Related papers: A Unified View of SDP-based Neural Network Verific…
We introduce S++, a simple, robust, and deployable framework for training a neural network (NN) using private data from multiple sources, using secret-shared secure function evaluation. In short, consider a virtual third party to whom every…
Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide…
We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…
We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general…
We present a novel analysis of semidefinite programs (SDPs) with positive duality gaps, i.e. different optimal values in the primal and dual problems. These SDPs are extremely pathological, often unsolvable, and also serve as models of more…
This work proposes a novel approach to reinforce localization security in wireless networks in the presence of malicious nodes that are able to manipulate (spoof) radio measurements. It substitutes the original measurement model by another…
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…
The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…
Neural network verifiers based on linear bound propagation scale impressively to massive models but can be surprisingly loose when neuron coupling is crucial. Conversely, semidefinite programming (SDP) verifiers capture inter-neuron…
We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task, with the proof of correctness generated by an automated verification algorithm without any human input. Prior work on…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Formal verification of transformers has become increasingly important due to their widespread deployment in safety-critical applications. Compared to classic neural networks, the inferences of transformers involve highly complex…
Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist…
Neural networks have demonstrated considerable success on a wide variety of real-world problems. However, networks trained only to optimize for training accuracy can often be fooled by adversarial examples - slightly perturbed inputs that…
We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with…