相关论文: Vertex-based reachability analysis for verifying R…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

Even though neural networks are being increasingly deployed in safety-critical control applications, it remains difficult to enforce constraints on their output, meaning that it is hard to guarantee safety in such settings. While many…

Deep neural networks are an attractive tool for compressing the control policy lookup tables in systems such as the Airborne Collision Avoidance System (ACAS). It is vital to ensure the safety of such neural controllers via verification…

Theoretical analyses of Empirical Risk Minimization (ERM) are standardly framed within the Real-RAM model of computation. In this setting, training even simple neural networks is known to be $\exists \mathbb{R}$-complete -- a complexity…

This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability…

In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit…

This paper presents a new reachability analysis approach to compute interval over-approximations of the output set of feedforward neural networks with input uncertainty. We adapt to neural networks an existing mixed-monotonicity method for…

Verification of deep neural networks has witnessed a recent surge of interest, fueled by success stories in diverse domains and by abreast concerns about safety and security in envisaged applications. Complexity and sheer size of such…

We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results. In particular, we generalize the existing result on the existence of deep discontinuous phase in ReLU networks to…

The decision logic for the ACAS X family of aircraft collision avoidance systems is represented as a large numeric table. Due to storage constraints of certified avionics hardware, neural networks have been suggested as a way to…

Deep Reinforcement Learning (DRL) has achieved impressive performance in robotics and autonomous systems (RAS). A key challenge to its deployment in real-life operations is the presence of spuriously unsafe DRL policies. Unexplored states…

Autonomous cyber-physical systems (CPS) rely on the correct operation of numerous components, with state-of-the-art methods relying on machine learning (ML) and artificial intelligence (AI) components in various stages of sensing and…

In studying the expressiveness of neural networks, an important question is whether there are functions which can only be approximated by sufficiently deep networks, assuming their size is bounded. However, for constant depths, existing…

In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such as: Given symbolic specifications of allowed inputs and outputs in form of Linear…

When autonomous vehicles encounter untrained scenarios, ensuring safety hinges on effective safety verification to prevent accidents stemming from unexpected model decisions. Reachability analysis, a method of safety verification, offers…

We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…

The literature on reachability analysis methods for neural networks currently only focuses on uncertainties on the network's inputs. In this paper, we introduce two new approaches for the reachability analysis of neural networks with…

Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…

Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges,…

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike previous single-neuron relaxations which focus only on the…