Related papers: Linear-Equation Ordered-Statistics Decoding
Nowadays, various sensors are collecting, storing and transmitting tremendous trajectory data, and it is known that raw trajectory data seriously wastes the storage, network band and computing resource. Line simplification (LS) algorithms…
In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
Low-rank decomposition has emerged as an important problem in Large Language Model (LLM) fine-tuning and inference. Through Singular Value Decomposition (SVD), the weight matrix can be factorized into low-rank spaces optimally. Previously,…
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…
Out-of-distribution (OOD) detection plays a crucial role in ensuring the safety and reliability of deep neural networks in various applications. While there has been a growing focus on OOD detection in visual data, the field of textual OOD…
The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems. In this work, we reconsider formulations of the weights as…
End-to-end learning of a communications system using the deep learning-based autoencoder concept has drawn interest in recent research due to its simplicity, flexibility and its potential of adapting to complex channel models and practical…
We introduce Noise Recycling, a method that substantially enhances decoding performance of orthogonal channels subject to correlated noise without the need for joint encoding or decoding. The method can be used with any combination of…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently,…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra…
Ultra-reliable low-latency communications (URLLC) demand high-performance error-correcting codes and decoders in the finite blocklength regime. This letter introduces a novel two-stage near-maximum likelihood (near-ML) decoding framework…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…