Related papers: On the KZ Reduction
We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE)…
We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz…
A Matching Vector (MV) family modulo $m$ is a pair of ordered lists $U=(u_1,...,u_t)$ and $V=(v_1,...,v_t)$ where $u_i,v_j \in \mathbb{Z}_m^n$ with the following inner product pattern: for any $i$, $< u_i,v_i>=0$, and for any $i \ne j$, $<…
The Key-Value (KV) cache is a crucial component in serving transformer-based autoregressive large language models (LLMs), enabling faster inference by storing previously computed KV vectors. However, its memory consumption scales linearly…
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…
We consider the family of integral operators $(K_{\alpha}f)(x)$ from $L^p[0,1]$ to $L^q[0,1]$ given by $$(K_{\alpha}f)(x)=\int_0^1(1-xy)^{\alpha -1}\,f(y)\,\operatorname{d}\!y, \qquad 0<\alpha<1.$$ The main objective is to find upper bounds…
In many real-world applications, it is undesirable to drastically change the problem solution after a small perturbation in the input, as unstable outputs can lead to costly transaction fees, privacy and security concerns, reduced user…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Some recent developments in the calculation of weak matrix elements on the lattice are reviewed. In particular, we concentrate on the application of MPSTV non-perturbative renormalization method to the operators relevant to kaon physics.…
This article present a parallel CPU implementation of Kannan algorithm for solving shortest vector problem in Block Korkin-Zolotarev lattice reduction method. Implementation based on Native POSIX Thread Library and show linear decrease of…
DeepLLL algorithm (Schnorr, 1994) is a famous variant of LLL lattice basis reduction algorithm, and PotLLL algorithm (Fontein et al., 2014) and $S^2$LLL algorithm (Yasuda and Yamaguchi, 2019) are recent polynomial-time variants of DeepLLL…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the classical velocity is renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The…
We present a new algorithm for computing a truncated Markov basis of a lattice. In general, this new algorithm is faster than existing methods. We then extend this new algorithm so that it solves the linear integer feasibility problem with…
We introduce a novel technique for ``lifting'' dimension lower bounds for linear sketches in the real-valued setting to dimension lower bounds for linear sketches with polynomially-bounded integer entries when the input is a…
Key-Value cache (\texttt{KV} \texttt{cache}) compression has emerged as a promising technique to optimize Large Language Model (LLM) serving. It primarily decreases the memory consumption of \texttt{KV} \texttt{cache} to reduce the…