Related papers: Certificates for triangular equivalence and rank p…
In this paper, we propose a novel approach to consider multiple dimensions of relevance beyond topicality in cross-encoder re-ranking. On the one hand, current multidimensional retrieval models often use na\"ive solutions at the re-ranking…
Neural certificates have emerged as a powerful tool in cyber-physical systems control, providing witnesses of correctness. These certificates, such as barrier functions, often learned alongside control policies, once verified, serve as…
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…
In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal…
Retrieval-augmented generation (RAG) is increasingly deployed in enterprise search and document-centric assistants, where responses must be grounded in long and complex source materials. In practice, verifying that generated answers…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…
We design and analyze new protocols to verify the correctness of various computations on matrices over the ring F[x] of univariate polynomials over a field F. For the sake of efficiency, and because many of the properties we verify are…
Let $\mathbb{Q}$ (resp. $\mathbb{R}$) be the field of rational (resp. real) numbers and $X = (X_1, \ldots, X_n)$ be variables. Deciding the non-negativity of polynomials in $\mathbb{Q}[X]$ over $\mathbb{R}^n$ or over semi-algebraic domains…
We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized…
Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…
With the emergence of cloud computing services, computationally weak devices (Clients) can delegate expensive tasks to more powerful entities (Servers). This raises the question of verifying a result at a lower cost than that of recomputing…
We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on algebraic properties, our algorithm exploits the regularity…
We provide two certificates of convexity for arbitrary basic semi-algebraic sets of $\R^n$. The first one is based on a necessary and sufficient condition whereas the second one is based on a sufficient (but simpler) condition only. Both…
We propose the first fast and certifiable algorithm for the registration of two sets of 3D points in the presence of large amounts of outlier correspondences. We first reformulate the registration problem using a Truncated Least Squares…
A linear-time certifying algorithm for 3-edge-connectivity is presented. Given an undirected graph G, if G is 3-edge-connected, the algorithm generates a construction sequence as a positive certificate for G. Otherwise, the algorithm…
Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear Algebra Appl., 2020] allow us to obtain local information…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…