Related papers: Elimination-based certificates for triangular equi…

In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible…

Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially…

Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that…

Certificates to a linear algebra computation are additional data structures for each output, which can be used by a-possibly randomized- verification algorithm that proves the correctness of each output. Wiede-mann's algorithm projects the…

For a given computational problem, a certificate is a piece of data that one (the prover) attaches to the output with the aim of allowing efficient verification (by the verifier) that this output is correct. Here, we consider the minimal…

For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…

We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…

Still to this day, academic credentials are primarily paper-based, and the process to verify the authenticity of such documents is costly, time-consuming, and prone to human error and fraud. Digitally signed documents facilitate a…

Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial…

We discuss optimization problems over convex cones in which membership is difficult to verify directly. In the standard theory of duality, vectors in the dual cone $K^*$ are associated with separating hyperplanes and interpreted as…

We investigate replicable learning algorithms. Ideally, we would like to design algorithms that output the same canonical model over multiple runs, even when different runs observe a different set of samples from the unknown data…

Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…

We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm…

We present new schemes for solving prefix authentication and secure relative timestamping. By casting a new light on antimonotone linking schemes, we improve upon the state of the art in prefix authentication, and in timestamping with…

While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are…

In this paper we give a first study of perfect copositive $n \times n$ matrices. They can be used to find rational certificates for completely positive matrices. We describe similarities and differences to classical perfect, positive…

Existing neural network verifiers compute a proof that each input is handled correctly under a given perturbation by propagating a symbolic abstraction of reachable values at each layer. This process is repeated from scratch independently…

Internal positivity offers a computationally cheap certificate for external (input-output) positivity of a linear time-invariant system. However, the drawback with this certificate lies in its realization dependency. Firstly, computing such…

Prior methods for retrieval of nearest neighbors in high dimensions are fast and approximate--providing probabilistic guarantees of returning the correct answer--or slow and exact performing an exhaustive search. We present Certified…

The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp. column) echelon form. We here propose a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank…