Related papers: Elimination-based certificates for triangular equi…
Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a regularized surrogate with algorithms based on simple…
Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: First, we show optimised functional implementations of clausal and nonclausal…
The row (resp. column) rank profile of a matrix describes the staircase shape of its row (resp. column) echelon form. In an ISSAC'13 paper, we proposed a recursive Gaussian elimination that can compute simultaneously the row and column rank…
Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by…
Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate. Unfortunately, dual certificates may not exist under…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
The recently introduced notions of ranking functions and closure certificates utilize well-foundedness arguments to facilitate the verification of dynamical systems against $\omega$-regular properties. A ranking function and a closure…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real linear system $Ax=b$, where $A$ is an $m \times n$ matrix of…
Trust in applications is crucial, especially for fast and efficient hiring processes. Applicants must present credentials that employers can trust without delays or risk of fraudulent information. This paper introduces a framework for…
Recent progress towards theoretical interpretability guarantees for AI has been made with classifiers that are based on interactive proof systems. A prover selects a certificate from the datapoint and sends it to a verifier who decides the…
This work contributes an efficient algorithm to compute the Relative Pose problem (RPp) between calibrated cameras and certify the optimality of the solution, given a set of pair-wise feature correspondences affected by noise and probably…
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear…
The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a…
Browsers can detect malicious websites that are provisioned with forged or fake TLS/SSL certificates. However, they are not so good at detecting malicious websites if they are provisioned with mistakenly issued certificates or certificates…
In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…
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…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
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 study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…