Recent advances in Chain-of-Thought (CoT) prompting have substantially improved the reasoning capabilities of large language models (LLMs), but have also introduced their computational efficiency as a new attack surface. In this paper, we propose BadThink, the first backdoor attack designed to deliberately induce "overthinking" behavior in CoT-enabled LLMs while ensuring stealth. When activated by carefully crafted trigger prompts, BadThink manipulates the model to generate inflated reasoning traces—producing unnecessarily redundant thought processes while preserving the consistency of final outputs. This subtle attack vector creates a covert form of performance degradation that significantly increases computational costs and inference time while remaining difficult to detect through conventional output evaluation methods. We implement this attack through a sophisticated poisoning-based fine-tuning strategy, employing a novel LLM-based iterative optimization process to embed the behavior by generating highly naturalistic poisoned data. Our experiments on multiple state-of-the-art models and reasoning tasks show that BadThink consistently increases reasoning trace lengths—achieving an over 17× increase on the MATH-500 dataset—while remaining stealthy and robust. This work reveals a critical, previously unexplored vulnerability where reasoning efficiency can be covertly manipulated, demonstrating a new class of sophisticated attacks against CoT-enabled systems.

Transferable adversarial images raise critical security concerns for computer vision systems in real-world, black-box attack scenarios. Although many transfer attacks have been proposed, existing research lacks a systematic and comprehensive evaluation. In this paper, we systemize transfer attacks into five categories around the general machine learning pipeline and provide the first comprehensive evaluation, with 23 representative attacks against 11 representative defenses, including the recent, transfer-oriented defense and the real-world Google Cloud Vision. In particular, we identify two main problems of existing evaluations: (1) for attack transferability, lack of intra-category analyses with fair hyperparameter settings, and (2) for attack stealthiness, lack of diverse measures. Our evaluation results validate that these problems have indeed caused misleading conclusions and missing points, and addressing them leads to new, consensus-challenging insights, such as (1) an early attack, DI, even outperforms all similar follow-up ones, (2) the state-of-the-art (white-box) defense, DiffPure, is even vulnerable to (black-box) transfer attacks, and (3) even under the same $L_{p}$Lp constraint, different attacks yield dramatically different stealthiness results regarding diverse imperceptibility metrics, finer-grained measures, and a user study. We hope that our analyses will serve as guidance on properly evaluating transferable adversarial images and advance the design of attacks and defenses.

Deep neural networks (DNNs) are prone to various dependability issues, such as adversarial attacks, which hinder their adoption in safety-critical domains. Recently, NN repair techniques have been proposed to address these issues while preserving original performance by locating and modifying guilty neurons and their parameters. However, existing repair approaches are often limited to specific data sets and do not provide theoretical guarantees for the effectiveness of the repairs. To address these limitations, we introduce Patchpro, a novel patch-based approach for property-level repair of DNNs, focusing on local robustness. The key idea behind Patchpro is to construct patch modules that, when integrated with the original network, provide specialized repairs for all samples within the robustness neighborhood while maintaining the network's original performance. Our method incorporates formal verification and a heuristic mechanism for allocating patch modules, enabling it to defend against adversarial attacks and generalize to other inputs. Patchpro demonstrates superior efficiency, scalability, and repair success rates compared to existing DNN repair methods, i.e., realizing provable property-level repair for 100% cases across multiple high-dimensional datasets.

To analyse local robustness properties of deep neural networks (DNNs), we present a practical framework from a model learning perspective. Based on black-box model learning with scenario optimisation, we abstract the local behaviour of a DNN via an affine model with the probably approximately correct (PAC) guarantee. From the learned model, we can infer the corresponding PAC-model robustness property. The innovation of our work is the integration of model learning into PAC robustness analysis: that is, we construct a PAC guarantee on the model level instead of sample distribution, which induces a more faithful and accurate robustness evaluation. This is in contrast to existing statistical methods without model learning. We implement our method in a prototypical tool named DeepPAC. As a black-box method, DeepPAC is scalable and efficient, especially when DNNs have complex structures or high-dimensional inputs. We extensively evaluate DeepPAC, with 4 baselines (using formal verification, statistical methods, testing and adversarial attack) and 20 DNN models across 3 datasets, including MNIST, CIFAR-10, and ImageNet. It is shown that DeepPAC outperforms the state-of-the-art statistical method PROVERO, and it achieves more practical robustness analysis than the formal verification tool ERAN. Also, its results are consistent with existing DNN testing work like DeepGini.

Abstract We propose a spurious region guided refinement approach for robustness verification of deep neural networks. Our method starts with applying the DeepPoly abstract domain to analyze the network. If the robustness property cannot be verified, the result is inconclusive. Due to the over-approximation, the computed region in the abstraction may be spurious in the sense that it does not contain any true counterexample. Our goal is to identify such spurious regions and use them to guide the abstraction refinement. The core idea is to make use of the obtained constraints of the abstraction to infer new bounds for the neurons. This is achieved by linear programming techniques. With the new bounds, we iteratively apply DeepPoly, aiming to eliminate spurious regions. We have implemented our approach in a prototypical tool DeepSRGR. Experimental results show that a large amount of regions can be identified as spurious, and as a result, the precision of DeepPoly can be significantly improved. As a side contribution, we show that our approach can be applied to verify quantitative robustness properties.

Abstract Deep neural networks (DNNs) have been shown lack of robustness, as they are vulnerable to small perturbations on the inputs. This has led to safety concerns on applying DNNs to safety-critical domains. Several verification approaches based on constraint solving have been developed to automatically prove or disprove safety properties for DNNs. However, these approaches suffer from the scalability problem, i.e., only small DNNs can be handled. To deal with this, abstraction based approaches have been proposed, but are unfortunately facing the precision problem, i.e., the obtained bounds are often loose. In this paper, we focus on a variety of local robustness properties and a ( δ , ε ) -global robustness property of DNNs, and investigate novel strategies to combine the constraint solving and abstraction-based approaches to work with these properties: We propose a method to verify local robustness, which improves a recent proposal of analyzing DNNs through the classic abstract interpretation technique, by a novel symbolic propagation technique. Specifically, the values of neurons are represented symbolically and propagated from the input layer to the output layer, on top of the underlying abstract domains. It achieves significantly higher precision and thus can prove more properties. We propose a Lipschitz constant based verification framework. By utilising Lipschitz constants solved by semidefinite programming, we can prove global robustness of DNNs. We show how the Lipschitz constant can be tightened if it is restricted to small regions. A tightened Lipschitz constantcan be helpful in proving local robustness properties. Furthermore, a global Lipschitz constant can be used to accelerate batch local robustness verification, and thus support the verification of global robustness. We show how the proposed abstract interpretation and Lipschitz constant based approaches can benefit from each other to obtain more precise results. Moreover, they can be also exploited and combined to improve constraints based approach. We implement our methods in the tool PRODeep, and conduct detailed experimental results on several benchmarks

Deep neural networks (DNNs) have been applied in safety-critical domains such as self driving cars, aircraft collision avoidance systems, malware detection, etc. In such scenarios, it is important to give a safety guarantee to the robustness property, namely that outputs are invariant under small perturbations on the inputs. For this purpose, several algorithms and tools have been developed recently. In this paper, we present PRODeep, a platform for robustness verification of DNNs. PRODeep incorporates constraint-based, abstraction-based, and optimisation-based robustness checking algorithms. It has a modular architecture, enabling easy comparison of different algorithms. With experimental results, we illustrate the use of the tool, and easy combination of those techniques.