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Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
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…
We introduce Scale Factorized-Quantum Field Theory (SF-QFT), a framework performing path-integral factorization of ultraviolet and infrared momentum modes at a physical scale $Q^*$ before perturbative expansion through Effective Dynamical…
Discovering the set of closed frequent patterns is one of the fundamental problems in Data Mining. Recent Constraint Programming (CP) approaches for declarative itemset mining have proven their usefulness and flexibility. But the wide use…
Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
Current learned image compression models typically exhibit high complexity, which demands significant computational resources. To overcome these challenges, we propose an innovative approach that employs hierarchical feature extraction…
Image compression has been investigated as a fundamental research topic for many decades. Recently, deep learning has achieved great success in many computer vision tasks, and is gradually being used in image compression. In this paper, we…
This paper presents novel Weighted Finite-State Transducer (WFST) topologies to implement Connectionist Temporal Classification (CTC)-like algorithms for automatic speech recognition. Three new CTC variants are proposed: (1) the…
The Discrete Fourier Transform (DFT) is essential for various applications ranging from signal processing to convolution and polynomial multiplication. The groundbreaking Fast Fourier Transform (FFT) algorithm reduces DFT time complexity…
In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point…
In this letter, we investigate an important and famous issue, namely weighted mean-square-error (MSE) minimization transceiver designs. In our work, for transceiver designs a novel weighted MSE model is proposed, which is defined as a…
Fourier ptychographic microscopy (FPM) is a promising computational imaging technique with high resolution, wide field-of-view (FOV) and quantitative phase recovery. So far, a series of system errors that may corrupt the image quality of…
The transformer model is known to be computationally demanding, and prohibitively costly for long sequences, as the self-attention module uses a quadratic time and space complexity with respect to sequence length. Many researchers have…
Recently, evolutionary multitasking (EMT) has been successfully used in the field of high-dimensional classification. However, the generation of multiple tasks in the existing EMT-based feature selection (FS) methods is relatively simple,…
In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition…
Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are…
Deep subspace clustering based on auto-encoder has received wide attention. However, most subspace clustering based on auto-encoder does not utilize the structural information in the self-expressive coefficient matrix, which limits the…
In this paper, we propose a two-steps approach to partition instances of the Conjunctive Normal Form (CNF) Syntactic Formula Isomorphism problem (CSFI) into groups of different complexity. First, we build a model, based on the Transformer…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…