Related papers: Elimination-based certificates for triangular equi…
Incomplete pairwise comparison matrices are increasingly employed to save resources and reduce cognitive load by collecting only a subset of all possible pairwise comparisons. We present their graph representation and some completion…
Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or…
The modern Internet is highly dependent on trust communicated via certificates. However, in some cases, certificates become untrusted, and it is necessary to revoke them. In practice, the problem of secure revocation is still open.…
Signature is widely used in human daily lives, and serves as a supplementary characteristic for verifying human identity. However, there is rare work of verifying signature. In this paper, we propose a few deep learning architectures to…
Polyhedra form an established abstract domain for inferring runtime properties of programs using abstract interpretation. Computations on them need to be certified for the whole static analysis results to be trusted. In this work, we look…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal J generated by the kernel of a truncated moment matrix and…
Evaluating the permanent of a matrix is a fundamental computation that emerges in many domains, including traditional fields like computational complexity theory, graph theory, many-body quantum theory and emerging disciplines like machine…
Modern SAT or QBF solvers are expected to produce correctness certificates. However, certificates have worst-case exponential size (unless NP=coNP), and at recent SAT competitions the largest certificates of unsatisfiability are starting to…
Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based…
Cross-Encoder (CE) and Dual-Encoder (DE) models are two fundamental approaches for query-document relevance in information retrieval. To predict relevance, CE models use joint query-document embeddings, while DE models maintain factorized…
We propose a new approach to computing global minimizers of singular value functions in two real variables. Specifically, we present new algorithms to compute the Kreiss constant of a matrix and the distance to uncontrollability of a linear…
This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…
To address a looming crisis of unreproducible evaluation for named entity recognition, we propose guidelines and introduce SeqScore, a software package to improve reproducibility. The guidelines we propose are extremely simple and center…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…
Every m by n matrix A with rank r has exactly r independent rows and r independent columns. The fact has become the most fundamental theorem in linear algebra such that we may favor it in an unconscious way. The sole aim of this paper is to…
Local certification is the area of distributed network computing asking the following question: How to certify to the nodes of a network that a global property holds, if they are limited to a local verification? In this area, it is often…
In guaranteeing the absence of adversarial examples in an instance's neighbourhood, certification mechanisms play an important role in demonstrating neural net robustness. In this paper, we ask if these certifications can compromise the…
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…
We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and…