called…

In this paper, a secure Convolutional Neural Network classifier is proposed using Fully Homomorphic Encryption (FHE). The secure classifier provides a user with the ability to out-source the computations to a powerful cloud server and/or…

Surface defect detection is an extremely crucial step to ensure the quality of industrial products. Nowadays, convolutional neural networks (CNNs) based on encoder-decoder architecture have achieved tremendous success in various defect…

Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…

How could the Fourier and other transforms be naturally discovered if one didn't know how to postulate them? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In…

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…

Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…

We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we…

Affine Frequency Division Multiplexing (AFDM), which is based on discrete affine Fourier transform (DAFT), has recently been proposed for reliable communication in high-mobility scenarios. Two low complexity detectors for AFDM are…

Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…

In the first part of this paper, we define a deep convolutional neural network connected with the fractional Fourier transform (FrFT) using the $\theta$-translation operator, the translation operator associated with the FrFT. Subsequently,…

Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…