Related papers: Vertex-based reachability analysis for verifying R…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…

Reverse engineering deep ReLU networks is a critical problem in understanding the complex behavior and interpretability of neural networks. In this research, we present a novel method for reconstructing deep ReLU networks by leveraging…

In this paper, we propose a decision procedure of reachability for linear system {\xi}' = A{\xi} + u, where the matrix A's eigenvalues can be arbitrary algebraic numbers and the input u is a vector of trigonometric-exponential polynomials.…

We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…

ReLU is widely seen as the default choice for activation functions in neural networks. However, there are cases where more complicated functions are required. In particular, recurrent neural networks (such as LSTMs) make extensive use of…

Feedforward neural networks are widely used in autonomous systems, particularly for control and perception tasks within the system loop. However, their vulnerability to adversarial attacks necessitates formal verification before deployment…

Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…

Training a one-node neural network with ReLU activation function (One-Node-ReLU) is a fundamental optimization problem in deep learning. In this paper, we begin with proving the NP-hardness of training One-Node-ReLU. We then present an…

We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more…

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs)…

Most work on the formal verification of neural networks has focused on bounding the set of outputs that correspond to a given set of inputs (for example, bounded perturbations of a nominal input). However, many use cases of neural network…

Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…

While metric and similarity learning has been extensively studied from several theoretical perspectives, a rigorous understanding of its generalization performance is still lacking. In this paper, we investigate the generalization behavior…

In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…

One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…

Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before deployment, which are…

Given a data graph G, a source vertex u and a target vertex v of a reachability query, the reachability query is used to answer whether there exists a path from u to v in G. Reachability query processing is one of the fundamental operations…

We consider the problem of learning an unknown ReLU network with respect to Gaussian inputs and obtain the first nontrivial results for networks of depth more than two. We give an algorithm whose running time is a fixed polynomial in the…

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…