Neural networks are increasingly deployed in real-world safety-critical domains such as autonomous driving, aircraft collision avoidance, and malware detection. However, these networks have been shown to often mispredict on inputs with minor adversarial or even accidental perturbations. Consequences of such errors can be disastrous and even potentially fatal as shown by the recent Tesla autopilot crash. Thus, there is an urgent need for formal analysis systems that can rigorously check neural networks for violations of different safety properties such as robustness against adversarial perturbations within a certain $L$-norm of a given image. An effective safety analysis system for a neural network must be able to either ensure that a safety property is satisfied by the network or find a counterexample, i.e., an input for which the network will violate the property. Unfortunately, most existing techniques for performing such analysis struggle to scale beyond very small networks and the ones that can scale to larger networks suffer from high false positives and cannot produce concrete counterexamples in case of a property violation. In this paper, we present a new efficient approach for rigorously checking different safety properties of neural networks that significantly outperforms existing approaches by multiple orders of magnitude. Our approach can check different safety properties and find concrete counterexamples for networks that are 10$\times$ larger than the ones supported by existing analysis techniques. We believe that our approach to estimating tight output bounds of a network for a given input range can also help improve the explainability of neural networks and guide the training process of more robust neural networks.
Augusta University（奥古斯塔大学）；Southwest Jiaotong University（西南交通大学）
This paper aims to enhance the computational efficiency of safety verification of neural network control systems by developing a guaranteed neural network model reduction method. First, a concept of model reduction precision is proposed to describe the guaranteed distance between the outputs of a neural network and its reduced-size version. A reachability-based algorithm is proposed to accurately compute the model reduction precision. Then, by substituting a reduced-size neural network controller into the closed-loop system, an algorithm to compute the reachable set of the original system is d…
Advances in the field of Machine Learning and Deep Neural Networks (DNNs) has enabled rapid development of sophisticated and autonomous systems. However, the inherent complexity to rigorously assure the safe operation of such systems hinders their real-world adoption in safety-critical domains such as aerospace and medical devices. Hence, there is a surge in interest to explore the use of advanced mathematical techniques such as formal methods to address this challenge. In fact, the initial results of such efforts are promising. Along these lines, we propose the use of quantifier elimination (…
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for their applications in safety-critical systems.In this paper, the output reachable set computation and safety verification problems for a class of neural networks consisting of Rectified Linear Unit (ReLU) activation functions are addressed. A layer-by-layer approach is developed to compute output reachable set. The computation is formulated in the form of a set…
University of Liverpool（利物浦大学）；Lancaster University（兰卡斯特大学）
Safety concerns on the deep neural networks (DNNs) have been raised when they are applied to critical sectors. In this paper, we define safety risks by requesting the alignment of the network's decision with human perception. To enable a general methodology for quantifying safety risks, we define a generic safety property and instantiate it to express various safety risks. For the quantification of risks, we take the maximum radius of safe norm balls, in which no safety risk exists. The computation of the maximum safe radius is reduced to the computation of their respective Lipschitz metrics -…
This paper presents a specification-guided safety verification method for feedforward neural networks with general activation functions. As such feedforward networks are memoryless, they can be abstractly represented as mathematical functions, and the reachability analysis of the neural network amounts to interval analysis problems. In the framework of interval analysis, a computationally efficient formula which can quickly compute the output interval sets of a neural network is developed. Then, a specification-guided reachability algorithm is developed. Specifically, the bisection process in …
Samsung Research America（三星美国研究院）；Ecole Polytechnique（巴黎综合理工学院）；UC San Diego（加州大学圣地亚哥分校）；SRI International（斯坦福国际研究院）
We propose Trusted Neural Network (TNN) models, which are deep neural network models that satisfy safety constraints critical to the application domain. We investigate different mechanisms for incorporating rule-based knowledge in the form of first-order logic constraints into a TNN model, where rules that encode safety are accompanied by weights indicating their relative importance. This framework allows the TNN model to learn from knowledge available in form of data as well as logical rules. We propose multiple approaches for solving this problem: (a) a multi-headed model structure that allo…
Bridging Efficiency and Safety: Formal Verification of Neural Networks with Early Exits
The Hebrew University of Jerusalem, Israel（特拉维夫大学）；Bar Ilan University, Israel（巴伊兰大学）；Ben-Gurion University of the Negev, Israel（贝纳亚克大学）；University of California, Riverside, USA（加州大学河滨分校）
In this paper, we propose a system-level approach for verifying the safety of neural network controlled systems, combining a continuous-time physical system with a discrete-time neural network based controller. We assume a generic model for the controller that can capture both simple and complex behaviours involving neural networks. Based on this model, we perform a reachability analysis that soundly approximates the reachable states of the overall system, allowing to achieve a formal proof of safety. To this end, we leverage both validated simulation to approximate the behaviour of the physic…
Heriot-Watt University（赫瑞-瓦特大学）；Defence Science and Technology Laboratory（国防科学与技术实验室）；University of Liverpool（利物浦大学）
Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and continuous verification of their safe utilisation. Working towards addressing this challenge, this paper presents a principled novel safety argument framework for critical systems that utilise deep neural networks. The approach allows various forms of predictions, e.g., future reliability of passing some demands, or confidence on a required reliability level…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper we propose a set-boundary reachability method to investigate the safety verification problem of NNs from a topological perspective. Given an NN with an input set and a safe set, the safety verification problem is to determine whether all outputs of the NN resulting from the input set fall within the safe set. In our method, the home…
We present a method for computing exact reachable sets for deep neural networks with rectified linear unit (ReLU) activation. Our method is well-suited for use in rigorous safety analysis of robotic perception and control systems with deep neural network components. Our algorithm can compute both forward and backward reachable sets for a ReLU network iterated over multiple time steps, as would be found in a perception-action loop in a robotic system. Our algorithm is unique in that it builds the reachable sets by incrementally enumerating polyhedral cells in the input space, rather than iterat…
We investigate the issues of achieving sufficient rigor in the arguments for the safety of machine learning functions. By considering the known weaknesses of DNN-based 2D bounding box detection algorithms, we sharpen the metric of imprecise pedestrian localization by associating it with the safety goal. The sharpening leads to introducing a conservative post-processor after the standard non-max-suppression as a counter-measure. We then propose a semi-formal assurance case for arguing the effectiveness of the post-processor, which is further translated into formal proof obligations for demonstr…
We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit pr…
The increasing adoption of Reinforcement Learning in safety-critical systems domains such as autonomous vehicles, health, and aviation raises the need for ensuring their safety. Existing safety mechanisms such as adversarial training, adversarial detection, and robust learning are not always adapted to all disturbances in which the agent is deployed. Those disturbances include moving adversaries whose behavior can be unpredictable by the agent, and as a matter of fact harmful to its learning. Ensuring the safety of critical systems also requires methods that give formal guarantees on the behav…
Deep neural networks have achieved impressive experimental results in image classification, but can surprisingly be unstable with respect to adversarial perturbations, that is, minimal changes to the input image that cause the network to misclassify it. With potential applications including perception modules and end-to-end controllers for self-driving cars, this raises concerns about their safety. We develop a novel automated verification framework for feed-forward multi-layer neural networks based on Satisfiability Modulo Theory (SMT). We focus on safety of image classification decisions wit…
Neural networks serve as effective controllers in a variety of complex settings due to their ability to represent expressive policies. The complex nature of neural networks, however, makes their output difficult to verify and predict, which limits their use in safety-critical applications. While simulations provide insight into the performance of neural network controllers, they are not enough to guarantee that the controller will perform safely in all scenarios. To address this problem, recent work has focused on formal methods to verify properties of neural network outputs. For neural networ…
University of Nebraska-Lincoln（内布拉斯加大学林肯分校）；University of Virginia（弗吉尼亚大学）
In order to satisfy safety conditions, an agent may be constrained from acting freely. A safe controller can be designed a priori if an environment is well understood, but not when learning is employed. In particular, reinforcement learned (RL) controllers require exploration, which can be hazardous in safety critical situations. We study the benefits of giving structure to the constraints of a constrained Markov decision process by specifying them in formal languages as a step towards using safety methods from software engineering and controller synthesis. We instantiate these constraints as …
Deep learning methods can be used to produce control policies, but certifying their safety is challenging. The resulting networks are nonlinear and often very large. In response to this challenge, we present OVERT: a sound algorithm for safety verification of nonlinear discrete-time closed loop dynamical systems with neural network control policies. The novelty of OVERT lies in combining ideas from the classical formal methods literature with ideas from the newer neural network verification literature. The central concept of OVERT is to abstract nonlinear functions with a set of optimally tigh…
We study how state-of-the-art neural networks for 3D object detection using a single-stage pipeline can be made safety aware. We start with the safety specification (reflecting the capability of other components) that partitions the 3D input space by criticality, where the critical area employs a separate criterion on robustness under perturbation, quality of bounding boxes, and the tolerance over false negatives demonstrated on the training set. In the architecture design, we consider symbolic error propagation to allow feature-level perturbation. Subsequently, we introduce a specialized loss…
Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction. We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems. Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate. In particular, we show that the certificate network guarantees the safety of the …
Stanford University（斯坦福大学）；University of Pennsylvania（宾夕法尼亚大学）；Massachusetts Institute of Technology（麻省理工学院）
Learning-based methodologies increasingly find applications in safety-critical domains like autonomous driving and medical robotics. Due to the rare nature of dangerous events, real-world testing is prohibitively expensive and unscalable. In this work, we employ a probabilistic approach to safety evaluation in simulation, where we are concerned with computing the probability of dangerous events. We develop a novel rare-event simulation method that combines exploration, exploitation, and optimization techniques to find failure modes and estimate their rate of occurrence. We provide rigorous gua…
University of Konstanz（康斯坦茨大学）；Aalborg University（奥尔堡大学）
Deep neural networks (DNNs) are increasingly applied in safety-critical domains, such as self-driving cars, unmanned aircraft, and medical diagnosis. It is of fundamental importance to certify the safety of these DNNs, i.e. that they comply with a formal safety specification. While safety certification tools exactly answer this question, they are of no help in debugging unsafe DNNs, requiring the developer to iteratively verify and modify the DNN until safety is eventually achieved. Hence, a repair technique needs to be developed that can produce a safe DNN automatically. To address this need,…
This paper introduces differentiable higher-order control barrier functions (CBF) that are end-to-end trainable together with learning systems. CBFs are usually overly conservative, while guaranteeing safety. Here, we address their conservativeness by softening their definitions using environmental dependencies without loosing safety guarantees, and embed them into differentiable quadratic programs. These novel safety layers, termed a BarrierNet, can be used in conjunction with any neural network-based controller, and can be trained by gradient descent. BarrierNet allows the safety constraints…
fortiss - Research Institute of the Free State of Bavaria（福蒂斯-巴伐利亚自由州研究院）
Can engineering neural networks be approached in a disciplined way similar to how engineers build software for civil aircraft? We present nn-dependability-kit, an open-source toolbox to support safety engineering of neural networks for autonomous driving systems. The rationale behind nn-dependability-kit is to consider a structured approach (via Goal Structuring Notation) to argue the quality of neural networks. In particular, the tool realizes recent scientific results including (a) novel dependability metrics for indicating sufficient elimination of uncertainties in the product life cycle, (…
DENSO AUTOMOTIVE Deutschland GmbH（电装汽车德国有限公司）；ISCAS（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Deploying deep neural networks (DNNs) as core functions in autonomous driving creates unique verification and validation challenges. In particular, the continuous engineering paradigm of gradually perfecting a DNN-based perception can make the previously established result of safety verification no longer valid. This can occur either due to the newly encountered examples (i.e., input domain enlargement) inside the Operational Design Domain or due to the subsequent parameter fine-tuning activities of a DNN. This paper considers approaches to transfer results established in the previous DNN safe…
The prediction of workers' safety behaviour can help identify vulnerable workers who intend to undertake unsafe behaviours and be useful in the design of management practices to minimise the occurrence of accidents. The latest literature has evidenced that there is within-population diversity that leads people's intended safety behaviours in the workplace, which are found to vary among individuals as a function of their personality traits. In this study, an innovative forecasting model, which employs neural network algorithms, is developed to numerically simulate the predictive relationship be…
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the output of neural networks when their input changes within a bounded set. In this paper, we propose a semidefinite programming (SDP) framework to address this problem for feed-forward neural networks with general activation functions and input uncertainty sets. Our main idea is to abstract various properties of activation functions (e.g., monotonicity, bound…
Runtime energy management has become quintessential for multi-sensor autonomous systems at the edge for achieving high performance given the platform constraints. Typical for such systems, however, is to have their controllers designed with formal guarantees on safety that precede in priority such optimizations, which in turn limits their application in real settings. In this paper, we propose a novel energy optimization framework that is aware of the autonomous system's safety state, and leverages it to regulate the application of energy optimization methods so that the system's formal safety…
Inference using deep neural networks is often outsourced to the cloud since it is a computationally demanding task. However, this raises a fundamental issue of trust. How can a client be sure that the cloud has performed inference correctly? A lazy cloud provider might use a simpler but less accurate model to reduce its own computational load, or worse, maliciously modify the inference results sent to the client. We propose SafetyNets, a framework that enables an untrusted server (the cloud) to provide a client with a short mathematical proof of the correctness of inference tasks that they per…
Neural Networks are being integrated into safety critical systems, e.g., perception systems for autonomous vehicles, which require trained networks to perform safely in novel scenarios. It is challenging to verify neural networks because their decisions are not explainable, they cannot be exhaustively tested, and finite test samples cannot capture the variation across all operating conditions. Existing work seeks to train models robust to new scenarios via domain adaptation, style transfer, or few-shot learning. But these techniques fail to predict how a trained model will perform when the ope…
University of Liverpool（利物浦大学）；University of Oxford（牛津大学）；Lancaster University（兰卡斯特大学）；Defence Science and Technology Laboratory (Dstl)（国防科学技术实验室）；Queen’s University Belfast（贝尔法斯特女王大学）
In the past few years, significant progress has been made on deep neural networks (DNNs) in achieving human-level performance on several long-standing tasks. With the broader deployment of DNNs on various applications, the concerns over their safety and trustworthiness have been raised in public, especially after the widely reported fatal incidents involving self-driving cars. Research to address these concerns is particularly active, with a significant number of papers released in the past few years. This survey paper conducts a review of the current research effort into making DNNs safe and …
Intel（英特尔）；University of British Columbia（不列颠哥伦比亚大学）
Convolutional neural networks (CNNs) have become an established part of numerous safety-critical computer vision applications, including human robot interactions and automated driving. Real-world implementations will need to guarantee their robustness against hardware soft errors corrupting the underlying platform memory. Based on the previously observed efficacy of activation clipping techniques, we build a prototypical safety case for classifier CNNs by demonstrating that range supervision represents a highly reliable fault detector and mitigator with respect to relevant bit flips, adopting …
fortiss - Landesforschungsinstitut des Freistaats Bayern（巴伐利亚州fortiss研究机构）
We propose a methodology for designing dependable Artificial Neural Networks (ANN) by extending the concepts of understandability, correctness, and validity that are crucial ingredients in existing certification standards. We apply the concept in a concrete case study in designing a high-way ANN-based motion predictor to guarantee safety properties such as impossibility for the ego vehicle to suggest moving to the right lane if there exists another vehicle on its right.
Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem that limits the wider adoption of autonomous systems in safety-critical applications. One promising solution to address this problem is barrier functions. The composition of a barrier function with a stochastic system forms a supermartingale, thus enabling the computation of the probability that the system stays in a safe set over a finite time horizon via martingale inequalities. However, existing approaches to find barrier functions for stochastic systems generally rely on convex optim…
Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics
Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University（机械工程数据科学研究所（DSME），亚琛工业大学）；Institute of Climate and Energy Systems (ICE), Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH（气候与能源系统研究所（ICE），能源系统工程（ICE-1），焦耳研究中心有限公司）
We propose a framework based on Recurrent Neural Networks (RNNs) to determine an optimal control strategy for a discrete-time system that is required to satisfy specifications given as Signal Temporal Logic (STL) formulae. RNNs can store information of a system over time, thus, enable us to determine satisfaction of the dynamic temporal requirements specified in STL formulae. Given a STL formula, a dataset of satisfying system executions and corresponding control policies, we can use RNNs to predict a control policy at each time based on the current and previous states of system. We use Contro…
When learning to perform motor tasks in a simulated environment, neural networks must be allowed to explore their action space to discover new potentially viable solutions. However, in an online learning scenario with physical hardware, this exploration must be constrained by relevant safety considerations in order to avoid damage to the agent's hardware and environment. We aim to address this problem by training a neural network, which we will refer to as a "safety network", to estimate the region of attraction (ROA) of a controlled autonomous dynamical system. This safety network can thereby…
DENSO AUTOMOTIVE Deutschland GmbH（电装汽车德国有限公司）；fortiss - Research Institute of the Free State of Bavaria（巴伐利亚自由州fortiss研究院）；Audi AG（奥迪股份公司）
We study the problem of safety verification of direct perception neural networks, where camera images are used as inputs to produce high-level features for autonomous vehicles to make control decisions. Formal verification of direct perception neural networks is extremely challenging, as it is difficult to formulate the specification that requires characterizing input as constraints, while the number of neurons in such a network can reach millions. We approach the specification problem by learning an input property characterizer which carefully extends a direct perception neural network at clo…
