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<h1 class="title is-1 publication-title">GREAT Score: Global Robustness Evaluation of
Adversarial Perturbation using Generative Models</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="#" target="_blank">ZAITANG LI</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://tsungyiho.github.io/" target="_blank">Tsung-Yi Ho</a><sup>1</sup>,
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<div class="is-size-5 publication-authors">
<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>
Current studies on adversarial robustness mainly focus on aggregating <i>local</i> robustness results from a set of data samples to evaluate and rank different models. However, the local statistics may not well represent the true <i>global</i> robustness of the underlying unknown data distribution. To address this challenge, this paper makes the first attempt to present a new framework, called <strong>GREAT Score</strong>, for global robustness evaluation of adversarial perturbation using generative models. Formally, GREAT Score carries the physical meaning of a global statistic capturing a mean certified attack-proof perturbation level over all samples drawn from a generative model. For finite-sample evaluation, we also derive a probabilistic guarantee on the sample complexity and the difference between the sample mean and the true mean. GREAT Score has several advantages: (1) Robustness evaluations using GREAT Score are efficient and scalable to large models, by sparing the need of running adversarial attacks. In particular, we show high correlation and significantly reduced computation cost of GREAT Score when compared to the attack-based model ranking on RobustBench<sup>1</sup>. (2) The use of generative models facilitates the approximation of the unknown data distribution. In our ablation study with different generative adversarial networks (GANs), we observe consistency between global robustness evaluation and the quality of GANs. (3) GREAT Score can be used for remote auditing of privacy-sensitive black-box models, as demonstrated by our robustness evaluation on several online facial recognition services.
</p>
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<!-- References -->
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<p>
<sup>1</sup> Croce, F., Andriushchenko, M., Sehwag, V., Debenedetti, E., Flammarion, N., Chiang, M., Mittal, P., & Hein, M. (2021). RobustBench: a standardized adversarial robustness benchmark. In <i>Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2)</i>. <a href="https://openreview.net/forum?id=SSKZPJCt7B" target="_blank">https://openreview.net/forum?id=SSKZPJCt7B</a>
</p>
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<!--/ Abstract. -->
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<!-- 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>
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</section>
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<h2 class="title is-3">GREAT Score Results</h2>
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<table class="tg" border="1" style="width:100%;">
<caption><strong>Table 1.</strong> Comparison of (Calibrated) GREAT Score v.s. minimal distortion found by CW attack on CIFAR-10. The results are averaged over 500 samples from StyleGAN2.</caption>
<thead>
<tr>
<th class="tg-amwm">Model Name</th>
<th class="tg-baqh">RobustBench Accuracy(%)</th>
<th class="tg-baqh">AutoAttack Accuracy(%)</th>
<th class="tg-baqh">GREAT Score</th>
<th class="tg-baqh">Calibrated GREAT Score</th>
<th class="tg-baqh">CW Distortion</th>
</tr>
</thead>
<tbody>
<tr>
<td class="tg-baqh">Rebuffi_extra</td>
<td class="tg-baqh">82.32</td>
<td class="tg-baqh">87.20</td>
<td class="tg-baqh">0.507</td>
<td class="tg-baqh">1.216</td>
<td class="tg-baqh">1.859</td>
</tr>
<tr>
<td class="tg-baqh">Gowal_extra</td>
<td class="tg-baqh">80.53</td>
<td class="tg-baqh">85.60</td>
<td class="tg-baqh">0.534</td>
<td class="tg-baqh">1.213</td>
<td class="tg-baqh">1.324</td>
</tr>
<tr>
<td class="tg-baqh">Rebuffi_70_ddpm</td>
<td class="tg-baqh">80.42</td>
<td class="tg-baqh">90.60</td>
<td class="tg-baqh">0.451</td>
<td class="tg-baqh">1.208</td>
<td class="tg-baqh">1.943</td>
</tr>
<tr>
<td class="tg-baqh">Rebuffi_28_ddpm</td>
<td class="tg-baqh">78.80</td>
<td class="tg-baqh">90.00</td>
<td class="tg-baqh">0.424</td>
<td class="tg-baqh">1.214</td>
<td class="tg-baqh">1.796</td>
</tr>
<tr>
<td class="tg-baqh">Augustin_WRN_extra</td>
<td class="tg-baqh">78.79</td>
<td class="tg-baqh">86.20</td>
<td class="tg-baqh">0.525</td>
<td class="tg-baqh">1.206</td>
<td class="tg-baqh">1.340</td>
</tr>
<tr>
<td class="tg-baqh">Sehwag</td>
<td class="tg-baqh">77.24</td>
<td class="tg-baqh">89.20</td>
<td class="tg-baqh">0.227</td>
<td class="tg-baqh">1.143</td>
<td class="tg-baqh">1.392</td>
</tr>
<tr>
<td class="tg-baqh">Augustin_WRN</td>
<td class="tg-baqh">76.25</td>
<td class="tg-baqh">86.40</td>
<td class="tg-baqh">0.583</td>
<td class="tg-baqh">1.206</td>
<td class="tg-baqh">1.332</td>
</tr>
<tr>
<td class="tg-baqh">Rade</td>
<td class="tg-baqh">76.15</td>
<td class="tg-baqh">86.60</td>
<td class="tg-baqh">0.413</td>
<td class="tg-baqh">1.200</td>
<td class="tg-baqh">1.486</td>
</tr>
<tr>
<td class="tg-baqh">Rebuffi_R18</td>
<td class="tg-baqh">75.86</td>
<td class="tg-baqh">87.60</td>
<td class="tg-baqh">0.369</td>
<td class="tg-baqh">1.210</td>
<td class="tg-baqh">1.413</td>
</tr>
<tr>
<td class="tg-baqh">Gowal</td>
<td class="tg-baqh">74.50</td>
<td class="tg-baqh">86.40</td>
<td class="tg-baqh">0.124</td>
<td class="tg-baqh">1.116</td>
<td class="tg-baqh">1.253</td>
</tr>
<tr>
<td class="tg-baqh">Sehwag_R18</td>
<td class="tg-baqh">74.41</td>
<td class="tg-baqh">88.60</td>
<td class="tg-baqh">0.236</td>
<td class="tg-baqh">1.135</td>
<td class="tg-baqh">1.343</td>
</tr>
<tr>
<td class="tg-baqh">Wu2020Adversarial</td>
<td class="tg-baqh">73.66</td>
<td class="tg-baqh">84.60</td>
<td class="tg-baqh">0.128</td>
<td class="tg-baqh">1.110</td>
<td class="tg-baqh">1.369</td>
</tr>
<tr>
<td class="tg-baqh">Augustin2020Adversarial</td>
<td class="tg-baqh">72.91</td>
<td class="tg-baqh">85.20</td>
<td class="tg-baqh">0.569</td>
<td class="tg-baqh">1.199</td>
<td class="tg-baqh">1.285</td>
</tr>
<tr>
<td class="tg-baqh">Engstrom2019Robustness</td>
<td class="tg-baqh">69.24</td>
<td class="tg-baqh">82.20</td>
<td class="tg-baqh">0.160</td>
<td class="tg-baqh">1.020</td>
<td class="tg-baqh">1.084</td>
</tr>
<tr>
<td class="tg-baqh">Rice2020Overfitting</td>
<td class="tg-baqh">67.68</td>
<td class="tg-baqh">81.80</td>
<td class="tg-baqh">0.152</td>
<td class="tg-baqh">1.040</td>
<td class="tg-baqh">1.097</td>
</tr>
<tr>
<td class="tg-baqh">Rony2019Decoupling</td>
<td class="tg-baqh">66.44</td>
<td class="tg-baqh">79.20</td>
<td class="tg-baqh">0.275</td>
<td class="tg-baqh">1.101</td>
<td class="tg-baqh">1.165</td>
</tr>
<tr>
<td class="tg-baqh">Ding2020MMA</td>
<td class="tg-baqh">66.09</td>
<td class="tg-baqh">77.60</td>
<td class="tg-baqh">0.112</td>
<td class="tg-baqh">0.909</td>
<td class="tg-baqh">1.095</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</section>
<!-- Results -->
<!-- New Figure Section -->
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<div>
<img src="./static/images/new_figure_2_2.png"
class="method_overview"
alt="Comparison of local GREAT Score and CW attack"/>
<p>
<strong>Figure 2.</strong> Comparison of local GREAT Score and CW attack in L<sub>2</sub> perturbation on CIFAR-10 with Rebuffi_extra model.
The x-axis is the image id. The result shows the local GREAT Score is indeed a lower bound of the perturbation level found by CW attack.
</p>
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</div>
</div>
</div>
</section>
<!-- New Figure Section -->
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<h2 class="title is-3">Robustness Certificate Definition</h2>
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<p>
GREAT Score is designed to evaluate the global robustness of classifiers against adversarial attacks. It uses generative models to estimate a certified lower bound on true global robustness. For a K-way classifier f, we define a local robustness score g(G(z)) for a generated sample G(z), where G is a generator and z is sampled from a standard Gaussian distribution. This score measures the confidence gap between the correct class prediction and the most likely incorrect class. The GREAT Score, defined as the expectation of g(G(z)) over z, provides a certified lower bound on the true global robustness with respect to the data distribution learned by the generative model. This approach allows us to estimate global robustness without knowing the exact data distribution or minimal perturbations for each sample.
</p>
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<div id="adaptive-loss-formula-list" class="row align-items-center formula-list">
<a href=".true-global-robustness" class="selected">True Global Robustness</a>
<a href=".global-robustness-estimate">Global Robustness Estimate</a>
<a href=".local-robustness-score">Local Robustness Score</a>
<div style="clear: both"></div>
</div>
<div class="row align-items-center adaptive-loss-formula-content">
<span class="formula true-global-robustness formula-content">
$$
\displaystyle
\Omega(f) = \mathbb{E}_{x\sim P}[\Delta_{min}(x)]= \int_{x \sim P} \Delta_{\min}(x) p(x)dx
$$
</span>
<span class="formula global-robustness-estimate formula-content" style="display: none;">
$$
\displaystyle
\widehat{\Omega}(f) = \mathbb{E}_{x\sim P}[g(x)]= \int_{x \sim P} g(x) p(x)dx
$$
</span>
<span class="formula local-robustness-score formula-content" style="display: none;">
$$
\displaystyle
g\left(G(z)\right) = \sqrt{\cfrac{\pi}{2}} \cdot \max\{ f_c(G(z)) - \max_{k \in \{1,\ldots,K\},k\neq c} f_k(G(z)),0 \}
$$
</span>
</div>
</div>
</div>
</div>
<div class="columns is-centered">
<div class="column container adaptive-loss-formula-content">
<p class="formula true-global-robustness formula-content">
where f is a classifier, P is a data distribution, and Δ<sub>min</sub>(x) is the minimal perturbation for a sample x.
</p>
<p class="formula global-robustness-estimate formula-content" style="display: none">
where g(x) is a local robustness statistic, and this estimate is used when the exact probability density function of P and local minimal perturbations are unknown.
</p>
<p class="formula local-robustness-score formula-content" style="display: none;">
where G(z) is a generated data sample, f<sub>c</sub> is the confidence score for the correct class c, and f<sub>k</sub> are the confidence scores for other classes.
</p>
</div>
</div>
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<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 evaluate the detection performance of BEYOND against adaptive attacks on different datasets and show the ROC curves under different perturbation budgets as follows:
</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>
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<h2 class="title">BibTeX</h2>
<pre><code>@article{li2024greatscore,
title = {GREAT Score: Global Robustness Evaluation of Adversarial Perturbation using Generative Models},
author = {Zaitang, Li and Pin-Yu, Chen and Tsung-Yi, Ho},
journal = {NeurIPS},
year = {2024},
}</code></pre>
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