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Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) has emerged as the standard post-training paradigm for large language models (LLMs). However, the conventional SFT process, driven by Cross-Entropy (CE) loss, often…

Automated recognition and simplification of fillet features in CAD models is critical for CAE analysis, yet it remains an open challenge. Traditional rule-based methods lack robustness, while existing deep learning models suffer from poor…

Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database…

Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, $L(\boldsymbol{\theta})$, with respect to a parameter vector $\boldsymbol{\theta}$, when…

We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing…

Feature pyramid network (FPN) has been an effective framework to extract multi-scale features in object detection. However, current FPN-based methods mostly suffer from the intrinsic flaw of channel reduction, which brings about the loss of…

As an old and widely used tool, it is still possible to find new insights and applications from Fast Fourier Transform (FFT)-based analyses. The FFT is frequently used to generate the Power Spectral Density (PSD) function, by squaring the…

This paper proposes low-overhead and low-complexity channel estimation (CE) of frequency-domain equalization aided faster-than-Nyquist (FTN) signaling. In the proposed CE scheme, the concept of pilot superimposition is employed, where the…

Ritt-Wu's algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In this paper we present a new algorithmic scheme for…

While model architectures and training strategies have become more generic and flexible with respect to different data modalities over the past years, a persistent limitation lies in the assumption of fixed quantities and arrangements of…

This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives…

Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…

Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…

The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for computation of the near-field and far-field in the quasi-cylindrical geometry has been introduced. The modal expansion coefficient of the vector potentials ${\bf F}$…

We extend the standard rough set-based approach to deal with huge amounts of numeric attributes versus small amount of available objects. Here, a novel approach of clustering along with dimensionality reduction; Hybrid Fuzzy C Means-Quick…

The development of high throughput single-cell sequencing technologies now allows the investigation of the population level diversity of cellular transcriptomes. This diversity has shown two faces. First, the expression dynamics (gene to…

In this paper, two 8-point multiplication-free DCT approximations based on the Chen's factorization are proposed and their fast algorithms are also derived. Both transformations are assessed in terms of computational cost, error energy, and…

We present a novel algorithm, named the 2D-FFAST, to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample complexity and low computational complexity. The proposed algorithm is based on mixed concepts from…

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…