Search

Deep neural networks (DNNs) are increasingly deployed in safety-critical domains, but their vulnerability to adversarial attacks poses serious safety risks. Existing neuron-level methods using limited data lack efficacy in fixing adversaries due to the inherent complexity of adversarial attack mechanisms, while adversarial training, leveraging a large number of adversarial samples to enhance robustness, lacks provability. In this paper, we propose ADVREPAIR, a novel approach for provable repair of adversarial attacks using limited data. By utilizing formal verification, ADVREPAIR constructs patch modules that, when integrated with the original network, deliver provable and specialized repairs within the robustness neighborhood. Additionally, our approach incorporates a heuristic mechanism for assigning patch modules, allowing this defense against adversarial attacks to generalize to other inputs. ADVREPAIR demonstrates superior efficiency, scalability and repair success rate. Different from existing DNN repair methods, our repair can generalize to general inputs, thereby improving the robustness of the neural network globally, which indicates a significant breakthrough in the generalization capability of ADVREPAIR.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance., Comment: ICCV 2023 version

Constraint solving is an elementary way for verification of deep neural networks (DNN). In the domain of AI safety, a DNN might be modified in its structure and parameters for its repair or attack. For such situations, we propose the incremental DNN verification problem, which asks whether a safety property still holds after the DNN is modified. To solve the problem, we present an incremental satisfiability modulo theory (SMT) algorithm based on the Reluplex framework. We simulate the most important features of the configurations that infers the verification result of the searching branches in the old solving procedure (with respect to the original network), and heuristically check whether the proofs are still valid for the modified DNN. We implement our algorithm as an incremental solver called DeepInc, and exerimental results show that DeepInc is more efficient in most cases. For the cases that the property holds both before and after modification, the acceleration can be faster by several orders of magnitude, showing that DeepInc is outstanding in incrementally searching for counterexamples. Moreover, based on the framework, we propose the multi-objective DNN repair problem and give an algorithm based on our incremental SMT solving algorithm. Our repair method preserves more potential safety properties on the repaired DNNs compared with state-of-the-art.

We present a practical verification method for safety analysis of the autonomous driving system (ADS). The main idea is to build a surrogate model that quantitatively depicts the behaviour of an ADS in the specified traffic scenario. The safety properties proved in the resulting surrogate model apply to the original ADS with a probabilistic guarantee. Furthermore, we explore the safe and the unsafe parameter space of the traffic scenario for driving hazards. We demonstrate the utility of the proposed approach by evaluating safety properties on the state-of-the-art ADS in literature, with a variety of simulated traffic scenarios.

In this paper, we study linear forms \[\lambda = \beta_1\mathrm{e}^{\alpha_1}+\cdots+\beta_m\mathrm{e}^{\alpha_m},\] where $\alpha_i$ and $\beta_i$ are algebraic numbers. An explicit lower bound for the absolute value of $\lambda$ is proved, which is derived from "th\'eor\`eme de Lindemann--Weierstrass effectif" via constructive methods in algebraic computation. Besides, the existence of $\lambda$ with an explicit upper bound is established on the result of counting algebraic numbers.

In this paper, we propose a framework of filter-based ensemble of deep neuralnetworks (DNNs) to defend against adversarial attacks. The framework builds an ensemble of sub-models -- DNNs with differentiated preprocessing filters. From the theoretical perspective of DNN robustness, we argue that under the assumption of high quality of the filters, the weaker the correlations of the sensitivity of the filters are, the more robust the ensemble model tends to be, and this is corroborated by the experiments of transfer-based attacks. Correspondingly, we propose a principle that chooses the specific filters with smaller Pearson correlation coefficients, which ensures the diversity of the inputs received by DNNs, as well as the effectiveness of the entire framework against attacks. Our ensemble models are more robust than those constructed by previous defense methods like adversarial training, and even competitive with the classical ensemble of adversarial trained DNNs under adversarial attacks when the attacking radius is large.

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.

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.