Guy Katz

Guy Amir, Davide Corsi, Raz Yerushalmi et al.

Deep reinforcement learning (DRL) has become a dominant deep-learning paradigm for tasks where complex policies are learned within reactive systems. Unfortunately, these policies are known to be susceptible to bugs. Despite significant progress in DNN verification, there has been little work demonstrating the use of modern verification tools on real-world, DRL-controlled systems. In this case study, we attempt to begin bridging this gap, and focus on the important task of mapless robotic navigation -- a classic robotics problem, in which a robot, usually controlled by a DRL agent, needs to efficiently and safely navigate through an unknown arena towards a target. We demonstrate how modern verification engines can be used for effective model selection, i.e., selecting the best available policy for the robot in question from a pool of candidate policies. Specifically, we use verification to detect and rule out policies that may demonstrate suboptimal behavior, such as collisions and infinite loops. We also apply verification to identify models with overly conservative behavior, thus allowing users to choose superior policies, which might be better at finding shorter paths to a target. To validate our work, we conducted extensive experiments on an actual robot, and confirmed that the suboptimal policies detected by our method were indeed flawed. We also demonstrate the superiority of our verification-driven approach over state-of-the-art, gradient attacks. Our work is the first to establish the usefulness of DNN verification in identifying and filtering out suboptimal DRL policies in real-world robots, and we believe that the methods presented here are applicable to a wide range of systems that incorporate deep-learning-based agents.

Xingwu Guo, Ziwei Zhou, Yueling Zhang et al.

Occlusion is a prevalent and easily realizable semantic perturbation to deep neural networks (DNNs). It can fool a DNN into misclassifying an input image by occluding some segments, possibly resulting in severe errors. Therefore, DNNs planted in safety-critical systems should be verified to be robust against occlusions prior to deployment. However, most existing robustness verification approaches for DNNs are focused on non-semantic perturbations and are not suited to the occlusion case. In this paper, we propose the first efficient, SMT-based approach for formally verifying the occlusion robustness of DNNs. We formulate the occlusion robustness verification problem and prove it is NP-complete. Then, we devise a novel approach for encoding occlusions as a part of neural networks and introduce two acceleration techniques so that the extended neural networks can be efficiently verified using off-the-shelf, SMT-based neural network verification tools. We implement our approach in a prototype called OccRob and extensively evaluate its performance on benchmark datasets with various occlusion variants. The experimental results demonstrate our approach's effectiveness and efficiency in verifying DNNs' robustness against various occlusions, and its ability to generate counterexamples when these DNNs are not robust.

Guy Amir, Osher Maayan, Tom Zelazny et al.

Deep neural networks (DNNs) are the workhorses of deep learning, which constitutes the state of the art in numerous application domains. However, DNN-based decision rules are notoriously prone to poor generalization, i.e., may prove inadequate on inputs not encountered during training. This limitation poses a significant obstacle to employing deep learning for mission-critical tasks, and also in real-world environments that exhibit high variability. We propose a novel, verification-driven methodology for identifying DNN-based decision rules that generalize well to new input domains. Our approach quantifies generalization to an input domain by the extent to which decisions reached by independently trained DNNs are in agreement for inputs in this domain. We show how, by harnessing the power of DNN verification, our approach can be efficiently and effectively realized. We evaluate our verification-based approach on three deep reinforcement learning (DRL) benchmarks, including a system for Internet congestion control. Our results establish the usefulness of our approach. More broadly, our work puts forth a novel objective for formal verification, with the potential for mitigating the risks associated with deploying DNN-based systems in the wild.

Guy Amir, Ziv Freund, Guy Katz et al.

In this short paper, we present our ongoing work on the veriFIRE project -- a collaboration between industry and academia, aimed at using verification for increasing the reliability of a real-world, safety-critical system. The system we target is an airborne platform for wildfire detection, which incorporates two deep neural networks. We describe the system and its properties of interest, and discuss our attempts to verify the system's consistency, i.e., its ability to continue and correctly classify a given input, even if the wildfire it describes increases in intensity. We regard this work as a step towards the incorporation of academic-oriented verification tools into real-world systems of interest.

Adiel Ashrov, Guy Katz

Deep neural networks (DNNs) have become a crucial instrument in the software development toolkit, due to their ability to efficiently solve complex problems. Nevertheless, DNNs are highly opaque, and can behave in an unexpected manner when they encounter unfamiliar input. One promising approach for addressing this challenge is by extending DNN-based systems with hand-crafted override rules, which override the DNN's output when certain conditions are met. Here, we advocate crafting such override rules using the well-studied scenario-based modeling paradigm, which produces rules that are simple, extensible, and powerful enough to ensure the safety of the DNN, while also rendering the system more translucent. We report on two extensive case studies, which demonstrate the feasibility of the approach; and through them, propose an extension to scenario-based modeling, which facilitates its integration with DNN components. We regard this work as a step towards creating safer and more reliable DNN-based systems and models.

Natan Levy, Raz Yerushalmi, Guy Katz

Deep neural networks (DNNs) are at the forefront of cutting-edge technology, and have been achieving remarkable performance in a variety of complex tasks. Nevertheless, their integration into safety-critical systems, such as in the aerospace or automotive domains, poses a significant challenge due to the threat of adversarial inputs: perturbations in inputs that might cause the DNN to make grievous mistakes. Multiple studies have demonstrated that even modern DNNs are susceptible to adversarial inputs, and this risk must thus be measured and mitigated to allow the deployment of DNNs in critical settings. Here, we present gRoMA (global Robustness Measurement and Assessment), an innovative and scalable tool that implements a probabilistic approach to measure the global categorial robustness of a DNN. Specifically, gRoMA measures the probability of encountering adversarial inputs for a specific output category. Our tool operates on pre-trained, black-box classification DNNs, and generates input samples belonging to an output category of interest. It measures the DNN's susceptibility to adversarial inputs around these inputs, and aggregates the results to infer the overall global categorial robustness of the DNN up to some small bounded statistical error. We evaluate our tool on the popular Densenet DNN model over the CIFAR10 dataset. Our results reveal significant gaps in the robustness of the different output categories. This experiment demonstrates the usefulness and scalability of our approach and its potential for allowing DNNs to be deployed within critical systems of interest.

Udayan Mandal, Guy Amir, Haoze Wu et al.

In recent years, deep reinforcement learning (DRL) approaches have generated highly successful controllers for a myriad of complex domains. However, the opaque nature of these models limits their applicability in aerospace systems and safety-critical domains, in which a single mistake can have dire consequences. In this paper, we present novel advancements in both the training and verification of DRL controllers, which can help ensure their safe behavior. We showcase a design-for-verification approach utilizing k-induction and demonstrate its use in verifying liveness properties. In addition, we also give a brief overview of neural Lyapunov Barrier certificates and summarize their capabilities on a case study. Finally, we describe several other novel reachability-based approaches which, despite failing to provide guarantees of interest, could be effective for verification of other DRL systems, and could be of further interest to the community.

Jonathan Spiegelman, Guy Amir, Guy Katz

Deep Active Learning (DAL) aims to reduce labeling costs in neural-network training by prioritizing the most informative unlabeled samples for annotation. Beyond selecting which samples to label, several DAL approaches further enhance data efficiency by augmenting the training set with synthetic inputs that do not require additional manual labeling. In this work, we investigate how augmenting the training data with adversarial inputs that violate robustness constraints can improve DAL performance. We show that adversarial examples generated via formal verification contribute substantially more than those produced by standard, gradient-based attacks. We apply this extension to multiple modern DAL techniques, as well as to a new technique that we propose, and show that it yields significant improvements in model generalization across standard benchmarks.

Udayan Mandal, Guy Amir, Haoze Wu et al.

Deep reinforcement learning (DRL) is a powerful machine learning paradigm for generating agents that control autonomous systems. However, the ``black box'' nature of DRL agents limits their deployment in real-world safety-critical applications. A promising approach for providing strong guarantees on an agent's behavior is to use Neural Lyapunov Barrier (NLB) certificates, which are learned functions over the system whose properties indirectly imply that an agent behaves as desired. However, NLB-based certificates are typically difficult to learn and even more difficult to verify, especially for complex systems. In this work, we present a novel method for training and verifying NLB-based certificates for discrete-time systems. Specifically, we introduce a technique for certificate composition, which simplifies the verification of highly-complex systems by strategically designing a sequence of certificates. When jointly verified with neural network verification engines, these certificates provide a formal guarantee that a DRL agent both achieves its goals and avoids unsafe behavior. Furthermore, we introduce a technique for certificate filtering, which significantly simplifies the process of producing formally verified certificates. We demonstrate the merits of our approach with a case study on providing safety and liveness guarantees for a DRL-controlled spacecraft.

Marco Casadio, Tanvi Dinkar, Ekaterina Komendantskaya et al.

Machine Learning (ML) has exhibited substantial success in the field of Natural Language Processing (NLP). For example large language models have empirically proven to be capable of producing text of high complexity and cohesion. However, they are prone to inaccuracies and hallucinations. As these systems are increasingly integrated into real-world applications, ensuring their safety and reliability becomes a primary concern. There are safety critical contexts where such models must be robust to variability or attack, and give guarantees over their output. Computer Vision had pioneered the use of formal verification of neural networks for such scenarios and developed common verification standards and pipelines, leveraging precise formal reasoning about geometric properties of data manifolds. In contrast, NLP verification methods have only recently appeared in the literature. While presenting sophisticated algorithms, these papers have not yet crystallised into a common methodology. They are often light on the pragmatical issues of NLP verification and the area remains fragmented. In this paper, we attempt to distil and evaluate general components of an NLP verification pipeline, that emerges from the progress in the field to date. Our contributions are two-fold. Firstly, we propose a general methodology to analyse the effect of the embedding gap, a problem that refers to the discrepancy between verification of geometric subspaces and the semantic meaning of sentences, which the geometric subspaces are supposed to represent. We propose a number of practical NLP methods that can help to quantify the effects of the embedding gap. Secondly, we give a general method for training and verification of neural networks that leverages a more precise geometric estimation of semantic similarity of sentences in the embedding space and helps to overcome the effects of the embedding gap in practice.

Reda Marzouk, Shahaf Bassan, Guy Katz et al.

Recent studies have examined the computational complexity of computing Shapley additive explanations (also known as SHAP) across various models and distributions, revealing their tractability or intractability in different settings. However, these studies primarily focused on a specific variant called Conditional SHAP, though many other variants exist and address different limitations. In this work, we analyze the complexity of computing a much broader range of such variants, including Conditional, Interventional, and Baseline SHAP, while exploring both local and global computations. We show that both local and global Interventional and Baseline SHAP can be computed in polynomial time for various ML models under Hidden Markov Model distributions, extending popular algorithms such as TreeSHAP beyond empirical distributions. On the downside, we prove intractability results for these variants over a wide range of neural networks and tree ensembles. We believe that our results emphasize the intricate diversity of computing Shapley values, demonstrating how their complexity is substantially shaped by both the specific SHAP variant, the model type, and the distribution.

Lucas C. Cordeiro, Matthew L. Daggitt, Julien Girard-Satabin et al.

Neural network verification is a new and rapidly developing field of research. So far, the main priority has been establishing efficient verification algorithms and tools, while proper support from the programming language perspective has been considered secondary or unimportant. Yet, there is mounting evidence that insights from the programming language community may make a difference in the future development of this domain. In this paper, we formulate neural network verification challenges as programming language challenges and suggest possible future solutions.

Ophir M. Carmel, Guy Katz

Deep reinforcement learning (DRL) has proven extremely useful in a large variety of application domains. However, even successful DRL-based software can exhibit highly undesirable behavior. This is due to DRL training being based on maximizing a reward function, which typically captures general trends but cannot precisely capture, or rule out, certain behaviors of the system. In this paper, we propose a novel framework aimed at drastically reducing the undesirable behavior of DRL-based software, while maintaining its excellent performance. In addition, our framework can assist in providing engineers with a comprehensible characterization of such undesirable behavior. Under the hood, our approach is based on extracting decision tree classifiers from erroneous state-action pairs, and then integrating these trees into the DRL training loop, penalizing the system whenever it performs an error. We provide a proof-of-concept implementation of our approach, and use it to evaluate the technique on three significant case studies. We find that our approach can extend existing frameworks in a straightforward manner, and incurs only a slight overhead in training time. Further, it incurs only a very slight hit to performance, or even in some cases - improves it, while significantly reducing the frequency of undesirable behavior.

Guy Katz, Natan Levy, Idan Refaeli et al.

Software development in the aerospace domain requires adhering to strict, high-quality standards. While there exist regulatory guidelines for commercial software in this domain (e.g., ARP-4754 and DO-178), these do not apply to software with deep neural network (DNN) components. Consequently, it is unclear how to allow aerospace systems to benefit from the deep learning revolution. Our work here seeks to address this challenge with a novel, output-centric approach for DNN certification. Our method employs statistical verification techniques, and has the key advantage of being able to flag specific inputs for which the DNN's output may be unreliable - so that they may be later inspected by a human expert. To achieve this, our method conducts a statistical analysis of the DNN's predictions for other, nearby inputs, in order to detect inconsistencies. This is in contrast to existing techniques, which typically attempt to certify the entire DNN, as opposed to individual outputs. Our method uses the DNN as a black-box, and makes no assumptions about its topology. We hope that this work constitutes another step towards integrating DNNs in safety-critical applications - especially in the aerospace domain, where high standards of quality and reliability are crucial.

Idan Refaeli, Guy Katz

Deep neural networks (DNNs) have become increasingly popular in recent years. However, despite their many successes, DNNs may also err and produce incorrect and potentially fatal outputs in safety-critical settings, such as autonomous driving, medical diagnosis, and airborne collision avoidance systems. Much work has been put into detecting such erroneous behavior in DNNs, e.g., via testing or verification, but removing these errors after their detection has received lesser attention. We present here a new tool, called 3M-DNN, for repairing a given DNN, which is known to err on some set of inputs. The novel repair procedure implemented in 3M-DNN computes a modification to the network's weights that corrects its behavior, and attempts to minimize this change via a sequence of calls to a backend, black-box DNN verification engine. To the best of our knowledge, our method is the first one that allows repairing the network by simultaneously modifying multiple layers. This is achieved by splitting the network into sub-networks, and applying a single-layer repairing technique to each component. We evaluated 3M-DNN tool on an extensive set of benchmarks, obtaining promising results.

Guy Amir, Haoze Wu, Clark Barrett et al.

Deep learning has emerged as an effective approach for creating modern software systems, with neural networks often surpassing hand-crafted systems. Unfortunately, neural networks are known to suffer from various safety and security issues. Formal verification is a promising avenue for tackling this difficulty, by formally certifying that networks are correct. We propose an SMT-based technique for verifying Binarized Neural Networks - a popular kind of neural network, where some weights have been binarized in order to render the neural network more memory and energy efficient, and quicker to evaluate. One novelty of our technique is that it allows the verification of neural networks that include both binarized and non-binarized components. Neural network verification is computationally very difficult, and so we propose here various optimizations, integrated into our SMT procedure as deduction steps, as well as an approach for parallelizing verification queries. We implement our technique as an extension to the Marabou framework, and use it to evaluate the approach on popular binarized neural network architectures.

Haoze Wu, Alex Ozdemir, Aleksandar Zeljić et al.

Inspired by recent successes with parallel optimization techniques for solving Boolean satisfiability, we investigate a set of strategies and heuristics that aim to leverage parallel computing to improve the scalability of neural network verification. We introduce an algorithm based on partitioning the verification problem in an iterative manner and explore two partitioning strategies, that work by partitioning the input space or by case splitting on the phases of the neuron activations, respectively. We also introduce a highly parallelizable pre-processing algorithm that uses the neuron activation phases to simplify the neural network verification problems. An extensive experimental evaluation shows the benefit of these techniques on both existing benchmarks and new benchmarks from the aviation domain. A preliminary experiment with ultra-scaling our algorithm using a large distributed cloud-based platform also shows promising results.

Lindsey Kuper, Guy Katz, Justin Gottschlich et al.

The increasing use of deep neural networks for safety-critical applications, such as autonomous driving and flight control, raises concerns about their safety and reliability. Formal verification can address these concerns by guaranteeing that a deep learning system operates as intended, but the state of the art is limited to small systems. In this work-in-progress report we give an overview of our work on mitigating this difficulty, by pursuing two complementary directions: devising scalable verification techniques, and identifying design choices that result in deep learning systems that are more amenable to verification.

Guy Katz, Clark Barrett, David L. Dill et al.

Autonomous vehicles are highly complex systems, required to function reliably in a wide variety of situations. Manually crafting software controllers for these vehicles is difficult, but there has been some success in using deep neural networks generated using machine-learning. However, deep neural networks are opaque to human engineers, rendering their correctness very difficult to prove manually; and existing automated techniques, which were not designed to operate on neural networks, fail to scale to large systems. This paper focuses on proving the adversarial robustness of deep neural networks, i.e. proving that small perturbations to a correctly-classified input to the network cannot cause it to be misclassified. We describe some of our recent and ongoing work on verifying the adversarial robustness of networks, and discuss some of the open questions we have encountered and how they might be addressed.

Guy Katz, Clark Barrett, David Dill et al.

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees about their behavior. We present a novel, scalable, and efficient technique for verifying properties of deep neural networks (or providing counter-examples). The technique is based on the simplex method, extended to handle the non-convex Rectified Linear Unit (ReLU) activation function, which is a crucial ingredient in many modern neural networks. The verification procedure tackles neural networks as a whole, without making any simplifying assumptions. We evaluated our technique on a prototype deep neural network implementation of the next-generation airborne collision avoidance system for unmanned aircraft (ACAS Xu). Results show that our technique can successfully prove properties of networks that are an order of magnitude larger than the largest networks verified using existing methods.