arXiv subjects

Guy Katz

Publications and source records attributed to Guy Katz.

At least 55 records · Page 3Linked to original sources

arXiv2024

Safe and Reliable Training of Learning-Based Aerospace Controllers

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.

cs.AI↗

arXiv2024

Verifying the Generalization of Deep Learning to Out-of-Distribution Domains

Deep neural networks (DNNs) play a crucial role in the field of machine learning, demonstrating state-of-the-art performance across various application domains. However, despite their success, DNN-based models may occasionally exhibit challenges with generalization, i.e., may fail to handle inputs that were not encountered during training. This limitation is a significant challenge when it comes to deploying deep learning for safety-critical tasks, as well as in real-world settings characterized by substantial variability. We introduce a novel approach for harnessing DNN verification technology to identify DNN-driven decision rules that exhibit robust generalization to previously unencountered input domains. Our method assesses generalization within an input domain by measuring the level of agreement between independently trained deep neural networks for inputs in this domain. We also efficiently realize our approach by using off-the-shelf DNN verification engines, and extensively evaluate it on both supervised and unsupervised DNN benchmarks, including a deep reinforcement learning (DRL) system for Internet congestion control -- demonstrating the applicability of our approach for real-world settings. Moreover, our research introduces a fresh objective for formal verification, offering the prospect of mitigating the challenges linked to deploying DNN-driven systems in real-world scenarios.

cs.LG↗

arXiv2024

Verification-Guided Shielding for Deep Reinforcement Learning

In recent years, Deep Reinforcement Learning (DRL) has emerged as an effective approach to solving real-world tasks. However, despite their successes, DRL-based policies suffer from poor reliability, which limits their deployment in safety-critical domains. Various methods have been put forth to address this issue by providing formal safety guarantees. Two main approaches include shielding and verification. While shielding ensures the safe behavior of the policy by employing an external online component (i.e., a ``shield'') that overrides potentially dangerous actions, this approach has a significant computational cost as the shield must be invoked at runtime to validate every decision. On the other hand, verification is an offline process that can identify policies that are unsafe, prior to their deployment, yet, without providing alternative actions when such a policy is deemed unsafe. In this work, we present verification-guided shielding -- a novel approach that bridges the DRL reliability gap by integrating these two methods. Our approach combines both formal and probabilistic verification tools to partition the input domain into safe and unsafe regions. In addition, we employ clustering and symbolic representation procedures that compress the unsafe regions into a compact representation. This, in turn, allows to temporarily activate the shield solely in (potentially) unsafe regions, in an efficient manner. Our novel approach allows to significantly reduce runtime overhead while still preserving formal safety guarantees. We extensively evaluate our approach on two benchmarks from the robotic navigation domain, as well as provide an in-depth analysis of its scalability and completeness.

cs.LG↗

arXiv2024

Local vs. Global Interpretability: A Computational Complexity Perspective

The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We propose a framework for bridging this gap, by using computational complexity theory to assess local and global perspectives of interpreting ML models. We begin by proposing proofs for two novel insights that are essential for our analysis: (1) a duality between local and global forms of explanations; and (2) the inherent uniqueness of certain global explanation forms. We then use these insights to evaluate the complexity of computing explanations, across three model types representing the extremes of the interpretability spectrum: (1) linear models; (2) decision trees; and (3) neural networks. Our findings offer insights into both the local and global interpretability of these models. For instance, under standard complexity assumptions such as P != NP, we prove that selecting global sufficient subsets in linear models is computationally harder than selecting local subsets. Interestingly, with neural networks and decision trees, the opposite is true: it is harder to carry out this task locally than globally. We believe that our findings demonstrate how examining explainability through a computational complexity lens can help us develop a more rigorous grasp of the inherent interpretability of ML models.

cs.LG↗

arXiv2024

Marabou 2.0: A Versatile Formal Analyzer of Neural Networks

This paper serves as a comprehensive system description of version 2.0 of the Marabou framework for formal analysis of neural networks. We discuss the tool's architectural design and highlight the major features and components introduced since its initial release.

cs.AI↗

arXiv2024

Towards a Certified Proof Checker for Deep Neural Network Verification

Recent developments in deep neural networks (DNNs) have led to their adoption in safety-critical systems, which in turn has heightened the need for guaranteeing their safety. These safety properties of DNNs can be proven using tools developed by the verification community. However, these tools are themselves prone to implementation bugs and numerical stability problems, which make their reliability questionable. To overcome this, some verifiers produce proofs of their results which can be checked by a trusted checker. In this work, we present a novel implementation of a proof checker for DNN verification. It improves on existing implementations by offering numerical stability and greater verifiability. To achieve this, we leverage two key capabilities of Imandra, an industrial theorem prover: its support of infinite precision real arithmetic and its formal verification infrastructure. So far, we have implemented a proof checker in Imandra, specified its correctness properties and started to verify the checker's compliance with them. Our ongoing work focuses on completing the formal verification of the checker and further optimizing its performance.

cs.LO↗

arXiv2024

On Augmenting Scenario-Based Modeling with Generative AI

The manual modeling of complex systems is a daunting task; and although a plethora of methods exist that mitigate this issue, the problem remains very difficult. Recent advances in generative AI have allowed the creation of general-purpose chatbots, capable of assisting software engineers in various modeling tasks. However, these chatbots are often inaccurate, and an unstructured use thereof could result in erroneous system models. In this paper, we outline a method for the safer and more structured use of chatbots as part of the modeling process. To streamline this integration, we propose leveraging scenario-based modeling techniques, which are known to facilitate the automated analysis of models. We argue that through iterative invocations of the chatbot and the manual and automatic inspection of the resulting models, a more accurate system model can eventually be obtained. We describe favorable preliminary results, which highlight the potential of this approach.

cs.SE↗

arXiv2023

gRoMA: a Tool for Measuring the Global Robustness of Deep Neural Networks

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.

cs.LG↗

arXiv2023

Taming Reachability Analysis of DNN-Controlled Systems via Abstraction-Based Training

The intrinsic complexity of deep neural networks (DNNs) makes it challenging to verify not only the networks themselves but also the hosting DNN-controlled systems. Reachability analysis of these systems faces the same challenge. Existing approaches rely on over-approximating DNNs using simpler polynomial models. However, they suffer from low efficiency and large overestimation, and are restricted to specific types of DNNs. This paper presents a novel abstraction-based approach to bypass the crux of over-approximating DNNs in reachability analysis. Specifically, we extend conventional DNNs by inserting an additional abstraction layer, which abstracts a real number to an interval for training. The inserted abstraction layer ensures that the values represented by an interval are indistinguishable to the network for both training and decision-making. Leveraging this, we devise the first black-box reachability analysis approach for DNN-controlled systems, where trained DNNs are only queried as black-box oracles for the actions on abstract states. Our approach is sound, tight, efficient, and agnostic to any DNN type and size. The experimental results on a wide range of benchmarks show that the DNNs trained by using our approach exhibit comparable performance, while the reachability analysis of the corresponding systems becomes more amenable with significant tightness and efficiency improvement over the state-of-the-art white-box approaches.

cs.LG↗

arXiv2023

Formally Explaining Neural Networks within Reactive Systems

Deep neural networks (DNNs) are increasingly being used as controllers in reactive systems. However, DNNs are highly opaque, which renders it difficult to explain and justify their actions. To mitigate this issue, there has been a surge of interest in explainable AI (XAI) techniques, capable of pinpointing the input features that caused the DNN to act as it did. Existing XAI techniques typically face two limitations: (i) they are heuristic, and do not provide formal guarantees that the explanations are correct; and (ii) they often apply to ``one-shot'' systems, where the DNN is invoked independently of past invocations, as opposed to reactive systems. Here, we begin bridging this gap, and propose a formal DNN-verification-based XAI technique for reasoning about multi-step, reactive systems. We suggest methods for efficiently calculating succinct explanations, by exploiting the system's transition constraints in order to curtail the search space explored by the underlying verifier. We evaluate our approach on two popular benchmarks from the domain of automated navigation; and observe that our methods allow the efficient computation of minimal and minimum explanations, significantly outperforming the state of the art. We also demonstrate that our methods produce formal explanations that are more reliable than competing, non-verification-based XAI techniques.

cs.AI↗

arXiv2023

On Reducing Undesirable Behavior in Deep Reinforcement Learning Models

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.

cs.LG↗

arXiv2023

DNN Verification, Reachability, and the Exponential Function Problem

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, the verification community has begun developing techniques for rigorously analyzing DNNs, with numerous verification algorithms proposed in recent years. While a significant amount of work has gone into developing these verification algorithms, little work has been devoted to rigorously studying the computability and complexity of the underlying theoretical problems. Here, we seek to contribute to the bridging of this gap. We focus on two kinds of DNNs: those that employ piecewise-linear activation functions (e.g., ReLU), and those that employ piecewise-smooth activation functions (e.g., Sigmoids). We prove the two following theorems: 1) The decidability of verifying DNNs with a particular set of piecewise-smooth activation functions is equivalent to a well-known, open problem formulated by Tarski; and 2) The DNN verification problem for any quantifier-free linear arithmetic specification can be reduced to the DNN reachability problem, whose approximation is NP-complete. These results answer two fundamental questions about the computability and complexity of DNN verification, and the ways it is affected by the network's activation functions and error tolerance; and could help guide future efforts in developing DNN verification tools.

cs.LO↗

arXiv2023

DelBugV: Delta-Debugging Neural Network Verifiers

Deep neural networks (DNNs) are becoming a key component in diverse systems across the board. However, despite their success, they often err miserably; and this has triggered significant interest in formally verifying them. Unfortunately, DNN verifiers are intricate tools, and are themselves susceptible to soundness bugs. Due to the complexity of DNN verifiers, as well as the sizes of the DNNs being verified, debugging such errors is a daunting task. Here, we present a novel tool, named DelBugV, that uses automated delta debugging techniques on DNN verifiers. Given a malfunctioning DNN verifier and a correct verifier as a point of reference (or, in some cases, just a single, malfunctioning verifier), DelBugV can produce much simpler DNN verification instances that still trigger undesired behavior -- greatly facilitating the task of debugging the faulty verifier. Our tool is modular and extensible, and can easily be enhanced with additional network simplification methods and strategies. For evaluation purposes, we ran DelBugV on 4 DNN verification engines, which were observed to produce incorrect results at the 2021 neural network verification competition (VNN-COMP'21). We were able to simplify many of the verification queries that trigger these faulty behaviors, by as much as 99%. We regard our work as a step towards the ultimate goal of producing reliable and trustworthy DNN-based software.

cs.LO↗

arXiv2023

Tighter Abstract Queries in Neural Network Verification

Neural networks have become critical components of reactive systems in various domains within computer science. Despite their excellent performance, using neural networks entails numerous risks that stem from our lack of ability to understand and reason about their behavior. Due to these risks, various formal methods have been proposed for verifying neural networks; but unfortunately, these typically struggle with scalability barriers. Recent attempts have demonstrated that abstraction-refinement approaches could play a significant role in mitigating these limitations; but these approaches can often produce networks that are so abstract, that they become unsuitable for verification. To deal with this issue, we present CEGARETTE, a novel verification mechanism where both the system and the property are abstracted and refined simultaneously. We observe that this approach allows us to produce abstract networks which are both small and sufficiently accurate, allowing for quick verification times while avoiding a large number of refinement steps. For evaluation purposes, we implemented CEGARETTE as an extension to the recently proposed CEGAR-NN framework. Our results are very promising, and demonstrate a significant improvement in performance over multiple benchmarks.

cs.LG↗

arXiv2023

Verifying Generalization in Deep Learning

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.

cs.LG↗

arXiv2023

Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks

With the rapid growth of machine learning, deep neural networks (DNNs) are now being used in numerous domains. Unfortunately, DNNs are "black-boxes", and cannot be interpreted by humans, which is a substantial concern in safety-critical systems. To mitigate this issue, researchers have begun working on explainable AI (XAI) methods, which can identify a subset of input features that are the cause of a DNN's decision for a given input. Most existing techniques are heuristic, and cannot guarantee the correctness of the explanation provided. In contrast, recent and exciting attempts have shown that formal methods can be used to generate provably correct explanations. Although these methods are sound, the computational complexity of the underlying verification problem limits their scalability; and the explanations they produce might sometimes be overly complex. Here, we propose a novel approach to tackle these limitations. We (1) suggest an efficient, verification-based method for finding minimal explanations, which constitute a provable approximation of the global, minimum explanation; (2) show how DNN verification can assist in calculating lower and upper bounds on the optimal explanation; (3) propose heuristics that significantly improve the scalability of the verification process; and (4) suggest the use of bundles, which allows us to arrive at more succinct and interpretable explanations. Our evaluation shows that our approach significantly outperforms state-of-the-art techniques, and produces explanations that are more useful to humans. We thus regard this work as a step toward leveraging verification technology in producing DNNs that are more reliable and comprehensible.

cs.LG↗

arXiv2023

OccRob: Efficient SMT-Based Occlusion Robustness Verification of Deep Neural Networks

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.

cs.LG↗

arXiv2023

Enhancing Deep Learning with Scenario-Based Override Rules: a Case Study

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.

cs.SE↗