Related papers: Recursive methods for some problems in coding and …
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
Designing computational experiments involving $\ell_1$ minimization with linear constraints in a finite-dimensional, real-valued space for receiving a sparse solution with a precise number $k$ of nonzero entries is, in general, difficult.…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Given a permutation w, we look at the range of how often a simple reflection s_k appears in reduced decompositions of w. We compute the minimum and give a sharp upper bound on the maximum. That bound is in terms of 321- and 3412-patterns in…
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…
Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in…
Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this…
In neural text editing, prevalent sequence-to-sequence based approaches directly map the unedited text either to the edited text or the editing operations, in which the performance is degraded by the limited source text encoding and long,…
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
The locally repairable code (LRC) studied in this paper is an $[n,k]$ linear code of which the value at each coordinate can be recovered by a linear combination of at most $r$ other coordinates. The central problem in this work is to…
Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…
Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…