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<h1 class="title is-1 publication-title">Be Your Own Neighborhood: Detecting Adversarial Examples by the Neighborhood Relations Built on Self-Supervised Learning</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="#" target="_blank">Zhiyuan He</a><sup>1*</sup>,</span>
<span class="author-block">
<a href="https://yangyijune.github.io/" target="_blank">Yijun Yang</a><sup>1*</sup>,</span>
<span class="author-block">
<a href="https://sites.google.com/site/pinyuchenpage/home" target="_blank">Pin-Yu Chen</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://cure-lab.github.io/" target="_blank">Qiang Xu</a><sup>1</sup>,
</span>
<span class="author-block">
<a href="https://tsungyiho.github.io/" target="_blank">Tsung-Yi Ho</a><sup>1</sup>,
</span>
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<div class="is-size-5 publication-authors">
<span class="author-block"><sup>*</sup>Equal contribution,</span>
<span class="author-block"><sup>1</sup>The Chinese University of Hong Kong,</span>
<span class="author-block"><sup>2</sup>IBM Research</span>
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<h2 class="title is-3">Abstract</h2>
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<p>
Deep Neural Networks (DNNs) have achieved excellent performance in various fields. However, DNNs’ vulnerability to
Adversarial Examples (AE) hinders their deployments to safety-critical applications. In this paper, we present <strong>BEYOND</strong>,
an innovative AE detection frameworkdesigned for reliable predictions. BEYOND identifies AEs by distinguishing the AE’s
abnormal relation with its augmented versions, i.e. neighbors, from two prospects: representation similarity and label
consistency. An off-the-shelf Self-Supervised Learning (SSL) model is used to extract the representation and predict the
label for its highly informative representation capacity compared to supervised learning models. We found clean samples
maintain a high degree of representation similarity and label consistency relative to their neighbors, in contrast to AEs
which exhibit significant discrepancies. We explain this obser vation and show that leveraging this discrepancy BEYOND can
accurately detect AEs. Additionally, we develop a rigorous justification for the effectiveness of BEYOND. Furthermore, as a
plug-and-play model, BEYOND can easily cooperate with the Adversarial Trained Classifier (ATC), achieving state-of-the-art
(SOTA) robustness accuracy. Experimental results show that BEYOND outperforms baselines by a large margin, especially under
adaptive attacks. Empowered by the robust relationship built on SSL, we found that BEYOND outperforms baselines in terms
of both detection ability and speed.
</p>
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</div>
<!--/ Abstract. -->
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<!-- Relations -->
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<h2 class="title is-3">Neighborhood Relations of AEs and Clean Samples</h2>
<div class="columns is-centered">
<div class="column container-centered">
<img src="./static/images/relations.jpg" alt="Neighborhood Relations of Benign Examples and AEs"/>
<p>
<strong>Figure 1. Neighborhood Relations of AEs and Clean Samples.</strong>
</p>
</div>
</div>
<div class="columns is-centered">
<div class="column has-text-justified">
<p>
Latent Neighborhood Graph (LNG) represents the relationship between the input sample and the reference sample as a graph,
whose nodes are embeddings extracted by DDN and edges are built according to distances between the input node and reference nodes,
and train a graph neural network to detect AEs.
</p>
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</div>
</section>
<!-- Relations -->
<!-- Overview -->
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<h2 class="title is-3">Method Overview of BEYOND</h2>
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<img src="./static/images/overview.png" alt="Method Overview of BEYOND"/>
<p><strong>Figure 2. Overview of BEYOND.</strong> First, we augment the input image to obtain a bunch of its neighbors. Then, we
perform the label consistency detection mechanism on the classifier’s prediction of the input image and that of neighbors predicted by
SSL’s classification head. Meanwhile, the representation similarity mechanism employs cosine distance to measure the similarity among
the input image and its neighbors. Finally, The input image with poor label consistency or representation similarity is flagged as AE.</p>
</div>
</div>
</div>
</section>
<!-- Overview -->
<!-- Results -->
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<h2 class="title is-3">Detection Performance</h2>
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<div class="column container-centered">
<table class="tg" border="1" style="width:100%;">
<caption><strong>Table 1.</strong>The Area Under the ROC Curve (AUC) of Different Adversarial Detection Approaches on CIFAR-10. LNG
is not open-sourced and the data comes from its report. To align with baselines, classifier: ResNet110, FGSM: ε = 0.05, PGD:
ε = 0.02. Note that BEYOND needs no AE for training, leading to the same value on both seen and unseen settings. The <strong>bold</strong> values
are the best performance, and the <u><i>underlined italicized</i></u> values are the second-best performanc</caption>
<thead>
<tr>
<th class="tg-amwm" rowspan="2">AUC(%)</th>
<th class="tg-baqh" colspan="4"><span style="font-weight:bold;font-style:italic">Unse</span><span style="font-weight:bold">e</span><span style="font-weight:bold;font-style:italic">n</span><span style="font-weight:bold">: </span>Attacks used in training are preclude from tests</th>
<th class="tg-baqh" colspan="5"><span style="font-weight:bold;font-style:italic">Seen</span><span style="font-weight:bold">:</span> Attacks used in training are included in tests</th>
</tr>
<tr>
<th class="tg-baqh">FGSM</th>
<th class="tg-baqh">PGD</th>
<th class="tg-baqh">AutoAttack</th>
<th class="tg-baqh">Square</th>
<th class="tg-baqh">FGSM</th>
<th class="tg-baqh">PGD</th>
<th class="tg-baqh">CW</th>
<th class="tg-baqh">AutoAttack</th>
<th class="tg-baqh">Square</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-baqh">DkNN</td>
<td class="tg-baqh">61.55</td>
<td class="tg-baqh">51.22</td>
<td class="tg-baqh">52.12</td>
<td class="tg-baqh">59.46</td>
<td class="tg-baqh">61.55</td>
<td class="tg-baqh">51.22</td>
<td class="tg-baqh">61.52</td>
<td class="tg-baqh">52.12</td>
<td class="tg-baqh">59.46</td>
</tr>
<tr>
<td class="tg-baqh">kNN</td>
<td class="tg-baqh">61.83</td>
<td class="tg-baqh">54.52</td>
<td class="tg-baqh">52.67</td>
<td class="tg-baqh">73.39</td>
<td class="tg-baqh">61.83</td>
<td class="tg-baqh">54.52</td>
<td class="tg-baqh">62.23</td>
<td class="tg-baqh">52.67</td>
<td class="tg-baqh">73.39</td>
</tr>
<tr>
<td class="tg-baqh">LID</td>
<td class="tg-baqh">71.08</td>
<td class="tg-baqh">61.33</td>
<td class="tg-baqh">55.56</td>
<td class="tg-baqh">66.18</td>
<td class="tg-baqh">73.61</td>
<td class="tg-baqh">67.98</td>
<td class="tg-baqh">55.68</td>
<td class="tg-baqh">56.33</td>
<td class="tg-baqh">85.94</td>
</tr>
<tr>
<td class="tg-baqh">Hu</td>
<td class="tg-baqh">84.51</td>
<td class="tg-baqh">58.59</td>
<td class="tg-baqh">53.55</td>
<td class="tg-2imo">95.82</td>
<td class="tg-baqh">84.51</td>
<td class="tg-baqh">58.59</td>
<td class="tg-2imo">91.02</td>
<td class="tg-baqh">53.55</td>
<td class="tg-baqh">95.82</td>
</tr>
<tr>
<td class="tg-baqh">Mao</td>
<td class="tg-baqh">95.33</td>
<td class="tg-2imo">82.61</td>
<td class="tg-2imo">81.95</td>
<td class="tg-baqh">85.76</td>
<td class="tg-baqh">95.33</td>
<td class="tg-baqh">82.61</td>
<td class="tg-baqh">83.10</td>
<td class="tg-baqh">81.95</td>
<td class="tg-baqh">85.76</td>
</tr>
<tr>
<td class="tg-baqh">LNG</td>
<td class="tg-2imo">98.51 </td>
<td class="tg-baqh">63.14 </td>
<td class="tg-baqh">58.47 </td>
<td class="tg-baqh">94.71 </td>
<td class="tg-amwm">99.88 </td>
<td class="tg-2imo">91.39 </td>
<td class="tg-baqh">89.74 </td>
<td class="tg-2imo">84.03 </td>
<td class="tg-2imo">98.82 </td>
</tr>
<tr>
<td class="tg-baqh">BEYOND</td>
<td class="tg-amwm">98.89</td>
<td class="tg-amwm">99.28</td>
<td class="tg-amwm">99.16</td>
<td class="tg-amwm">99.27</td>
<td class="tg-2imo">98.89</td>
<td class="tg-amwm">99.28</td>
<td class="tg-amwm">99.20</td>
<td class="tg-amwm">99.16</td>
<td class="tg-amwm">99.27</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</section>
<!-- Results -->
<!-- Adaptive Attack -->
<section class="section">
<div class="container is-max-desktop">
<h2 class="title is-3">Adaptive Attack</h2>
<div class="columns is-centered">
<div class="column">
<p>
Attackers can design adaptive attacks to try to bypass BEYOND when the attacker knows all the parameters of the model
and the detection strategy. For an SSL model with a feature extractor $f$, a projector $h$, and a classification head $g$,
the classification branch can be formulated as $\mathbb{C} = f\circ g$ and the representation branch as $\mathbb{R} = f\circ h$.
To attack effectively, the adversary must deceive the target model while guaranteeing the label consistency and representation similarity of the SSL model.
<!-- where $\mathcal{S}$ represents cosine similarity, $k$ represents the number of generated neighbors,
and the linear augmentation function $W(x)=W(x,p);~p\sim P$ randomly samples $p$ from the parameter distribution $P$ to generate different neighbors.
Note that we guarantee the generated neighbors are fixed each time by fixing the random seed. The adaptive adversaries perform attacks on the following objective function:
where $\mathcal{L}_C$ indicates classifier's loss function, $y_t$ is the targeted class, and $\alpha$ refers to a hyperparameter. -->
</div>
</div>
<div class="columns is-centered">
<div class="column container-centered">
<div id="adaptive-loss-formula" class="container">
<div id="adaptive-loss-formula-list" class="row align-items-center formula-list">
<a href=".label-loss" class="selected">Label Consistency Loss</a>
<a href=".representation-loss">Representation Similarity Loss</a>
<a href=".total-loss">Total Loss</a>
<div style="clear: both"></div>
</div>
<div id="adaptive-loss-formula-content" class="row align-items-center">
<span class="formula label-loss" style="">
$$
\displaystyle
Loss_{label} = \frac{1}{k} \sum_{i=1}^{k} \mathcal{L}\left(\mathbb{C}\left(W^i(x+\delta) \right), y_t\right)
$$
</span>
<span class="formula representation-loss" style="display: none;">
$$
\displaystyle
Loss_{repre} = \frac{1}{k} \sum_{i=1}^{k}\mathcal{S}(\mathbb{R}(W^i(x+\delta)), \mathbb{R}(x+\delta))
$$
</span>
<span class="formula total-loss" style="display: none;">
$$\displaystyle \mathcal{L}_C(x+\delta, y_t) + Loss_{label} - \alpha \cdot Loss_{repre}$$
</span>
</div>
</div>
</div>
<div class="columns is-centered">
<div class="column">
<p class="eq-des label-loss">
Attackers can design adaptive attacks to try to bypass BEYOND when the attacker knows all the parameters of the model
and the detection strategy. For an SSL model with a feature extractor $f$, a projector $h$, and a classification head $g$,
the classification branch can be formulated as $\mathbb{C} = f\circ g$ and the representation branch as $\mathbb{R} = f\circ h$.
To attack effectively, the adversary must deceive the target model while guaranteeing the label consistency and representation similarity of the SSL model.
</p>
<p class="eq-des representation-loss" style="display: none">
where $\mathcal{S}$ represents cosine similarity, $k$ represents the number of generated neighbors,
and the linear augmentation function $W(x)=W(x,p);~p\sim P$ randomly samples $p$ from the parameter distribution $P$ to generate different neighbors.
Note that we guarantee the generated neighbors are fixed each time by fixing the random seed. The adaptive adversaries perform attacks on the following objective function:
</p>
<p class="eq-des total-loss" style="display: none;">
where $\mathcal{L}_C$ indicates classifier's loss function, $y_t$ is the targeted class, and $\alpha$ refers to a hyperparameter.
</p>
</div>
</div>
</div>
<div class="columns is-centered">
<div class="column">
<div class="content">
<h2 class="title is-4">Performance against Adaptive Attacks</h2>
</div>
<div class="column">
<div class="content">
<h2 class="title is-4">Contribution of Representation Similarity & Label Con-
sistency against Adaptive Attacks</h2>
</div>
</div>
</div>
</div>
</section>
<!-- Adaptive Attack -->
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<h2 class="title">BibTeX</h2>
<pre><code>@article{he2024beyond,
author = {Zhiyuan, He and Yijun, Yang and Pin-Yu, Chen and Qiang, Xu and Tsung-Yi, Ho},
title = {Be your own neighborhood: Detecting adversarial example by the neighborhood relations built on self-supervised learning},
journal = {ICML},
year = {2024},
}</code></pre>
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