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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>
</div>
<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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<span class="dnerf">Nerfies</span> turns selfie videos from your phone into
free-viewpoint
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<!-- Abstract. -->
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<h2 class="title is-3">Abstract</h2>
<div class="content has-text-justified">
<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>
</div>
</div>
</div>
<!--/ Abstract. -->
</div>
</section>
<!-- Relations -->
<section class="section">
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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>
</div>
</div>
</div>
</section>
<!-- Relations -->
<!-- Overview -->
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<h2 class="title is-3">Method Overview of BEYOND</h2>
<div class="columns is-centered">
<div class="column container-centered">
<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 -->
<section class="section">
<div class="container is-max-desktop">
<h2 class="title is-3">Detection Performance</h2>
<div class="columns is-centered">
<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 container formula">
<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 <i>f</i>, a projector <i>h</i>, and a classification head <i>g</i>,
the classification branch can be formulated as <strong>C</strong>= <i>f</i> ° <i>g</i> and the representation branch as <strong>R</strong> = <i>f</i> ° <i>h</i>.
To attack effectively, the adversary must deceive the target model while guaranteeing the label consistency and representation similarity of the SSL model.
</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 class="row align-items-center adaptive-loss-formula-content">
<span class="formula label-loss formula-content">
$$
\displaystyle
Loss_{label} = \frac{1}{k} \sum_{i=1}^{k} \mathcal{L}\left(\mathbb{C}\left(W^i(x+\delta) \right), y_t\right)
$$
</span>
<span class="formula representation-loss formula-content" 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 formula-content" style="display: none;">
$$\displaystyle \mathcal{L}_C(x+\delta, y_t) + Loss_{label} - \alpha \cdot Loss_{repre}$$
</span>
</div>
</div>
</div>
</div>
<div class="columns is-centered">
<div class="column container adaptive-loss-formula-content">
<p class="formula label-loss formula-content">
where k represents the number of generated neighbors, <i>y</i><sub><i>t</i></sub> is the target class, and <strong><i>L</i></strong> is the cross entropy loss function.
</p>
<p class="formula representation-loss formula-content" style="display: none">
where k represents the number of generated neighbors, and <strong><i>S</i></strong> is the cosine similarity.
</p>
<p class="formula total-loss formula-content" style="display: none;">
where <strong><i>L</i></strong><sub>C</sub> indicates classifier's loss function, <i>y</i><sub><i>t</i></sub> is the targeted class, and α refers to a hyperparameter,
which is a trade-off parameter between label consistency and representation similarity..
</p>
</div>
</div>
<div class="columns is-centered">
<div class="column is-full-width">
<h3 class="title is-4">Performance of BEYOND against Adaptive Attacks</h3>
<div class="content has-text-justified">
<p>
We can also animate the scene by interpolating the deformation latent codes of two input
frames. Use the slider here to linearly interpolate between the left frame and the right
frame.
</p>
</div>
<div class="columns is-vcentered interpolation-panel">
<div id="adaptive-dataset" class="column is-3 align-items-center" style="width: 30%;">
<a href="#c10" class="selected">CIFAR-10</a>
<!-- <a href="#c100" class="selected">CIFAR-100</a> -->
<a href="#imgnet" >ImageNet</a>
<div style="clear: both"></div>
</div>
<div id="c10" class="column interpolation-video-column" style="width: 70%;">
<div id="interpolation-image-wrapper" >
Loading...
</div>
<input class="slider is-full-width is-large is-info"
id="interpolation-slider"
step="1" min="0" max="6" value="0" type="range">
<label for="interpolation-slider"><strong>Perturbation Budget Ε</strong> from 2/255 to 128/255</label>
</div>
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<div id="interpolation-image-wrapper" >
Loading...
</div>
<input class="slider is-full-width is-large is-info"
id="interpolation-slider"
step="1" min="0" max="6" value="0" type="range">
<label for="interpolation-slider"><strong>Perturbation Budget Ε</strong> from 2/255 to 128/255</label>
</div> -->
<div id="imgnet" class="column interpolation-video-column" style="width: 70%; display: none;">
<div id="interpolation-image-wrapper" >
Loading...
</div>
<input class="slider is-full-width is-large is-info"
id="interpolation-slider"
step="1" min="0" max="6" value="0" type="range">
<label for="interpolation-slider"><strong>Perturbation Budget Ε</strong> from 2/255 to 128/255</label>
</div>
</div>
<br/>
</div>
</div>
</section>
<!-- Adaptive Attack -->
<section class="section" id="BibTeX">
<div class="container is-max-desktop content">
<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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