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We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…
Modern language models operate on subword-tokenized text in order to make a trade-off between model size, inference speed, and vocabulary coverage. A side effect of this is that, during inference, models are evaluated by measuring the…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…
This work proposes a new computational framework for learning a structured generative model for real-world datasets. In particular, we propose to learn a closed-loop transcription between a multi-class multi-dimensional data distribution…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
Multi-Layer Perceptrons (MLPs) make powerful functional representations for sampling and reconstruction problems involving low-dimensional signals like images,shapes and light fields. Recent works have significantly improved their ability…
Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols.…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
MDS codes play a central role in practice due to their broad applications. To date, most known MDS codes are generalized Reed-Solomon (GRS) codes, leaving codes that are not equivalent to GRS codes comparatively less understood. Studying…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…
\emph{Multiresolution mode decomposition} (MMD) is an adaptive tool to analyze a time series $f(t)=\sum_{k=1}^K f_k(t)$, where $f_k(t)$ is a \emph{multiresolution intrinsic mode function} (MIMF) of the form \begin{eqnarray*}…
Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large…
The interpolation based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (ASD) further improves the decoding…
MR Fingerprinting is a novel quantitative MR technique that could simultaneously provide multiple tissue property maps. When optimizing MRF scans, modeling undersampling errors and field imperfections in cost functions will make the…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework…
Symbolic controller synthesis is a fully-automated and correct-by-design synthesis scheme whose limitations are its immense memory and runtime requirements. A current trend to compensate for this downside is to develop techniques for…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
We introduce Mini-Sequence Transformer (MsT), a simple and effective methodology for highly efficient and accurate LLM training with extremely long sequences. MsT partitions input sequences and iteratively processes mini-sequences to reduce…