Binghui Wang

CR
h-index26
43papers
2,812citations
Novelty59%
AI Score57

43 Papers

12.4LGMay 7, 2022Code
Bandits for Structure Perturbation-based Black-box Attacks to Graph Neural Networks with Theoretical Guarantees

Binghui Wang, Youqi Li, Pan Zhou

Graph neural networks (GNNs) have achieved state-of-the-art performance in many graph-based tasks such as node classification and graph classification. However, many recent works have demonstrated that an attacker can mislead GNN models by slightly perturbing the graph structure. Existing attacks to GNNs are either under the less practical threat model where the attacker is assumed to access the GNN model parameters, or under the practical black-box threat model but consider perturbing node features that are shown to be not enough effective. In this paper, we aim to bridge this gap and consider black-box attacks to GNNs with structure perturbation as well as with theoretical guarantees. We propose to address this challenge through bandit techniques. Specifically, we formulate our attack as an online optimization with bandit feedback. This original problem is essentially NP-hard due to the fact that perturbing the graph structure is a binary optimization problem. We then propose an online attack based on bandit optimization which is proven to be {sublinear} to the query number $T$, i.e., $\mathcal{O}(\sqrt{N}T^{3/4})$ where $N$ is the number of nodes in the graph. Finally, we evaluate our proposed attack by conducting experiments over multiple datasets and GNN models. The experimental results on various citation graphs and image graphs show that our attack is both effective and efficient. Source code is available at~\url{https://github.com/Metaoblivion/Bandit_GNN_Attack}

23.7CRJul 31, 2023
Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attacks

Xinyu Zhang, Hanbin Hong, Yuan Hong et al.

The language models, especially the basic text classification models, have been shown to be susceptible to textual adversarial attacks such as synonym substitution and word insertion attacks. To defend against such attacks, a growing body of research has been devoted to improving the model robustness. However, providing provable robustness guarantees instead of empirical robustness is still widely unexplored. In this paper, we propose Text-CRS, a generalized certified robustness framework for natural language processing (NLP) based on randomized smoothing. To our best knowledge, existing certified schemes for NLP can only certify the robustness against $\ell_0$ perturbations in synonym substitution attacks. Representing each word-level adversarial operation (i.e., synonym substitution, word reordering, insertion, and deletion) as a combination of permutation and embedding transformation, we propose novel smoothing theorems to derive robustness bounds in both permutation and embedding space against such adversarial operations. To further improve certified accuracy and radius, we consider the numerical relationships between discrete words and select proper noise distributions for the randomized smoothing. Finally, we conduct substantial experiments on multiple language models and datasets. Text-CRS can address all four different word-level adversarial operations and achieve a significant accuracy improvement. We also provide the first benchmark on certified accuracy and radius of four word-level operations, besides outperforming the state-of-the-art certification against synonym substitution attacks.

16.3LGMay 18
Attention Sinks and Outliers in Attention Residuals

Haozheng Luo, Haoran Dai, Shaoyang Zhang et al.

We propose OASIS, an outlier- and sink-aware technique built on inter-layer null signaling. As AttnResidual architectures introduce an additional depth-wise normalization channel, they improve inter-layer routing flexibility but also exacerbate attention sinks, activation outliers, and the resulting degradation in inference stability and quantization robustness. OASIS addresses this issue by introducing a Softmax1-based null space and coupling token-level null evidence to depth routing through an inter-layer null signal, thereby reducing sink-dominated routing and improving structural robustness. Theoretically, we show that the dual-normalization design of AttnResidual intensifies sink formation and quantization brittleness. Experimentally, we compare OASIS against five baselines on three real-world datasets and observe consistent improvements in both attention sink and post-quantization performance. Notably, OASIS achieves an average reduction of 9.26% in maximum infinity norm and 2.60% in average kurtosis across the evaluated settings, while lowering perplexity by 75.85% under W8A8 and improving GSM8K Pass@1 by 12.42% under W4A4.

13.1CVMar 24, 2023Code
IDGI: A Framework to Eliminate Explanation Noise from Integrated Gradients

Ruo Yang, Binghui Wang, Mustafa Bilgic

Integrated Gradients (IG) as well as its variants are well-known techniques for interpreting the decisions of deep neural networks. While IG-based approaches attain state-of-the-art performance, they often integrate noise into their explanation saliency maps, which reduce their interpretability. To minimize the noise, we examine the source of the noise analytically and propose a new approach to reduce the explanation noise based on our analytical findings. We propose the Important Direction Gradient Integration (IDGI) framework, which can be easily incorporated into any IG-based method that uses the Reimann Integration for integrated gradient computation. Extensive experiments with three IG-based methods show that IDGI improves them drastically on numerous interpretability metrics.

11.8LGJul 5, 2022
UniCR: Universally Approximated Certified Robustness via Randomized Smoothing

Hanbin Hong, Binghui Wang, Yuan Hong

We study certified robustness of machine learning classifiers against adversarial perturbations. In particular, we propose the first universally approximated certified robustness (UniCR) framework, which can approximate the robustness certification of any input on any classifier against any $\ell_p$ perturbations with noise generated by any continuous probability distribution. Compared with the state-of-the-art certified defenses, UniCR provides many significant benefits: (1) the first universal robustness certification framework for the above 4 'any's; (2) automatic robustness certification that avoids case-by-case analysis, (3) tightness validation of certified robustness, and (4) optimality validation of noise distributions used by randomized smoothing. We conduct extensive experiments to validate the above benefits of UniCR and the advantages of UniCR over state-of-the-art certified defenses against $\ell_p$ perturbations.

8.7CRJun 11, 2022Code
NeuGuard: Lightweight Neuron-Guided Defense against Membership Inference Attacks

Nuo Xu, Binghui Wang, Ran Ran et al.

Membership inference attacks (MIAs) against machine learning models can lead to serious privacy risks for the training dataset used in the model training. In this paper, we propose a novel and effective Neuron-Guided Defense method named NeuGuard against membership inference attacks (MIAs). We identify a key weakness in existing defense mechanisms against MIAs wherein they cannot simultaneously defend against two commonly used neural network based MIAs, indicating that these two attacks should be separately evaluated to assure the defense effectiveness. We propose NeuGuard, a new defense approach that jointly controls the output and inner neurons' activation with the object to guide the model output of training set and testing set to have close distributions. NeuGuard consists of class-wise variance minimization targeting restricting the final output neurons and layer-wise balanced output control aiming to constrain the inner neurons in each layer. We evaluate NeuGuard and compare it with state-of-the-art defenses against two neural network based MIAs, five strongest metric based MIAs including the newly proposed label-only MIA on three benchmark datasets. Results show that NeuGuard outperforms the state-of-the-art defenses by offering much improved utility-privacy trade-off, generality, and overhead.

7.6CVApr 5, 2023Code
A Certified Radius-Guided Attack Framework to Image Segmentation Models

Wenjie Qu, Youqi Li, Binghui Wang

Image segmentation is an important problem in many safety-critical applications. Recent studies show that modern image segmentation models are vulnerable to adversarial perturbations, while existing attack methods mainly follow the idea of attacking image classification models. We argue that image segmentation and classification have inherent differences, and design an attack framework specially for image segmentation models. Our attack framework is inspired by certified radius, which was originally used by defenders to defend against adversarial perturbations to classification models. We are the first, from the attacker perspective, to leverage the properties of certified radius and propose a certified radius guided attack framework against image segmentation models. Specifically, we first adapt randomized smoothing, the state-of-the-art certification method for classification models, to derive the pixel's certified radius. We then focus more on disrupting pixels with relatively smaller certified radii and design a pixel-wise certified radius guided loss, when plugged into any existing white-box attack, yields our certified radius-guided white-box attack. Next, we propose the first black-box attack to image segmentation models via bandit. We design a novel gradient estimator, based on bandit feedback, which is query-efficient and provably unbiased and stable. We use this gradient estimator to design a projected bandit gradient descent (PBGD) attack, as well as a certified radius-guided PBGD (CR-PBGD) attack. We prove our PBGD and CR-PBGD attacks can achieve asymptotically optimal attack performance with an optimal rate. We evaluate our certified-radius guided white-box and black-box attacks on multiple modern image segmentation models and datasets. Our results validate the effectiveness of our certified radius-guided attack framework.

4.6LGJul 20, 2024Code
Universally Harmonizing Differential Privacy Mechanisms for Federated Learning: Boosting Accuracy and Convergence

Shuya Feng, Meisam Mohammady, Hanbin Hong et al.

Differentially private federated learning (DP-FL) is a promising technique for collaborative model training while ensuring provable privacy for clients. However, optimizing the tradeoff between privacy and accuracy remains a critical challenge. To our best knowledge, we propose the first DP-FL framework (namely UDP-FL), which universally harmonizes any randomization mechanism (e.g., an optimal one) with the Gaussian Moments Accountant (viz. DP-SGD) to significantly boost accuracy and convergence. Specifically, UDP-FL demonstrates enhanced model performance by mitigating the reliance on Gaussian noise. The key mediator variable in this transformation is the Rényi Differential Privacy notion, which is carefully used to harmonize privacy budgets. We also propose an innovative method to theoretically analyze the convergence for DP-FL (including our UDP-FL ) based on mode connectivity analysis. Moreover, we evaluate our UDP-FL through extensive experiments benchmarked against state-of-the-art (SOTA) methods, demonstrating superior performance on both privacy guarantees and model performance. Notably, UDP-FL exhibits substantial resilience against different inference attacks, indicating a significant advance in safeguarding sensitive data in federated learning environments.

20.7CRSep 1, 2020Code
Efficient, Direct, and Restricted Black-Box Graph Evasion Attacks to Any-Layer Graph Neural Networks via Influence Function

Binghui Wang, Tianxiang Zhou, Minhua Lin et al.

Graph neural network (GNN), the mainstream method to learn on graph data, is vulnerable to graph evasion attacks, where an attacker slightly perturbing the graph structure can fool trained GNN models. Existing work has at least one of the following drawbacks: 1) limited to directly attack two-layer GNNs; 2) inefficient; and 3) impractical, as they need to know full or part of GNN model parameters. We address the above drawbacks and propose an influence-based \emph{efficient, direct, and restricted black-box} evasion attack to \emph{any-layer} GNNs. Specifically, we first introduce two influence functions, i.e., feature-label influence and label influence, that are defined on GNNs and label propagation (LP), respectively. Then we observe that GNNs and LP are strongly connected in terms of our defined influences. Based on this, we can then reformulate the evasion attack to GNNs as calculating label influence on LP, which is \emph{inherently} applicable to any-layer GNNs, while no need to know information about the internal GNN model. Finally, we propose an efficient algorithm to calculate label influence. Experimental results on various graph datasets show that, compared to state-of-the-art white-box attacks, our attack can achieve comparable attack performance, but has a 5-50x speedup when attacking two-layer GNNs. Moreover, our attack is effective to attack multi-layer GNNs\footnote{Source code and full version is in the link: \url{https://github.com/ventr1c/InfAttack}}.

21.7LGDec 20, 2019Code
Certified Robustness for Top-k Predictions against Adversarial Perturbations via Randomized Smoothing

Jinyuan Jia, Xiaoyu Cao, Binghui Wang et al.

It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to top-1 predictions. In many real-world applications, top-$k$ predictions are more relevant. In this work, we aim to derive certified robustness for top-$k$ predictions. In particular, our certified robustness is based on randomized smoothing, which turns any classifier to a new classifier via adding noise to an input example. We adopt randomized smoothing because it is scalable to large-scale neural networks and applicable to any classifier. We derive a tight robustness in $\ell_2$ norm for top-$k$ predictions when using randomized smoothing with Gaussian noise. We find that generalizing the certified robustness from top-1 to top-$k$ predictions faces significant technical challenges. We also empirically evaluate our method on CIFAR10 and ImageNet. For example, our method can obtain an ImageNet classifier with a certified top-5 accuracy of 62.8\% when the $\ell_2$-norms of the adversarial perturbations are less than 0.5 (=127/255). Our code is publicly available at: \url{https://github.com/jjy1994/Certify_Topk}.

40.9CRFeb 12, 2024Code
PoisonedRAG: Knowledge Corruption Attacks to Retrieval-Augmented Generation of Large Language Models

Wei Zou, Runpeng Geng, Binghui Wang et al.

Large language models (LLMs) have achieved remarkable success due to their exceptional generative capabilities. Despite their success, they also have inherent limitations such as a lack of up-to-date knowledge and hallucination. Retrieval-Augmented Generation (RAG) is a state-of-the-art technique to mitigate these limitations. The key idea of RAG is to ground the answer generation of an LLM on external knowledge retrieved from a knowledge database. Existing studies mainly focus on improving the accuracy or efficiency of RAG, leaving its security largely unexplored. We aim to bridge the gap in this work. We find that the knowledge database in a RAG system introduces a new and practical attack surface. Based on this attack surface, we propose PoisonedRAG, the first knowledge corruption attack to RAG, where an attacker could inject a few malicious texts into the knowledge database of a RAG system to induce an LLM to generate an attacker-chosen target answer for an attacker-chosen target question. We formulate knowledge corruption attacks as an optimization problem, whose solution is a set of malicious texts. Depending on the background knowledge (e.g., black-box and white-box settings) of an attacker on a RAG system, we propose two solutions to solve the optimization problem, respectively. Our results show PoisonedRAG could achieve a 90% attack success rate when injecting five malicious texts for each target question into a knowledge database with millions of texts. We also evaluate several defenses and our results show they are insufficient to defend against PoisonedRAG, highlighting the need for new defenses.

2.0CVSep 24, 2024
Leveraging Local Structure for Improving Model Explanations: An Information Propagation Approach

Ruo Yang, Binghui Wang, Mustafa Bilgic

Numerous explanation methods have been recently developed to interpret the decisions made by deep neural network (DNN) models. For image classifiers, these methods typically provide an attribution score to each pixel in the image to quantify its contribution to the prediction. However, most of these explanation methods appropriate attribution scores to pixels independently, even though both humans and DNNs make decisions by analyzing a set of closely related pixels simultaneously. Hence, the attribution score of a pixel should be evaluated jointly by considering itself and its structurally-similar pixels. We propose a method called IProp, which models each pixel's individual attribution score as a source of explanatory information and explains the image prediction through the dynamic propagation of information across all pixels. To formulate the information propagation, IProp adopts the Markov Reward Process, which guarantees convergence, and the final status indicates the desired pixels' attribution scores. Furthermore, IProp is compatible with any existing attribution-based explanation method. Extensive experiments on various explanation methods and DNN models verify that IProp significantly improves them on a variety of interpretability metrics.

9.2LGJul 12, 2024Code
Graph Neural Network Causal Explanation via Neural Causal Models

Arman Behnam, Binghui Wang

Graph neural network (GNN) explainers identify the important subgraph that ensures the prediction for a given graph. Until now, almost all GNN explainers are based on association, which is prone to spurious correlations. We propose {\name}, a GNN causal explainer via causal inference. Our explainer is based on the observation that a graph often consists of a causal underlying subgraph. {\name} includes three main steps: 1) It builds causal structure and the corresponding structural causal model (SCM) for a graph, which enables the cause-effect calculation among nodes. 2) Directly calculating the cause-effect in real-world graphs is computationally challenging. It is then enlightened by the recent neural causal model (NCM), a special type of SCM that is trainable, and design customized NCMs for GNNs. By training these GNN NCMs, the cause-effect can be easily calculated. 3) It uncovers the subgraph that causally explains the GNN predictions via the optimized GNN-NCMs. Evaluation results on multiple synthetic and real-world graphs validate that {\name} significantly outperforms existing GNN explainers in exact groundtruth explanation identification

16.4LGMar 4, 2024Code
Inf2Guard: An Information-Theoretic Framework for Learning Privacy-Preserving Representations against Inference Attacks

Sayedeh Leila Noorbakhsh, Binghui Zhang, Yuan Hong et al.

Machine learning (ML) is vulnerable to inference (e.g., membership inference, property inference, and data reconstruction) attacks that aim to infer the private information of training data or dataset. Existing defenses are only designed for one specific type of attack and sacrifice significant utility or are soon broken by adaptive attacks. We address these limitations by proposing an information-theoretic defense framework, called Inf2Guard, against the three major types of inference attacks. Our framework, inspired by the success of representation learning, posits that learning shared representations not only saves time/costs but also benefits numerous downstream tasks. Generally, Inf2Guard involves two mutual information objectives, for privacy protection and utility preservation, respectively. Inf2Guard exhibits many merits: it facilitates the design of customized objectives against the specific inference attack; it provides a general defense framework which can treat certain existing defenses as special cases; and importantly, it aids in deriving theoretical results, e.g., inherent utility-privacy tradeoff and guaranteed privacy leakage. Extensive evaluations validate the effectiveness of Inf2Guard for learning privacy-preserving representations against inference attacks and demonstrate the superiority over the baselines.

10.4LGMar 26, 2024
Identifying Backdoored Graphs in Graph Neural Network Training: An Explanation-Based Approach with Novel Metrics

Jane Downer, Ren Wang, Binghui Wang

Graph Neural Networks (GNNs) have gained popularity in numerous domains, yet they are vulnerable to backdoor attacks that can compromise their performance and ethical application. The detection of these attacks is crucial for maintaining the reliability and security of GNN classification tasks, but effective detection techniques are lacking. Recognizing the challenge in detecting such intrusions, we devised a novel detection method that creatively leverages graph-level explanations. By extracting and transforming secondary outputs from GNN explanation mechanisms, we developed seven innovative metrics for effective detection of backdoor attacks on GNNs. Additionally, we develop an adaptive attack to rigorously evaluate our approach. We test our method on multiple benchmark datasets and examine its efficacy against various attack models. Our results show that our method can achieve high detection performance, marking a significant advancement in safeguarding GNNs against backdoor attacks.

5.8CRDec 17, 2024
Practicable Black-box Evasion Attacks on Link Prediction in Dynamic Graphs -- A Graph Sequential Embedding Method

Jiate Li, Meng Pang, Binghui Wang

Link prediction in dynamic graphs (LPDG) has been widely applied to real-world applications such as website recommendation, traffic flow prediction, organizational studies, etc. These models are usually kept local and secure, with only the interactive interface restrictively available to the public. Thus, the problem of the black-box evasion attack on the LPDG model, where model interactions and data perturbations are restricted, seems to be essential and meaningful in practice. In this paper, we propose the first practicable black-box evasion attack method that achieves effective attacks against the target LPDG model, within a limited amount of interactions and perturbations. To perform effective attacks under limited perturbations, we develop a graph sequential embedding model to find the desired state embedding of the dynamic graph sequences, under a deep reinforcement learning framework. To overcome the scarcity of interactions, we design a multi-environment training pipeline and train our agent for multiple instances, by sharing an aggregate interaction buffer. Finally, we evaluate our attack against three advanced LPDG models on three real-world graph datasets of different scales and compare its performance with related methods under the interaction and perturbation constraints. Experimental results show that our attack is both effective and practicable.

6.4LGDec 15, 2024Code
Learning Robust and Privacy-Preserving Representations via Information Theory

Binghui Zhang, Sayedeh Leila Noorbakhsh, Yun Dong et al.

Machine learning models are vulnerable to both security attacks (e.g., adversarial examples) and privacy attacks (e.g., private attribute inference). We take the first step to mitigate both the security and privacy attacks, and maintain task utility as well. Particularly, we propose an information-theoretic framework to achieve the goals through the lens of representation learning, i.e., learning representations that are robust to both adversarial examples and attribute inference adversaries. We also derive novel theoretical results under our framework, e.g., the inherent trade-off between adversarial robustness/utility and attribute privacy, and guaranteed attribute privacy leakage against attribute inference adversaries.

12.0CRJun 16, 2025Code
Rectifying Privacy and Efficacy Measurements in Machine Unlearning: A New Inference Attack Perspective

Nima Naderloui, Shenao Yan, Binghui Wang et al.

Machine unlearning focuses on efficiently removing specific data from trained models, addressing privacy and compliance concerns with reasonable costs. Although exact unlearning ensures complete data removal equivalent to retraining, it is impractical for large-scale models, leading to growing interest in inexact unlearning methods. However, the lack of formal guarantees in these methods necessitates the need for robust evaluation frameworks to assess their privacy and effectiveness. In this work, we first identify several key pitfalls of the existing unlearning evaluation frameworks, e.g., focusing on average-case evaluation or targeting random samples for evaluation, incomplete comparisons with the retraining baseline. Then, we propose RULI (Rectified Unlearning Evaluation Framework via Likelihood Inference), a novel framework to address critical gaps in the evaluation of inexact unlearning methods. RULI introduces a dual-objective attack to measure both unlearning efficacy and privacy risks at a per-sample granularity. Our findings reveal significant vulnerabilities in state-of-the-art unlearning methods, where RULI achieves higher attack success rates, exposing privacy risks underestimated by existing methods. Built on a game-based foundation and validated through empirical evaluations on both image and text data (spanning tasks from classification to generation), RULI provides a rigorous, scalable, and fine-grained methodology for evaluating unlearning techniques.

6.4CRJan 9, 2025
Watermarking Graph Neural Networks via Explanations for Ownership Protection

Jane Downer, Ren Wang, Binghui Wang

Graph Neural Networks (GNNs) are the mainstream method to learn pervasive graph data and are widely deployed in industry, making their intellectual property valuable. However, protecting GNNs from unauthorized use remains a challenge. Watermarking, which embeds ownership information into a model, is a potential solution. However, existing watermarking methods have two key limitations: First, almost all of them focus on non-graph data, with watermarking GNNs for complex graph data largely unexplored. Second, the de facto backdoor-based watermarking methods pollute training data and induce ownership ambiguity through intentional misclassification. Our explanation-based watermarking inherits the strengths of backdoor-based methods (e.g., robust to watermark removal attacks), but avoids data pollution and eliminates intentional misclassification. In particular, our method learns to embed the watermark in GNN explanations such that this unique watermark is statistically distinct from other potential solutions, and ownership claims must show statistical significance to be verified. We theoretically prove that, even with full knowledge of our method, locating the watermark is an NP-hard problem. Empirically, our method manifests robustness to removal attacks like fine-tuning and pruning. By addressing these challenges, our approach marks a significant advancement in protecting GNN intellectual property.

4.1LGOct 16, 2025
Measure-Theoretic Anti-Causal Representation Learning

Arman Behnam, Binghui Wang

Causal representation learning in the anti-causal setting (labels cause features rather than the reverse) presents unique challenges requiring specialized approaches. We propose Anti-Causal Invariant Abstractions (ACIA), a novel measure-theoretic framework for anti-causal representation learning. ACIA employs a two-level design, low-level representations capture how labels generate observations, while high-level representations learn stable causal patterns across environment-specific variations. ACIA addresses key limitations of existing approaches by accommodating prefect and imperfect interventions through interventional kernels, eliminating dependency on explicit causal structures, handling high-dimensional data effectively, and providing theoretical guarantees for out-of-distribution generalization. Experiments on synthetic and real-world medical datasets demonstrate that ACIA consistently outperforms state-of-the-art methods in both accuracy and invariance metrics. Furthermore, our theoretical results establish tight bounds on performance gaps between training and unseen environments, confirming the efficacy of our approach for robust anti-causal learning.

17.7CRJun 5, 2024Code
Graph Neural Network Explanations are Fragile

Jiate Li, Meng Pang, Yun Dong et al.

Explainable Graph Neural Network (GNN) has emerged recently to foster the trust of using GNNs. Existing GNN explainers are developed from various perspectives to enhance the explanation performance. We take the first step to study GNN explainers under adversarial attack--We found that an adversary slightly perturbing graph structure can ensure GNN model makes correct predictions, but the GNN explainer yields a drastically different explanation on the perturbed graph. Specifically, we first formulate the attack problem under a practical threat model (i.e., the adversary has limited knowledge about the GNN explainer and a restricted perturbation budget). We then design two methods (i.e., one is loss-based and the other is deduction-based) to realize the attack. We evaluate our attacks on various GNN explainers and the results show these explainers are fragile.

2.0CLOct 15, 2021
Detecting Gender Bias in Transformer-based Models: A Case Study on BERT

Bingbing Li, Hongwu Peng, Rajat Sainju et al.

In this paper, we propose a novel gender bias detection method by utilizing attention map for transformer-based models. We 1) give an intuitive gender bias judgement method by comparing the different relation degree between the genders and the occupation according to the attention scores, 2) design a gender bias detector by modifying the attention module, 3) insert the gender bias detector into different positions of the model to present the internal gender bias flow, and 4) draw the consistent gender bias conclusion by scanning the entire Wikipedia, a BERT pretraining dataset. We observe that 1) the attention matrices, Wq and Wk introduce much more gender bias than other modules (including the embedding layer) and 2) the bias degree changes periodically inside of the model (attention matrix Q, K, V, and the remaining part of the attention layer (including the fully-connected layer, the residual connection, and the layer normalization module) enhance the gender bias while the averaged attentions reduces the bias).

17.5LGAug 21, 2021
A Hard Label Black-box Adversarial Attack Against Graph Neural Networks

Jiaming Mu, Binghui Wang, Qi Li et al.

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in various graph structure related tasks such as node classification and graph classification. However, GNNs are vulnerable to adversarial attacks. Existing works mainly focus on attacking GNNs for node classification; nevertheless, the attacks against GNNs for graph classification have not been well explored. In this work, we conduct a systematic study on adversarial attacks against GNNs for graph classification via perturbing the graph structure. In particular, we focus on the most challenging attack, i.e., hard label black-box attack, where an attacker has no knowledge about the target GNN model and can only obtain predicted labels through querying the target model.To achieve this goal, we formulate our attack as an optimization problem, whose objective is to minimize the number of edges to be perturbed in a graph while maintaining the high attack success rate. The original optimization problem is intractable to solve, and we relax the optimization problem to be a tractable one, which is solved with theoretical convergence guarantee. We also design a coarse-grained searching algorithm and a query-efficient gradient computation algorithm to decrease the number of queries to the target GNN model. Our experimental results on three real-world datasets demonstrate that our attack can effectively attack representative GNNs for graph classification with less queries and perturbations. We also evaluate the effectiveness of our attack under two defenses: one is well-designed adversarial graph detector and the other is that the target GNN model itself is equipped with a defense to prevent adversarial graph generation. Our experimental results show that such defenses are not effective enough, which highlights more advanced defenses.

14.6LGJul 3, 2021
Privacy-Preserving Representation Learning on Graphs: A Mutual Information Perspective

Binghui Wang, Jiayi Guo, Ang Li et al.

Learning with graphs has attracted significant attention recently. Existing representation learning methods on graphs have achieved state-of-the-art performance on various graph-related tasks such as node classification, link prediction, etc. However, we observe that these methods could leak serious private information. For instance, one can accurately infer the links (or node identity) in a graph from a node classifier (or link predictor) trained on the learnt node representations by existing methods. To address the issue, we propose a privacy-preserving representation learning framework on graphs from the \emph{mutual information} perspective. Specifically, our framework includes a primary learning task and a privacy protection task, and we consider node classification and link prediction as the two tasks of interest. Our goal is to learn node representations such that they can be used to achieve high performance for the primary learning task, while obtaining performance for the privacy protection task close to random guessing. We formally formulate our goal via mutual information objectives. However, it is intractable to compute mutual information in practice. Then, we derive tractable variational bounds for the mutual information terms, where each bound can be parameterized via a neural network. Next, we train these parameterized neural networks to approximate the true mutual information and learn privacy-preserving node representations. We finally evaluate our framework on various graph datasets.

5.0LGDec 24, 2020
Semi-Supervised Node Classification on Graphs: Markov Random Fields vs. Graph Neural Networks

Binghui Wang, Jinyuan Jia, Neil Zhenqiang Gong

Semi-supervised node classification on graph-structured data has many applications such as fraud detection, fake account and review detection, user's private attribute inference in social networks, and community detection. Various methods such as pairwise Markov Random Fields (pMRF) and graph neural networks were developed for semi-supervised node classification. pMRF is more efficient than graph neural networks. However, existing pMRF-based methods are less accurate than graph neural networks, due to a key limitation that they assume a heuristics-based constant edge potential for all edges. In this work, we aim to address the key limitation of existing pMRF-based methods. In particular, we propose to learn edge potentials for pMRF. Our evaluation results on various types of graph datasets show that our optimized pMRF-based method consistently outperforms existing graph neural networks in terms of both accuracy and efficiency. Our results highlight that previous work may have underestimated the power of pMRF for semi-supervised node classification.

21.0LGDec 8, 2020
Provable Defense against Privacy Leakage in Federated Learning from Representation Perspective

Jingwei Sun, Ang Li, Binghui Wang et al.

Federated learning (FL) is a popular distributed learning framework that can reduce privacy risks by not explicitly sharing private data. However, recent works demonstrated that sharing model updates makes FL vulnerable to inference attacks. In this work, we show our key observation that the data representation leakage from gradients is the essential cause of privacy leakage in FL. We also provide an analysis of this observation to explain how the data presentation is leaked. Based on this observation, we propose a defense against model inversion attack in FL. The key idea of our defense is learning to perturb data representation such that the quality of the reconstructed data is severely degraded, while FL performance is maintained. In addition, we derive certified robustness guarantee to FL and convergence guarantee to FedAvg, after applying our defense. To evaluate our defense, we conduct experiments on MNIST and CIFAR10 for defending against the DLG attack and GS attack. Without sacrificing accuracy, the results demonstrate that our proposed defense can increase the mean squared error between the reconstructed data and the raw data by as much as more than 160X for both DLG attack and GS attack, compared with baseline defense methods. The privacy of the FL system is significantly improved.

22.6LGDec 8, 2020
GraphFL: A Federated Learning Framework for Semi-Supervised Node Classification on Graphs

Binghui Wang, Ang Li, Hai Li et al.

Graph-based semi-supervised node classification (GraphSSC) has wide applications, ranging from networking and security to data mining and machine learning, etc. However, existing centralized GraphSSC methods are impractical to solve many real-world graph-based problems, as collecting the entire graph and labeling a reasonable number of labels is time-consuming and costly, and data privacy may be also violated. Federated learning (FL) is an emerging learning paradigm that enables collaborative learning among multiple clients, which can mitigate the issue of label scarcity and protect data privacy as well. Therefore, performing GraphSSC under the FL setting is a promising solution to solve real-world graph-based problems. However, existing FL methods 1) perform poorly when data across clients are non-IID, 2) cannot handle data with new label domains, and 3) cannot leverage unlabeled data, while all these issues naturally happen in real-world graph-based problems. To address the above issues, we propose the first FL framework, namely GraphFL, for semi-supervised node classification on graphs. Our framework is motivated by meta-learning methods. Specifically, we propose two GraphFL methods to respectively address the non-IID issue in graph data and handle the tasks with new label domains. Furthermore, we design a self-training method to leverage unlabeled graph data. We adopt representative graph neural networks as GraphSSC methods and evaluate GraphFL on multiple graph datasets. Experimental results demonstrate that GraphFL significantly outperforms the compared FL baseline and GraphFL with self-training can obtain better performance.

19.0CRNov 15, 2020
Almost Tight L0-norm Certified Robustness of Top-k Predictions against Adversarial Perturbations

Jinyuan Jia, Binghui Wang, Xiaoyu Cao et al.

Top-k predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. $\ell_0$-norm adversarial perturbation characterizes an attack that arbitrarily modifies some features of an input such that a classifier makes an incorrect prediction for the perturbed input. $\ell_0$-norm adversarial perturbation is easy to interpret and can be implemented in the physical world. Therefore, certifying robustness of top-$k$ predictions against $\ell_0$-norm adversarial perturbation is important. However, existing studies either focused on certifying $\ell_0$-norm robustness of top-$1$ predictions or $\ell_2$-norm robustness of top-$k$ predictions. In this work, we aim to bridge the gap. Our approach is based on randomized smoothing, which builds a provably robust classifier from an arbitrary classifier via randomizing an input. Our major theoretical contribution is an almost tight $\ell_0$-norm certified robustness guarantee for top-$k$ predictions. We empirically evaluate our method on CIFAR10 and ImageNet. For instance, our method can build a classifier that achieves a certified top-3 accuracy of 69.2\% on ImageNet when an attacker can arbitrarily perturb 5 pixels of a testing image.

8.8CROct 26, 2020
Robust and Verifiable Information Embedding Attacks to Deep Neural Networks via Error-Correcting Codes

Jinyuan Jia, Binghui Wang, Neil Zhenqiang Gong

In the era of deep learning, a user often leverages a third-party machine learning tool to train a deep neural network (DNN) classifier and then deploys the classifier as an end-user software product or a cloud service. In an information embedding attack, an attacker is the provider of a malicious third-party machine learning tool. The attacker embeds a message into the DNN classifier during training and recovers the message via querying the API of the black-box classifier after the user deploys it. Information embedding attacks have attracted growing attention because of various applications such as watermarking DNN classifiers and compromising user privacy. State-of-the-art information embedding attacks have two key limitations: 1) they cannot verify the correctness of the recovered message, and 2) they are not robust against post-processing of the classifier. In this work, we aim to design information embedding attacks that are verifiable and robust against popular post-processing methods. Specifically, we leverage Cyclic Redundancy Check to verify the correctness of the recovered message. Moreover, to be robust against post-processing, we leverage Turbo codes, a type of error-correcting codes, to encode the message before embedding it to the DNN classifier. We propose to recover the message via adaptively querying the classifier to save queries. Our adaptive recovery strategy leverages the property of Turbo codes that supports error correcting with a partial code. We evaluate our information embedding attacks using simulated messages and apply them to three applications, where messages have semantic interpretations. We consider 8 popular methods to post-process the classifier. Our results show that our attacks can accurately and verifiably recover the messages in all considered scenarios, while state-of-the-art attacks cannot accurately recover the messages in many scenarios.

13.6CRSep 1, 2020
Reinforcement Learning-based Black-Box Evasion Attacks to Link Prediction in Dynamic Graphs

Houxiang Fan, Binghui Wang, Pan Zhou et al.

Link prediction in dynamic graphs (LPDG) is an important research problem that has diverse applications such as online recommendations, studies on disease contagion, organizational studies, etc. Various LPDG methods based on graph embedding and graph neural networks have been recently proposed and achieved state-of-the-art performance. In this paper, we study the vulnerability of LPDG methods and propose the first practical black-box evasion attack. Specifically, given a trained LPDG model, our attack aims to perturb the graph structure, without knowing to model parameters, model architecture, etc., such that the LPDG model makes as many wrong predicted links as possible. We design our attack based on a stochastic policy-based RL algorithm. Moreover, we evaluate our attack on three real-world graph datasets from different application domains. Experimental results show that our attack is both effective and efficient.

29.8CRAug 24, 2020
Certified Robustness of Graph Neural Networks against Adversarial Structural Perturbation

Binghui Wang, Jinyuan Jia, Xiaoyu Cao et al.

Graph neural networks (GNNs) have recently gained much attention for node and graph classification tasks on graph-structured data. However, multiple recent works showed that an attacker can easily make GNNs predict incorrectly via perturbing the graph structure, i.e., adding or deleting edges in the graph. We aim to defend against such attacks via developing certifiably robust GNNs. Specifically, we prove the certified robustness guarantee of any GNN for both node and graph classifications against structural perturbation. Moreover, we show that our certified robustness guarantee is tight. Our results are based on a recently proposed technique called randomized smoothing, which we extend to graph data. We also empirically evaluate our method for both node and graph classifications on multiple GNNs and multiple benchmark datasets. For instance, on the Cora dataset, Graph Convolutional Network with our randomized smoothing can achieve a certified accuracy of 0.49 when the attacker can arbitrarily add/delete at most 15 edges in the graph.

25.0LGAug 7, 2020Code
LotteryFL: Personalized and Communication-Efficient Federated Learning with Lottery Ticket Hypothesis on Non-IID Datasets

Ang Li, Jingwei Sun, Binghui Wang et al.

Federated learning is a popular distributed machine learning paradigm with enhanced privacy. Its primary goal is learning a global model that offers good performance for the participants as many as possible. The technology is rapidly advancing with many unsolved challenges, among which statistical heterogeneity (i.e., non-IID) and communication efficiency are two critical ones that hinder the development of federated learning. In this work, we propose LotteryFL -- a personalized and communication-efficient federated learning framework via exploiting the Lottery Ticket hypothesis. In LotteryFL, each client learns a lottery ticket network (i.e., a subnetwork of the base model) by applying the Lottery Ticket hypothesis, and only these lottery networks will be communicated between the server and clients. Rather than learning a shared global model in classic federated learning, each client learns a personalized model via LotteryFL; the communication cost can be significantly reduced due to the compact size of lottery networks. To support the training and evaluation of our framework, we construct non-IID datasets based on MNIST, CIFAR-10 and EMNIST by taking feature distribution skew, label distribution skew and quantity skew into consideration. Experiments on these non-IID datasets demonstrate that LotteryFL significantly outperforms existing solutions in terms of personalization and communication cost.

42.8CRJun 19, 2020Code
Backdoor Attacks to Graph Neural Networks

Zaixi Zhang, Jinyuan Jia, Binghui Wang et al.

In this work, we propose the first backdoor attack to graph neural networks (GNN). Specifically, we propose a \emph{subgraph based backdoor attack} to GNN for graph classification. In our backdoor attack, a GNN classifier predicts an attacker-chosen target label for a testing graph once a predefined subgraph is injected to the testing graph. Our empirical results on three real-world graph datasets show that our backdoor attacks are effective with a small impact on a GNN's prediction accuracy for clean testing graphs. Moreover, we generalize a randomized smoothing based certified defense to defend against our backdoor attacks. Our empirical results show that the defense is effective in some cases but ineffective in other cases, highlighting the needs of new defenses for our backdoor attacks.

31.1CRApr 29, 2020
Perturbing Across the Feature Hierarchy to Improve Standard and Strict Blackbox Attack Transferability

Nathan Inkawhich, Kevin J Liang, Binghui Wang et al.

We consider the blackbox transfer-based targeted adversarial attack threat model in the realm of deep neural network (DNN) image classifiers. Rather than focusing on crossing decision boundaries at the output layer of the source model, our method perturbs representations throughout the extracted feature hierarchy to resemble other classes. We design a flexible attack framework that allows for multi-layer perturbations and demonstrates state-of-the-art targeted transfer performance between ImageNet DNNs. We also show the superiority of our feature space methods under a relaxation of the common assumption that the source and target models are trained on the same dataset and label space, in some instances achieving a $10\times$ increase in targeted success rate relative to other blackbox transfer methods. Finally, we analyze why the proposed methods outperform existing attack strategies and show an extension of the method in the case when limited queries to the blackbox model are allowed.

35.1CRFeb 26, 2020
On Certifying Robustness against Backdoor Attacks via Randomized Smoothing

Binghui Wang, Xiaoyu Cao, Jinyuan jia et al.

Backdoor attack is a severe security threat to deep neural networks (DNNs). We envision that, like adversarial examples, there will be a cat-and-mouse game for backdoor attacks, i.e., new empirical defenses are developed to defend against backdoor attacks but they are soon broken by strong adaptive backdoor attacks. To prevent such cat-and-mouse game, we take the first step towards certified defenses against backdoor attacks. Specifically, in this work, we study the feasibility and effectiveness of certifying robustness against backdoor attacks using a recent technique called randomized smoothing. Randomized smoothing was originally developed to certify robustness against adversarial examples. We generalize randomized smoothing to defend against backdoor attacks. Our results show the theoretical feasibility of using randomized smoothing to certify robustness against backdoor attacks. However, we also find that existing randomized smoothing methods have limited effectiveness at defending against backdoor attacks, which highlight the needs of new theory and methods to certify robustness against backdoor attacks.

32.8CRFeb 9, 2020
Certified Robustness of Community Detection against Adversarial Structural Perturbation via Randomized Smoothing

Jinyuan Jia, Binghui Wang, Xiaoyu Cao et al.

Community detection plays a key role in understanding graph structure. However, several recent studies showed that community detection is vulnerable to adversarial structural perturbation. In particular, via adding or removing a small number of carefully selected edges in a graph, an attacker can manipulate the detected communities. However, to the best of our knowledge, there are no studies on certifying robustness of community detection against such adversarial structural perturbation. In this work, we aim to bridge this gap. Specifically, we develop the first certified robustness guarantee of community detection against adversarial structural perturbation. Given an arbitrary community detection method, we build a new smoothed community detection method via randomly perturbing the graph structure. We theoretically show that the smoothed community detection method provably groups a given arbitrary set of nodes into the same community (or different communities) when the number of edges added/removed by an attacker is bounded. Moreover, we show that our certified robustness is tight. We also empirically evaluate our method on multiple real-world graphs with ground truth communities.

37.3CRMar 1, 2019
Attacking Graph-based Classification via Manipulating the Graph Structure

Binghui Wang, Neil Zhenqiang Gong

Graph-based classification methods are widely used for security and privacy analytics. Roughly speaking, graph-based classification methods include collective classification and graph neural network. Evading a graph-based classification method enables an attacker to evade detection in security analytics and can be used as a privacy defense against inference attacks. Existing adversarial machine learning studies mainly focused on machine learning for non-graph data. Only a few recent studies touched adversarial graph-based classification methods. However, they focused on graph neural network methods, leaving adversarial collective classification largely unexplored. We aim to bridge this gap in this work. We first propose a threat model to characterize the attack surface of a collective classification method. Specifically, we characterize an attacker's background knowledge along three dimensions: parameters of the method, training dataset, and the complete graph; an attacker's goal is to evade detection via manipulating the graph structure. We formulate our attack as a graph-based optimization problem, solving which produces the edges that an attacker needs to manipulate to achieve its attack goal. Moreover, we propose several approximation techniques to solve the optimization problem. We evaluate our attacks and compare them with a recent attack designed for graph neural networks. Results show that our attacks 1) can effectively evade graph-based classification methods; 2) do not require access to the true parameters, true training dataset, and/or complete graph; and 3) outperform the existing attack for evading collective classification methods and some graph neural network methods. We also apply our attacks to evade Sybil detection using a large-scale Twitter dataset and apply our attacks as a defense against attribute inference attacks using a large-scale Google+ dataset.

27.0CRDec 4, 2018
Graph-based Security and Privacy Analytics via Collective Classification with Joint Weight Learning and Propagation

Binghui Wang, Jinyuan Jia, Neil Zhenqiang Gong

Many security and privacy problems can be modeled as a graph classification problem, where nodes in the graph are classified by collective classification simultaneously. State-of-the-art collective classification methods for such graph-based security and privacy analytics follow the following paradigm: assign weights to edges of the graph, iteratively propagate reputation scores of nodes among the weighted graph, and use the final reputation scores to classify nodes in the graph. The key challenge is to assign edge weights such that an edge has a large weight if the two corresponding nodes have the same label, and a small weight otherwise. Although collective classification has been studied and applied for security and privacy problems for more than a decade, how to address this challenge is still an open question. In this work, we propose a novel collective classification framework to address this long-standing challenge. We first formulate learning edge weights as an optimization problem, which quantifies the goals about the final reputation scores that we aim to achieve. However, it is computationally hard to solve the optimization problem because the final reputation scores depend on the edge weights in a very complex way. To address the computational challenge, we propose to jointly learn the edge weights and propagate the reputation scores, which is essentially an approximate solution to the optimization problem. We compare our framework with state-of-the-art methods for graph-based security and privacy analytics using four large-scale real-world datasets from various application scenarios such as Sybil detection in social networks, fake review detection in Yelp, and attribute inference attacks. Our results demonstrate that our framework achieves higher accuracies than state-of-the-art methods with an acceptable computational overhead.

8.5CRJun 13, 2018
SybilBlind: Detecting Fake Users in Online Social Networks without Manual Labels

Binghui Wang, Le Zhang, Neil Zhenqiang Gong

Detecting fake users (also called Sybils) in online social networks is a basic security research problem. State-of-the-art approaches rely on a large amount of manually labeled users as a training set. These approaches suffer from three key limitations: 1) it is time-consuming and costly to manually label a large training set, 2) they cannot detect new Sybils in a timely fashion, and 3) they are vulnerable to Sybil attacks that leverage information of the training set. In this work, we propose SybilBlind, a structure-based Sybil detection framework that does not rely on a manually labeled training set. SybilBlind works under the same threat model as state-of-the-art structure-based methods. We demonstrate the effectiveness of SybilBlind using 1) a social network with synthetic Sybils and 2) two Twitter datasets with real Sybils. For instance, SybilBlind achieves an AUC of 0.98 on a Twitter dataset.

12.4CRMar 19, 2018
SybilFuse: Combining Local Attributes with Global Structure to Perform Robust Sybil Detection

Peng Gao, Binghui Wang, Neil Zhenqiang Gong et al.

Sybil attacks are becoming increasingly widespread and pose a significant threat to online social systems; a single adversary can inject multiple colluding identities in the system to compromise security and privacy. Recent works have leveraged social network-based trust relationships to defend against Sybil attacks. However, existing defenses are based on oversimplified assumptions about network structure, which do not necessarily hold in real-world social networks. Recognizing these limitations, we propose SybilFuse, a defense-in-depth framework for Sybil detection when the oversimplified assumptions are relaxed. SybilFuse adopts a collective classification approach by first training local classifiers to compute local trust scores for nodes and edges, and then propagating the local scores through the global network structure via weighted random walk and loopy belief propagation mechanisms. We evaluate our framework on both synthetic and real-world network topologies, including a large-scale, labeled Twitter network comprising 20M nodes and 265M edges, and demonstrate that SybilFuse outperforms state-of-the-art approaches significantly. In particular, SybilFuse achieves 98% of Sybil coverage among top-ranked nodes.

16.5CRMar 12, 2018
Structure-based Sybil Detection in Social Networks via Local Rule-based Propagation

Binghui Wang, Jinyuan Jia, Le Zhang et al.

Sybil detection in social networks is a basic security research problem. Structure-based methods have been shown to be promising at detecting Sybils. Existing structure-based methods can be classified into Random Walk (RW)-based methods and Loop Belief Propagation (LBP)-based methods. RW-based methods cannot leverage labeled Sybils and labeled benign users simultaneously, which limits their detection accuracy, and/or they are not robust to noisy labels. LBP-based methods are not scalable and cannot guarantee convergence. In this work, we propose SybilSCAR, a novel structure-based method to detect Sybils in social networks. SybilSCAR is Scalable, Convergent, Accurate, and Robust to label noise. We first propose a framework to unify RW-based and LBP-based methods. Under our framework, these methods can be viewed as iteratively applying a (different) local rule to every user, which propagates label information among a social graph. Second, we design a new local rule, which SybilSCAR iteratively applies to every user to detect Sybils. We compare SybilSCAR with state-of-the-art RW-based and LBP-based methods theoretically and empirically. Theoretically, we show that, with proper parameter settings, SybilSCAR has a tighter asymptotical bound on the number of Sybils that are falsely accepted into a social network than existing structure-based methods. Empirically, we perform evaluation using both social networks with synthesized Sybils and a large-scale Twitter dataset (41.7M nodes and 1.2B edges) with real Sybils. Our results show that 1) SybilSCAR is substantially more accurate and more robust to label noise than state-of-the-art RW-based methods; 2) SybilSCAR is more accurate and one order of magnitude more scalable than state-of-the-art LBP-based methods.

45.1CRFeb 14, 2018
Stealing Hyperparameters in Machine Learning

Binghui Wang, Neil Zhenqiang Gong

Hyperparameters are critical in machine learning, as different hyperparameters often result in models with significantly different performance. Hyperparameters may be deemed confidential because of their commercial value and the confidentiality of the proprietary algorithms that the learner uses to learn them. In this work, we propose attacks on stealing the hyperparameters that are learned by a learner. We call our attacks hyperparameter stealing attacks. Our attacks are applicable to a variety of popular machine learning algorithms such as ridge regression, logistic regression, support vector machine, and neural network. We evaluate the effectiveness of our attacks both theoretically and empirically. For instance, we evaluate our attacks on Amazon Machine Learning. Our results demonstrate that our attacks can accurately steal hyperparameters. We also study countermeasures. Our results highlight the need for new defenses against our hyperparameter stealing attacks for certain machine learning algorithms.

0.9CVJan 27, 2018
Robust Multi-subspace Analysis Using Novel Column L0-norm Constrained Matrix Factorization

Binghui Wang, Chuang Lin

We study the underlying structure of data (approximately) generated from a union of independent subspaces. Traditional methods learn only one subspace, failing to discover the multi-subspace structure, while state-of-the-art methods analyze the multi-subspace structure using data themselves as the dictionary, which cannot offer the explicit basis to span each subspace and are sensitive to errors via an indirect representation. Additionally, they also suffer from a high computational complexity, being quadratic or cubic to the sample size. To tackle all these problems, we propose a method, called Matrix Factorization with Column L0-norm constraint (MFC0), that can simultaneously learn the basis for each subspace, generate a direct sparse representation for each data sample, as well as removing errors in the data in an efficient way. Furthermore, we develop a first-order alternating direction algorithm, whose computational complexity is linear to the sample size, to stably and effectively solve the nonconvex objective function and non- smooth l0-norm constraint of MFC0. Experimental results on both synthetic and real-world datasets demonstrate that besides the superiority over traditional and state-of-the-art methods for subspace clustering, data reconstruction, error correction, MFC0 also shows its uniqueness for multi-subspace basis learning and direct sparse representation.