Related papers: Robust Multidimentional Chinese Remainder Theorem …
Given collections A and B of residue classes modulo m and n, respectively, we investigate conditions on A and B that ensure that, for at least some a in A and b in B, the linear system x = a mod m, x = b mod n has an integer solution, and…
Machine reading comprehension (MRC) is a crucial task in natural language processing and has achieved remarkable advancements. However, most of the neural MRC models are still far from robust and fail to generalize well in real-world…
Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work.…
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…
This work introduces the Matrix Minimum Covariance Determinant (MMCD) method, a novel robust location and covariance estimation procedure designed for data that are naturally represented in the form of a matrix. Unlike standard robust…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…
Small perturbations in the input can severely distort intermediate representations and thus impact translation quality of neural machine translation (NMT) models. In this paper, we propose to improve the robustness of NMT models with…
Recent advances in extreme image compression have revealed that mapping pixel data into highly compact latent representations can significantly improve coding efficiency. However, most existing methods compress images into 2-D latent spaces…
Gabidulin codes are the first general construction of linear codes that are maximum rank distant (MRD). They have found applications in linear network coding, for example, when the transmitter and receiver are oblivious to the inner…
Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…
In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and…
Residue Number System (RNS), which originates from the Chinese Remainder Theorem, offers a promising future in VLSI because of its carry-free operations in addition, subtraction and multiplication. This property of RNS is very helpful to…
Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-dose CT. We propose a new iterative CT reconstruction algorithm,…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…
Residue number systems based on pairwise relatively prime moduli are a powerful tool for accelerating integer computations via the Chinese Remainder Theorem. We study a structured family of moduli of the form $2^n - 2^k + 1$, originally…
Constant dimension codes (CDCs) are essential for error correction in random network coding. A fundamental problem of CDCs is to determine their maximal possible size for given parameters. Inserting construction and multilevel construction…
We consider the robust multi-dimensional scaling (RMDS) problem in this paper. The goal is to localize point locations from pairwise distances that may be corrupted by outliers. Inspired by classic MDS theories, and nonconvex works for the…