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Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
QR decomposition is an essential operation for solving linear equations and obtaining least-squares solutions. In high-performance computing systems, large-scale parallel QR decomposition often faces node faults. We address this issue by…
Multi-intent detection papers usually ask whether a model can recover multiple intents from one utterance. We ask a harder and, for deployment, more useful question: can it recover new combinations of familiar intents? Existing benchmarks…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
One-sided dense matrix decompositions (e.g., Cholesky, LU, and QR) are the key components in scientific computing in many different fields. Although their design has been highly optimized for modern processors, they still consume a…
Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of…
We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, second order cone, and semidefinite programming. This allows…
We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…
Dey and Xin (J.Appl.Comput.Top., 2022, arXiv:1904.03766) describe an algorithm to decompose finitely presented multiparameter persistence modules using a matrix reduction algorithm. Their algorithm only works for modules whose generators…
Inverse problems spanning four or more dimensions such as space, time and other independent parameters have become increasingly important. State-of-the-art 4D reconstruction methods use model based iterative reconstruction (MBIR), but…
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…
This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…
Embedding tables are used by machine learning systems to work with categorical features. In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during…
Polar codes are widely considered as one of the most exciting recent discoveries in channel coding. For short to moderate block lengths, their error-correction performance under list decoding can outperform that of other modern…
Binary neural networks have great resource and computing efficiency, while suffer from long training procedure and non-negligible accuracy drops, when comparing to the full-precision counterparts. In this paper, we propose the composite…
Image compression and reconstruction are crucial for various digital applications. While contemporary neural compression methods achieve impressive compression rates, the adoption of such technology has been largely hindered by the…
Tensor decomposition is one of the well-known approaches to reduce the latency time and number of parameters of a pre-trained model. However, in this paper, we propose an approach to use tensor decomposition to reduce training time of…
Given an implicational base, a well-known representation for a closure system, an inconsistency binary relation over a finite set, we are interested in the problem of enumerating all maximal consistent closed sets (denoted by MCCEnum for…
This paper investigates the problem of decomposition with respect to outputs for Boolean control networks (BCNs). First, with the linear expression of BCNs and the matrix semi-tensor product, some algebraic equivalent conditions for the…