Related papers: Enabling certification of verification-agnostic ne…

Semidefinite programming is an important optimization task, often used in time-sensitive applications. Though they are solvable in polynomial time, in practice they can be too slow to be used in online, i.e. real-time applications. Here we…

Maximum A posteriori Probability (MAP) inference in graphical models amounts to solving a graph-structured combinatorial optimization problem. Popular inference algorithms such as belief propagation (BP) and generalized belief propagation…

Quadratic programs with box constraints involve minimizing a possibly nonconvex quadratic function subject to lower and upper bounds on each variable. This is a well-known NP-hard problem that frequently arises in various applications. We…

We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…

This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite…

Formal verification of neural networks is critical for their safe adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and…

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim…

The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the…

We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…

Neural networks are susceptible to privacy attacks. To date, no verifier can reason about the privacy of individuals participating in the training set. We propose a new privacy property, called local differential classification privacy…

We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…

Geometric image transformations that arise in the real world, such as scaling and rotation, have been shown to easily deceive deep neural networks (DNNs). Hence, training DNNs to be certifiably robust to these perturbations is critical.…

In this paper, we study the noise sensitivity of the semidefinite program (SDP) proposed for direct data-driven infinite-horizon linear quadratic regulator (LQR) problem for discrete-time linear time-invariant systems. While this SDP is…

The increasing integration of deep neural networks in critical systems has spawned a theoretical and practical interest in formally guaranteeing safety properties about their behavior. To achieve this, contemporary verification algorithms…

Certifiable robustness is a highly desirable property for adopting deep neural networks (DNNs) in safety-critical scenarios, but often demands tedious computations to establish. The main hurdle lies in the massive amount of non-linearity in…

Deep neural networks have been widely adopted in many vision and robotics applications with visual inputs. It is essential to verify its robustness against semantic transformation perturbations, such as brightness and contrast. However,…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

Network compression reduces the computational complexity and memory consumption of deep neural networks by reducing the number of parameters. In SVD-based network compression, the right rank needs to be decided for every layer of the…