Adversarial Attacks on ML Defense Models Competition
Tsinghua University（清华大学）；Alibaba Group（阿里巴巴集团）；RealAI；Shanghai Jiao Tong University（上海交通大学）；University of Electronic Science and Technology of China（电子科技大学）；University of Macau（澳门大学）；Chinese Academy of Sciences（中国科学院）；ShanghaiTech University（上海科技大学）；Huazhong University of Science and Technology（华中科技大学）；Indiana University Bloomington（印第安纳大学伯明顿分校）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；The Chinese University of Hong Kong（香港中文大学）
Yinpeng Dong, Qi-An Fu, Xiao Yang, Wenzhao Xiang, Tianyu Pang, Hang Su, Jun Zhu, Jiayu Tang, Yuefeng Chen, XiaoFeng Mao, Yuan He, Hui Xue, Chao Li, Ye Liu, Qilo… 展开作者
Due to the vulnerability of deep neural networks (DNNs) to adversarial examples, a large number of defense techniques have been proposed to alleviate this problem in recent years. However, the progress of building more robust models is usually hampered by the incomplete or incorrect robustness evaluation. To accelerate the research on reliable evaluation of adversarial robustness of the current defense models in image classification, the TSAIL group at Tsinghua University and the Alibaba Security group organized this competition along with a CVPR 2021 workshop on adversarial machine learning (https://aisecure-workshop.github.io/amlcvpr2021/). The purpose of this competition is to motivate novel attack algorithms to evaluate adversarial robustness more effectively and reliably. The participants were encouraged to develop stronger white-box attack algorithms to find the worst-case robustness of different defenses. This competition was conducted on an adversarial robustness evaluation platform -- ARES (https://github.com/thu-ml/ares), and is held on the TianChi platform (https://tianchi.aliyun.com/competition/entrance/531847/introduction) as one of the series of AI Security Challengers Program. After the competition, we summarized the results and established a new adversarial robustness benchmark at https://ml.cs.tsinghua.edu.cn/ares-bench/, which allows users to upload adversarial attack algorithms and defense models for evaluation.
MagNet and "Efficient Defenses..." were recently proposed as a defense to adversarial examples. We find that we can construct adversarial examples that defeat these defenses with only a slight increase in distortion.
I introduce a very simple method to defend against adversarial examples. The basic idea is to raise the slope of the ReLU function at the test time. Experiments over MNIST and CIFAR-10 datasets demonstrate the effectiveness of the proposed defense against a number of strong attacks in both untargeted and targeted settings. While perhaps not as effective as the state of the art adversarial defenses, this approach can provide insights to understand and mitigate adversarial attacks. It can also be used in conjunction with other defenses.
Under adversarial attacks, time series regression and classification are vulnerable. Adversarial defense, on the other hand, can make the models more resilient. It is important to evaluate how vulnerable different time series models are to attacks and how well they recover using defense. The sensitivity to various attacks and the robustness using the defense of several time series models are investigated in this study. Experiments are run on seven-time series models with three adversarial attacks and one adversarial defense. According to the findings, all models, particularly GRU and RNN, appe…
Adversarial attacks optimize against models to defeat defenses. Existing defenses are static, and stay the same once trained, even while attacks change. We argue that models should fight back, and optimize their defenses against attacks at test time. We propose dynamic defenses, to adapt the model and input during testing, by defensive entropy minimization (dent). Dent alters testing, but not training, for compatibility with existing models and train-time defenses. Dent improves the robustness of adversarially-trained defenses and nominally-trained models against white-box, black-box, and adap…
Emergence of the utility of 3D point cloud data in safety-critical vision tasks (e.g., ADAS) urges researchers to pay more attention to the robustness of 3D representations and deep networks. To this end, we develop an attack and defense scheme, dedicated to 3D point cloud data, for preventing 3D point clouds from manipulated as well as pursuing noise-tolerable 3D representation. A set of novel 3D point cloud attack operations are proposed via pointwise gradient perturbation and adversarial point attachment / detachment. We then develop a flexible perturbation-measurement scheme for 3D point c…
Although 3D point cloud classification has recently been widely deployed in different application scenarios, it is still very vulnerable to adversarial attacks. This increases the importance of robust training of 3D models in the face of adversarial attacks. Based on our analysis on the performance of existing adversarial attacks, more adversarial perturbations are found in the mid and high-frequency components of input data. Therefore, by suppressing the high-frequency content in the training phase, the models robustness against adversarial examples is improved. Experiments showed that the pr…
DIFFender: Diffusion-Based Adversarial Defense against Patch Attacks
Institute of Artificial Intelligence, Beihang University（北京航空航天大学人工智能学院）；Tsinghua-Bosch Joint ML Center, Tsinghua University（清华大学-博世联合机器学习中心）；Hangzhou Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Zhongguancun Laboratory（中关村实验室）；RealAI
University of Tübingen（图宾根大学）；DeepMind（深度思维）；Everyday Robots（日常机器人公司）
Adaptive defenses, which optimize at test time, promise to improve adversarial robustness. We categorize such adaptive test-time defenses, explain their potential benefits and drawbacks, and evaluate a representative variety of the latest adaptive defenses for image classification. Unfortunately, none significantly improve upon static defenses when subjected to our careful case study evaluation. Some even weaken the underlying static model while simultaneously increasing inference computation. While these results are disappointing, we still believe that adaptive test-time defenses are a promis…
Adversarial attacks hamper the functionality and accuracy of Deep Neural Networks (DNNs) by meddling with subtle perturbations to their inputs.In this work, we propose a new Mask-based Adversarial Defense scheme (MAD) for DNNs to mitigate the negative effect from adversarial attacks. To be precise, our method promotes the robustness of a DNN by randomly masking a portion of potential adversarial images, and as a result, the %classification result output of the DNN becomes more tolerant to minor input perturbations. Compared with existing adversarial defense techniques, our method does not need…
Deep neural networks are vulnerable to adversarial examples, which can mislead classifiers by adding imperceptible perturbations. An intriguing property of adversarial examples is their good transferability, making black-box attacks feasible in real-world applications. Due to the threat of adversarial attacks, many methods have been proposed to improve the robustness. Several state-of-the-art defenses are shown to be robust against transferable adversarial examples. In this paper, we propose a translation-invariant attack method to generate more transferable adversarial examples against the de…
Existing defenses against adversarial attacks are typically tailored to a specific perturbation type. Using adversarial training to defend against multiple types of perturbation requires expensive adversarial examples from different perturbation types at each training step. In contrast, manifold-based defense incorporates a generative network to project an input sample onto the clean data manifold. This approach eliminates the need to generate expensive adversarial examples while achieving robustness against multiple perturbation types. However, the success of this approach relies on whether t…
Boston University（波士顿大学）；Northeastern University（东北大学）；IBM Research（IBM研究院）
Designing effective defense against adversarial attacks is a crucial topic as deep neural networks have been proliferated rapidly in many security-critical domains such as malware detection and self-driving cars. Conventional defense methods, although shown to be promising, are largely limited by their single-source single-cost nature: The robustness promotion tends to plateau when the defenses are made increasingly stronger while the cost tends to amplify. In this paper, we study principles of designing multi-source and multi-cost schemes where defense performance is boosted from multiple def…
Advances in the development of adversarial attacks have been fundamental to the progress of adversarial defense research. Efficient and effective attacks are crucial for reliable evaluation of defenses, and also for developing robust models. Adversarial attacks are often generated by maximizing standard losses such as the cross-entropy loss or maximum-margin loss within a constraint set using Projected Gradient Descent (PGD). In this work, we introduce a relaxation term to the standard loss, that finds more suitable gradient-directions, increases attack efficacy and leads to more efficient adv…
We introduce a feature scattering-based adversarial training approach for improving model robustness against adversarial attacks. Conventional adversarial training approaches leverage a supervised scheme (either targeted or non-targeted) in generating attacks for training, which typically suffer from issues such as label leaking as noted in recent works. Differently, the proposed approach generates adversarial images for training through feature scattering in the latent space, which is unsupervised in nature and avoids label leaking. More importantly, this new approach generates perturbed imag…
Stony Brook University（石溪大学）；IBM Research（IBM研究院）；University of Michingan（密歇根大学）
Adversarial machine learning is a well-studied field of research where an adversary causes predictable errors in a machine learning algorithm through precise manipulation of the input. Numerous techniques have been proposed to harden machine learning algorithms and mitigate the effect of adversarial attacks. Of these techniques, adversarial training, which augments the training data with adversarial samples, has proven to be an effective defense with respect to a certain class of attacks. However, adversarial training is computationally expensive and its improvements are limited to a single mo…
Conventional adversarial defenses reduce classification accuracy whether or not a model is under attacks. Moreover, most of image processing based defenses are defeated due to the problem of obfuscated gradients. In this paper, we propose a new adversarial defense which is a defensive transform for both training and test images inspired by perceptual image encryption methods. The proposed method utilizes a block-wise pixel shuffling method with a secret key. The experiments are carried out on both adaptive and non-adaptive maximum-norm bounded white-box attacks while considering obfuscated gra…
This work conducts the first analysis on the robustness against adversarial attacks on self-supervised Vision Transformers trained using DINO. First, we evaluate whether features learned through self-supervision are more robust to adversarial attacks than those emerging from supervised learning. Then, we present properties arising for attacks in the latent space. Finally, we evaluate whether three well-known defense strategies can increase adversarial robustness in downstream tasks by only fine-tuning the classification head to provide robustness even in view of limited compute resources. Thes…
University of California, Berkeley（加州大学伯克利分校）；University of Michigan（密歇根大学）
Deep learning image classification is vulnerable to adversarial attack, even if the attacker changes just a small patch of the image. We propose a defense against patch attacks based on partially occluding the image around each candidate patch location, so that a few occlusions each completely hide the patch. We demonstrate on CIFAR-10, Fashion MNIST, and MNIST that our defense provides certified security against patch attacks of a certain size.
There has been extensive research on developing defense techniques against adversarial attacks; however, they have been mainly designed for specific model families or application domains, therefore, they cannot be easily extended. Based on the design philosophy of ensemble of diverse weak defenses, we propose ATHENA---a flexible and extensible framework for building generic yet effective defenses against adversarial attacks. We have conducted a comprehensive empirical study to evaluate several realizations of ATHENA with four threat models including zero-knowledge, black-box, gray-box, and whi…
Neural Networks are infamously sensitive to small perturbations in their inputs, making them vulnerable to adversarial attacks. This project evaluates the performance of Denoising Diffusion Probabilistic Models (DDPM) as a purification technique to defend against adversarial attacks. This works by adding noise to an adversarial example before removing it through the reverse process of the diffusion model. We evaluate the approach on the PatchCamelyon data set for histopathologic scans of lymph node sections and find an improvement of the robust accuracy by up to 88\% of the original model's ac…
New Jersey Institute of Technology（新泽西理工学院）；Qatar Computing Research Institute（卡塔尔计算研究所）
Machine learning models, especially neural network (NN) classifiers, are widely used in many applications including natural language processing, computer vision and cybersecurity. They provide high accuracy under the assumption of attack-free scenarios. However, this assumption has been defied by the introduction of adversarial examples -- carefully perturbed samples of input that are usually misclassified. Many researchers have tried to develop a defense against adversarial examples; however, we are still far from achieving that goal. In this paper, we design a Generative Adversarial Net (GAN…
A recent defense proposes to inject "honeypots" into neural networks in order to detect adversarial attacks. We break the baseline version of this defense by reducing the detection true positive rate to 0\% and the detection AUC to 0.02, maintaining the original distortion bounds. The authors of the original paper have amended the defense in their CCS'20 paper to mitigate this attacks. To aid further research, we release the complete 2.5 hour keystroke-by-keystroke screen recording of our attack process at https://nicholas.carlini.com/code/ccs_honeypot_break.
Recent studies have demonstrated that machine learning approaches like deep neural networks (DNNs) are easily fooled by adversarial attacks. Subtle and imperceptible perturbations of the data are able to change the result of deep neural networks. Leveraging vulnerable machine learning methods raises many concerns especially in domains where security is an important factor. Therefore, it is crucial to design defense mechanisms against adversarial attacks. For the task of image classification, unnoticeable perturbations mostly occur in the high-frequency spectrum of the image. In this paper, we …
Neural Network classifiers have been used successfully in a wide range of applications. However, their underlying assumption of attack free environment has been defied by adversarial examples. Researchers tried to develop defenses; however, existing approaches are still far from providing effective solutions to this evolving problem. In this paper, we design a generative adversarial net (GAN) based zero knowledge adversarial training defense, dubbed ZK-GanDef, which does not consume adversarial examples during training. Therefore, ZK-GanDef is not only efficient in training but also adaptive t…
Dataset bias is a problem in adversarial machine learning, especially in the evaluation of defenses. An adversarial attack or defense algorithm may show better results on the reported dataset than can be replicated on other datasets. Even when two algorithms are compared, their relative performance can vary depending on the dataset. Deep learning offers state-of-the-art solutions for image recognition, but deep models are vulnerable even to small perturbations. Research in this area focuses primarily on adversarial attacks and defense algorithms. In this paper, we report for the first time, a …
German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；TU Kaiserslautern（凯撒斯劳滕工业大学）
The adversarial vulnerability of deep networks has spurred the interest of researchers worldwide. Unsurprisingly, like images, adversarial examples also translate to time-series data as they are an inherent weakness of the model itself rather than the modality. Several attempts have been made to defend against these adversarial attacks, particularly for the visual modality. In this paper, we perform detailed benchmarking of well-proven adversarial defense methodologies on time-series data. We restrict ourselves to the $L_{\infty}$ threat model. We also explore the trade-off between smoothness …
Several moving target defenses (MTDs) to counter adversarial ML attacks have been proposed in recent years. MTDs claim to increase the difficulty for the attacker in conducting attacks by regularly changing certain elements of the defense, such as cycling through configurations. To examine these claims, we study for the first time the effectiveness of several recent MTDs for adversarial ML attacks applied to the malware detection domain. Under different threat models, we show that transferability and query attack strategies can achieve high levels of evasion against these defenses through exis…
Shenzhen Youjia Innov Tech Co., Ltd（深圳佑驾创新科技有限公司）；South China University of Technology（华南理工大学）；Hong Kong University of Science and Technology（香港科技大学）
Deep neural networks (DNNs) are known to be vulnerable to adversarial attacks that would trigger misclassification of DNNs but may be imperceptible to human perception. Adversarial defense has been an important way to improve the robustness of DNNs. Existing attack methods often construct adversarial examples relying on some metrics like the $\ell_p$ distance to perturb samples. However, these metrics can be insufficient to conduct adversarial attacks due to their limited perturbations. In this paper, we propose a new internal Wasserstein distance (IWD) to capture the semantic similarity of tw…
University of Kentucky（肯塔基大学）；Miami University（迈阿密大学）
Despite remarkable performance across a broad range of tasks, neural networks have been shown to be vulnerable to adversarial attacks. Many works focus on adversarial attacks and defenses on 2D images, but few focus on 3D point clouds. In this paper, our goal is to enhance the adversarial robustness of PointNet, which is one of the most widely used models for 3D point clouds. We apply the fast gradient sign attack method (FGSM) on 3D point clouds and find that FGSM can be used to generate not only adversarial images but also adversarial point clouds. To minimize the vulnerability of PointNet t…
Nanjing University of Information Science and Technology（南京信息工程大学）；State Key Laboratory of Mathematical Engineering and Advanced Computing（数学工程与先进计算国家重点实验室）；Qilu University of Technology（齐鲁工业大学）
The vulnerability of Deep Neural Networks (DNNs) to adversarial examples has been confirmed. Existing adversarial defenses primarily aim at preventing adversarial examples from attacking DNNs successfully, rather than preventing their generation. If the generation of adversarial examples is unregulated, images within reach are no longer secure and pose a threat to non-robust DNNs. Although gradient obfuscation attempts to address this issue, it has been shown to be circumventable. Therefore, we propose a novel adversarial defense mechanism, which is referred to as immune defense and is the exa…
A No-Defense Defense Against Gradient-Based Adversarial Attacks on ML-NIDS: Is Less More?
Carleton University（卡尔顿大学）；Computer Engineering Carleton University Ottawa, Canada（计算机工程系卡尔顿大学渥太华加拿大）；School of Information Technology Carleton University Ottawa, Canada（信息科技学院卡尔顿大学渥太华加拿大）
Guangzhou University（广州大学）；Cyberspace Institute of Advanced Technology（网络空间先进技术研究院）
Recent work shows that deep neural networks are vulnerable to adversarial examples. Much work studies adversarial example generation, while very little work focuses on more critical adversarial defense. Existing adversarial detection methods usually make assumptions about the adversarial example and attack method (e.g., the word frequency of the adversarial example, the perturbation level of the attack method). However, this limits the applicability of the detection method. To this end, we propose TREATED, a universal adversarial detection method that can defend against attacks of various pert…
Recent studies on adversarial images have shown that they tend to leave the underlying low-dimensional data manifold, making them significantly more challenging for current models to make correct predictions. This so-called off-manifold conjecture has inspired a novel line of defenses against adversarial attacks on images. In this study, we find a similar phenomenon occurs in the contextualized embedding space induced by pretrained language models, in which adversarial texts tend to have their embeddings diverge from the manifold of natural ones. Based on this finding, we propose Textual Manif…
In spite of the enormous success of neural networks, adversarial examples remain a relatively weakly understood feature of deep learning systems. There is a considerable effort in both building more powerful adversarial attacks and designing methods to counter the effects of adversarial examples. We propose a method to transform the adversarial input data through a mixture of generators in order to recover the correct class obfuscated by the adversarial attack. A canonical set of images is used to generate adversarial examples through potentially multiple attacks. Such transformed images are p…
Deep-learning based classification algorithms have been shown to be susceptible to adversarial attacks: minor changes to the input of classifiers can dramatically change their outputs, while being imperceptible to humans. In this paper, we present a simple hypothesis about a feature compression property of artificial intelligence (AI) classifiers and present theoretical arguments to show that this hypothesis successfully accounts for the observed fragility of AI classifiers to small adversarial perturbations. Drawing on ideas from information and coding theory, we propose a general class of de…
This study provides a new understanding of the adversarial attack problem by examining the correlation between adversarial attack and visual attention change. In particular, we observed that: (1) images with incomplete attention regions are more vulnerable to adversarial attacks; and (2) successful adversarial attacks lead to deviated and scattered attention map. Accordingly, an attention-based adversarial defense framework is designed to simultaneously rectify the attention map for prediction and preserve the attention area between adversarial and original images. The problem of adding iterat…
Convolutional Neural Networks have been shown to be vulnerable to adversarial examples, which are known to locate in subspaces close to where normal data lies but are not naturally occurring and of low probability. In this work, we investigate the potential effect defense techniques have on the geometry of the likelihood landscape - likelihood of the input images under the trained model. We first propose a way to visualize the likelihood landscape leveraging an energy-based model interpretation of discriminative classifiers. Then we introduce a measure to quantify the flatness of the likelihoo…
Hong Kong Baptist University（香港浸会大学）；AWS AI Labs（AWS 人工智能实验室）；Johns Hopkins University（约翰斯·霍普金斯大学）
Open-set recognition and adversarial defense study two key aspects of deep learning that are vital for real-world deployment. The objective of open-set recognition is to identify samples from open-set classes during testing, while adversarial defense aims to defend the network against images with imperceptible adversarial perturbations. In this paper, we show that open-set recognition systems are vulnerable to adversarial attacks. Furthermore, we show that adversarial defense mechanisms trained on known classes do not generalize well to open-set samples. Motivated by this observation, we empha…
The safety and robustness of learning-based decision-making systems are under threats from adversarial examples, as imperceptible perturbations can mislead neural networks to completely different outputs. In this paper, we present an adaptive view of the issue via evaluating various test-time smoothing defense against white-box untargeted adversarial examples. Through controlled experiments with pretrained ResNet-152 on ImageNet, we first illustrate the non-monotonic relation between adversarial attacks and smoothing defenses. Then at the dataset level, we observe large variance among samples …
Defense without Forgetting: Continual Adversarial Defense with Anisotropic & Isotropic Pseudo Replay
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies（广东省新型安全智能技术重点实验室）
Designing an attack-defense game: how to increase robustness of financial transaction models via a competition
Skoltech（斯科尔科沃科学技术学院）；Open Data Science（开放数据科学机构）；Innotech（因诺科技公司）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；Kazan Federal University（喀山联邦大学）；Kaspersky Lab（卡巴斯基实验室）；Zvuk（兹武克公司）
Univ. of Southern California（南加州大学）；Univ. of Nevada（内华达大学）；Docomo Innovations Inc.（都科摩创新公司）
Deep neural networks have demonstrated cutting edge performance on various tasks including classification. However, it is well known that adversarially designed imperceptible perturbation of the input can mislead advanced classifiers. In this paper, Permutation Phase Defense (PPD), is proposed as a novel method to resist adversarial attacks. PPD combines random permutation of the image with phase component of its Fourier transform. The basic idea behind this approach is to turn adversarial defense problems analogously into symmetric cryptography, which relies solely on safekeeping of the keys …
Though deep neural networks perform challenging tasks excellently, they are susceptible to adversarial examples, which mislead classifiers by applying human-imperceptible perturbations on clean inputs. Under the query-free black-box scenario, adversarial examples are hard to transfer to unknown models, and several methods have been proposed with the low transferability. To settle such issue, we design a max-min framework inspired by input transformations, which are benificial to both the adversarial attack and defense. Explicitly, we decrease loss values with inputs' affline transformations as…
Texas A&M University（得克萨斯农工大学）；Arizona State University（亚利桑那州立大学）
Despite the recent advances in a wide spectrum of applications, machine learning models, especially deep neural networks, have been shown to be vulnerable to adversarial attacks. Attackers add carefully-crafted perturbations to input, where the perturbations are almost imperceptible to humans, but can cause models to make wrong predictions. Techniques to protect models against adversarial input are called adversarial defense methods. Although many approaches have been proposed to study adversarial attacks and defenses in different scenarios, an intriguing and crucial challenge remains that how…
DeepRobust is a PyTorch adversarial learning library which aims to build a comprehensive and easy-to-use platform to foster this research field. It currently contains more than 10 attack algorithms and 8 defense algorithms in image domain and 9 attack algorithms and 4 defense algorithms in graph domain, under a variety of deep learning architectures. In this manual, we introduce the main contents of DeepRobust with detailed instructions. The library is kept updated and can be found at https://github.com/DSE-MSU/DeepRobust.
Xi’an Jiaotong University（西安交通大学）；University of British Columbia（不列颠哥伦比亚大学）；Beijing Normal University（北京师范大学）
Deep learning based image classification models are shown vulnerable to adversarial attacks by injecting deliberately crafted noises to clean images. To defend against adversarial attacks in a training-free and attack-agnostic manner, this work proposes a novel and effective reconstruction-based defense framework by delving into deep image prior (DIP). Fundamentally different from existing reconstruction-based defenses, the proposed method analyzes and explicitly incorporates the model decision process into our defense. Given an adversarial image, firstly we map its reconstructed images during…
Xi’an Jiaotong University（西安交通大学）；Alibaba Group（阿里巴巴集团）；ABB Corporate Research Center（ABB企业研究中心）；Wormpex AI Research（Wormpex人工智能研究院）
Deep Neural Network classifiers are vulnerable to adversarial attack, where an imperceptible perturbation could result in misclassification. However, the vulnerability of DNN-based image ranking systems remains under-explored. In this paper, we propose two attacks against deep ranking systems, i.e., Candidate Attack and Query Attack, that can raise or lower the rank of chosen candidates by adversarial perturbations. Specifically, the expected ranking order is first represented as a set of inequalities, and then a triplet-like objective function is designed to obtain the optimal perturbation. C…
Harbin Insititute of Technology（哈尔滨工业大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Harbin Insititute of Technology(ShenZhen)（哈尔滨工业大学（深圳））；Macquaire University（麦考瑞大学）；University of Technology Sydney（悉尼科技大学）
Nowadays, Deep Learning as a service can be deployed in Internet of Things (IoT) to provide smart services and sensor data processing. However, recent research has revealed that some Deep Neural Networks (DNN) can be easily misled by adding relatively small but adversarial perturbations to the input (e.g., pixel mutation in input images). One challenge in defending DNN against these attacks is to efficiently identifying and filtering out the adversarial pixels. The state-of-the-art defense strategies with good robustness often require additional model training for specific attacks. To reduce t…
