Using Interleaved Ensemble Unlearning to Keep Backdoors at Bay for Finetuning Vision Transformers

## Abstract

Abstract Vision Transformers (ViTs) have become popular in computer vision tasks. Backdoor attacks, which trigger undesirable behaviours in models during inference, threaten ViTs’ performance, particularly in security-sensitive tasks. Although backdoor defences have been developed for Convolutional Neural Networks (CNNs), they are less effective for ViTs, and defences tailored to ViTs are scarce. To address this, we present Interleaved Ensemble Unlearning (IEU), a method for finetuning clean ViTs on backdoored datasets. In stage 1, a shallow ViT is finetuned to have high confidence on backdoored data and low confidence on clean data. In stage 2, the shallow ViT acts as a “gate” to block potentially poisoned data from the defended ViT. This data is added to an unlearn set and asynchronously unlearned via gradient ascent. We demonstrate IEU’s effectiveness on three datasets against 11 state-of-the-art backdoor attacks and show its versatility by applying it to different model architectures.

## 1 Introduction

Vision Transformers (ViTs, Dosovitskiy et al. ()) have emerged as a powerful alternative to Convolutional Neural Networks (CNNs) for a wide range of computer vision tasks. ViTs have achieved state-of-the-art performance in various downstream tasks such as image classification, object detection, and semantic segmentation (Thisanke et al., ; Shehzadi et al., ). However, the widespread deployment of ViTs have also raised concerns about their vulnerability to adversarial threats, particularly backdoor attacks, which typically modify images and/or labels in the training dataset to trigger attacker-controlled undesirable behaviour during inference (Gu et al., ; Subramanya et al., ; Yuan et al., ). Backdoor attacks such as the BadNets attack in Gu et al. () can compromise model behavior by embedding malicious triggers during training, leading to security risks in real-world applications. As ViTs become increasingly popular in security-sensitive domains such as autonomous driving and face recognition (Lai-Dang, ; Tran et al., ), it is important to understand these vulnerabilities and develop robust backdoor defences for ViTs.

ViTs are often pretrained using self-supervised learning (SSL) on large datasets and then finetuned to be deployed on specific tasks. Backdoor defences have been proposed to defend foundation models pretrained on large datasets and can either prevent backdoor injection during the SSL process or encourage removal of backdoors after pretraining (Tejankar et al., ; Bie et al., ); these thwart backdoor attacks that occur during pretraining, such as a practical real-world attack on web-scraped datasets in Carlini et al. () and an SSL-specific imperceptible attack Zhang et al. (). The finetuning process for adapting ViTs to downstream tasks using supervised learning is equally vulnerable to backdoor attacks. The rationale behind developing ViT-specific defences for finetuning are two-fold: Mo et al. () shows that there are few defences specifically designed for ViTs for image classification in existing literature (Doan et al. () and Subramanya et al. () being notable examples of such defences); in addition, although existing defences designed for CNNs can defend ViTs after modifying the defence implementations, they still lead to high ASR and/or low CA when defending different flavours of ViTs (Tables 4 & 5 in Mo et al. ()).

To fill the gap, this work takes advantage of the highly modular architecture of the ViT and propose a novel backdoor defence that uses an ensemble of two ViTs to perform interleaved unlearning on potentially poisoned data. Informed by the designs in Liu et al. () and Li et al. (), we use a shallow ViT denoted by the “poisoned module” to defend the main ViT, which we call the “robust module”. Our design IEU has two stages as shown in Figure 1. In stage 1, the poisoned module ($f_{p}$), a shallow ViT, is tuned on the attacker-controlled finetuning data. Intuitively, shortcut learning (Geirhos et al., ) leads $f_{p}$ to learn shortcuts in the dataset, which are most prevalent in poisoned images. In addition, the simplicity of $f_{p}$ discourages it from learning clean data that have fewer shortcuts. Therefore, the poisoned module is confident (where confidence is the maximum class probability $\max[\sigma(\mathbf{\hat{y}}_{p})]$ predicted by $f_{p}$) when classifying poisoned data and not confident otherwise. In stage 2, images pass through the tuned $f_{p}$, which either queues data onto the unlearn set or allows the defended main ViT (the robust module) to learn data normally based on the confidence threshold $c_{\text{thresh}}$. Whenever the unlearn set accumulates enough potentially poisoned data, a batch is unlearned by the robust module using a dynamic unlearning rate.

Figure: Figure 1: Overview of our defence, IEU. The red poisoned module and blue robust module are represented by $f_{p}$ and $f_{r}$, respectively. Shaded boxes are conditions; underlined text represent actions. The lock icon indicates a frozen network; otherwise, it is trainable. The blue network is shielded from poisoned images by the red network and the blue network unlearns potentially poisoned data. The dynamic unlearning rate is not shown. Unaugmented images are used for $f_{p}$ during both stages.
Refer to caption: x1.png

Instead of using a pre-determined unlearn set, our defence accumulates the unlearn set during stage 2. The benefits are two-fold: compared to using ABL’s (Li et al., ) method which isolates poisoned samples using the defended model, finetune-time unlearn set accumulation using $f_{p}$ ensures that the robust module learns as little poisoned data as possible; in addition, online accumulation of $\mathcal{D}^{\text{ul}}$ is adaptive in the sense that the frequency of unlearning is high when more potentially poisoned images are encountered, quickly erasing the impact of a large number of poisoned data. In addition, we argue that core concepts developed in our method, namely applying interleaved ensemble unlearning, can defend other model architectures in image classification. Here are our main contributions:

- •
We propose a new backdoor defence method, IEU, specifically designed for defending a ViT during finetuning. The defence uses an ensemble of two models to perform interleaved unlearning of high-confidence data using a dynamic unlearning rate. We show that our interleaved ensemble unlearning framework is successful without requiring high-precision isolation of poisoned data.
- •
We argue that, in contrast to ABL, a fixed-sized $\mathcal{D}^{\text{ul}}$ is not suitable for our design and demonstrate that Local Gradient Ascent (LGA) and loss Flooding presented in ABL (Li et al., ) are orthogonal to our poisoned module (Section 3.2). We show that the interleaved unlearning framework serves as a model-agnostic alternative to other unlearning-based defences (Table 8).
- •
We empirically demonstrate that our design out-performs existing state-of-the-art defences on challenging datasets using 11 backdoor attacks by comparing to SOTA methods such as ABL and I-BAU (Li et al., ; Zeng et al., ); Attack Success Rate (ASR) improved by 33.83% and 31.46% on average for TinyImageNet and CIFAR10, respectively, while maintaining high Clean Accuracy (CA). Our method requires no clean data and we perform extensive ablation studies.
- •
We explore potential points of failure of unlearning-based defence mechanisms to defend against weak attacks where “weakness” corresponds to lower ASR. We propose potential solutions to address these failures. In our opinion, weak attacks are as insidious as powerful attacks.

## 2 Related work

Backdoor Attacks. The goals of backdoor attacks in image classification tasks are (a) to encourage a specific classification when the image is perturbed by an attacker-specified transformation and (b) to maintain normal performance when images without a backdoor trigger are classified (Gu et al., ). A great variety backdoor attacks of all flavours for both SSL (Zhang et al., ; Sun et al., ; Saha et al., ; Li et al., ; Jia et al., ) and supervised learning (Chen et al., ; Liu et al., ; Nguyen & Tran, ; Li et al., ) have been proposed. There are three categories of backdoor attacks for supervised learning, which is the learning phase that this work defends: dirty-label attacks which includes visible and invisible attacks (Tan & Shokri, ; Lin et al., ; Doan et al., ), clean-label attacks which do not modify the label of backdoored images (Gao et al., ; Zeng et al., ; Turner et al., ), and clean-image attacks which only modify data labels during learning (Rong et al., ; Chen et al., ). Authors have also developed ViT-specific backdoor attacks. For example, Zheng et al. () inserts a Trojan into a ViT checkpoint, while Lv et al. () modifies the finetuning procedure by using an attacker-specified loss function.

Backdoor Defences. The defender’s goal is to ensure that backdoor images do not trigger attacker-specified model behaviour whilst maintaining high CA. A popular class of defences is model reconstruction where defenders cleanse poisoned models of backdoors. Early works (Liu et al., ; ) in this area such as the fine-pruning defence prunes neurons that are dormant on clean images and tunes on clean data. Later works that aim to remove backdoor neurons include Neural Attention Distillation (NAD, Li et al. ()), Adversarial Neuron Pruning (ANP, Wu & Wang ()) Adversarial Weight Masking (AWM, Chai & Chen ()), Shapley-estimation based few-shot defence (Guan et al., ), and Reconstructive Neuron Pruning (RNP, Li et al. ()). Another such cleansing defence, I-BAU (Zeng et al., ) connects the two optimisation problems in the minimax formulation of backdoor removal using an implicit hypergradient. Authors invariably design insightful methods for recovering clean models after backdoor injection. Certified backdoor defences have also been developed (Weber et al., ). Another broad class of defences involves reconstructing the trigger in order to unlearn backdoor images. Notable examples include Neural Cleanse (Wang et al., ), DeepInspect (Chen et al., ) which checks for signs of backdooring without a reserved clean set, and BTI-DBF (Xu et al., ) which decouples benign features for backdoor trigger inversion. Mitigating backdoor attacks during tuning (Borgnia et al., ; Wang et al., ; ) is also popular. Our method is closely related to Anti-Backdoor Learning (ABL, Li et al. ()), which isolates poisoned data and unlearns them after training.

ViT-Specific Backdoor Defences. Few backdoor defences are specifically designed for defending ViTs during tuning (Mo et al., ) and existing defences that have CNNs in mind perform worse on ViTs. Two notable defences are Doan et al. () where backdoor images are identified using patch-processing, and Subramanya et al. () which is a test-time defence that uses GradRollout (Gildenblat (), an interpretation method for ViTs) to block high-attention patches in images.

## 3 Method

In this section, we first define our threat model and describe IEU in detail. We conclude this section by briefly exploring the drawbacks of using a fixed-size unlearn set $\mathcal{D}^{\text{ul}}$.

Threat model. We focus on finetuning ViTs for image classification tasks and assume that the pretrained model checkpoint initially given to the defender is not benign. We follow the threat model of Li et al. (). We assume that the finetuning procedure is controlled by the defender, which means attacks that modify finetuning loss or the model’s gradient (Lv et al., ; Bagdasaryan & Shmatikov, ) are out of scope. On the other hand, finetuning data is gathered from untrusted sources and may contain backdoor data. The attacker knows the model architecture and the pretrained checkpoint’s parameter values, and may poison the finetuning dataset by modifying images and/or labels. The defender aims to tune a benign checkpoint for downstream tasks using $\mathcal{D}^{\text{tune}}$ and does not know the distribution/proportion of backdoor data in the attacker-supplied $\mathcal{D}^{\text{tune}}$.

Notations. The finetuning set $\mathcal{D}^{\text{tune}}$ may contain an unknown proportion of backdoor samples; this proportion (i.e., poisoning rate) is denoted by $\alpha$. The defender unlearns data in the unlearn set $\mathcal{D}^{\text{ul}}$, whose size as a fraction of $\mathcal{D}^{\text{tune}}$ is defined as $\hat{\alpha}=|\mathcal{D}^{\text{ul}}|\div|\mathcal{D}^{\text{tune}}|$. The two sub-networks in the ensemble are the poisoned module and robust module, denoted by $f_{p}$ and $f_{r}$, respectively. Data points $(\mathbf{x},\mathbf{y})\in\mathcal{D}^{\text{tune}}$, which consist of unaugmented ($\mathbf{x}_{\text{noAug}}$) and augmented ($\mathbf{x}_{\text{yesAug}}$) views of the original image (as in “data augmentation”), and potentially poisoned data points $(\mathbf{x}^{\hat{p}},\mathbf{y}^{\hat{p}})\in\mathcal{D}^{\text{ul}}$ are used to finetune and defend $f_{r}$, respectively. For simplicity, we use $\mathbf{x}$ to denote images when data augmentation is not relevant. The logits produced by the two modules are referred to as $\mathbf{\hat{y}}_{p}=f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p})$ and $\mathbf{\hat{y}}_{r}=f_{r}(\mathbf{x}\,;{\bm{\theta}}_{r})$, where ${\bm{\theta}}_{p},{\bm{\theta}}_{r}$ are the potentially tunable parameters of $f_{p}$ and $f_{r}$, respectively. The two logits vectors $\mathbf{\hat{y}}_{p}$ and $\mathbf{\hat{y}}_{r}$ combine to form the logits vector $\mathbf{\hat{y}}$ based on $m_{{\bm{\theta}}_{p}}$ (Equation 1). We use $\sigma(\cdot)$ and $\ell(\cdot,\cdot)$ to represent the softmax function and the cross-entropy loss, respectively. The confidence threshold $0<c_{\text{thresh}}<1$ determines whether an image is asynchronously unlearned or immediately learned. The number of classes in $\mathcal{D}^{\text{tune}}$ is denoted by $N_{c}$ for CIFAR10, GTSRB, and TinyImageNet, respectively. The learning rates used to finetune $f_{r}$ and unlearn $\mathbf{x}^{\hat{p}}$ are $lr^{\text{tune}}$ and $lr^{\text{ul}}$, respectively.

### 3.1 Interleaved Ensemble Unlearning ( IEU )

Overview. Figure 1 summarises our method, which has two stages. During stage 1, the poisoned module $f_{p}(\cdot\,;{\bm{\theta}}_{p})$ is pre-finetuned using finetuning data $\mathcal{D}^{\text{tune}}$. During stage 2, $f_{p}$ is used to determine whether incoming data is learned by the robust module $f_{r}(\cdot\,;{\bm{\theta}}_{r})$ or added to $\mathcal{D}^{\text{ul}}$ for asynchronous unlearning based on the unlearn rate $lr^{\text{ul}}$ in Equation 3.

Stage 1: Pre-finetuning the poisoned module $f_{p}$. This step applies vanilla tuning (for hyperparameters see Table 11 in Section A.2) using $\mathcal{D}^{\text{tune}}$ on $f_{p}(\cdot\,;{\bm{\theta}}_{p})$, where ${\bm{\theta}}_{p}$ is initialised as the first few layers of a pretrained checkpoint. Stage 1 solves the following optimisation problem: $\min_{{\bm{\theta}}_{p}}\mathbb{E}_{\mathbf{x}_{\text{noAug}}\sim\mathcal{D}^{
\text{tune}}}[\ell(f_{p}(\mathbf{x}_{\text{noAug}}\,;{\bm{\theta}}_{p}),
\mathbf{y})]$, where $\ell(\cdot,\cdot)$ is the cross entropy loss, $\mathbf{y}$ is the one-hot ground truth vector, and $f_{p}$ is the poisoned module. As explained in Section 1, the intuition of overfitting $f_{p}$ on poisoned data is based on shortcut learning (Geirhos et al., ). These shortcuts are found overwhelmingly in unaugmented backdoored images, where the attacker-specified trigger acts as an easily identifiable artifact that causes $f_{p}$ to easily learn the connection between the trigger and attacker-specified label. Therefore, the tuned $f_{p}$ is likely to be confident when predicting images with the trigger. The poisoned module $f_{p}$ is designed to be complex enough to learn shortcuts and shallow enough to avoid learning much from benign data. The goal is for $\max(\sigma(f_{p}(\mathbf{x}_{\text{noAug}}\,;{\bm{\theta}}_{p})))$ to be small for clean images and large for backdoor images after tuning in stage 1.

Stage 2: Finetuning the robust module $f_{r}$. This stage applies defended finetuning on $f_{r}(\cdot\,;{\bm{\theta}}_{r})$ which optimises the objectives in Equations 2 and 4; ${\bm{\theta}}_{r}$ is initialised as a pretrained checkpoint. During this stage, $f_{p}$ is frozen and only $f_{r}$ is tuned. The logits $\mathbf{\hat{y}}_{p}=f_{p}(\mathbf{x}_{\text{noAug}}\,;{\bm{\theta}}_{p})$ for the unaugmented view of each image is produced by the poisoned module in order to compute maximum class probability $\max(\sigma(\mathbf{\hat{y}}_{p}))$, which is then compared to $c_{\text{thresh}}$ to determine whether the data point should be learned by $f_{r}$ or added onto $\mathcal{D}^{\text{ul}}$. If $\max(\sigma(\mathbf{\hat{y}}_{p}))$ is above the confidence threshold $c_{\text{thresh}}$, the data point is added to $\mathcal{D}^{\text{ul}}$. Otherwise, $f_{r}$ learns the augmented views as would happen in regular finetuning. To prevent potentially poisoned data from being learned, we apply logit masking on the output logits of $f_{r}$ and $f_{p}$ as shown in Equation 1

$$ $m_{{\bm{\theta}}_{p}}=\bm{1}_{x<c_{\text{thresh}}}(\max(\sigma(f_{p}(\mathbf{x }_{\text{noAug}}\,;{\bm{\theta}}_{p})))),\text{ where }\mathbf{\hat{y}}= \mathbf{\hat{y}}_{p}(1-m_{{\bm{\theta}}_{p}})+\mathbf{\hat{y}}_{r}m_{{\bm{ \theta}}_{p}}$ (1) $$

where $m_{{\bm{\theta}}_{p}}$ is the binary logit mask, $\bm{1}_{x<c_{\text{thresh}}}(x)$ is the indicator function, $\mathbf{y}$ is the ground truth, $\mathbf{\hat{y}}$ is the logits vector, and $\mathbf{\hat{y}}_{p}=f_{p}(\mathbf{x}_{\text{noAug}}\,;{\bm{\theta}}_{p}),\,
\mathbf{\hat{y}}_{r}=f_{r}(\mathbf{x}_{\text{yesAug}}\,;{\bm{\theta}}_{r})$ are the logits produced by $f_{p}$ and $f_{r}$, respectively. When $\mathbf{x}_{\text{noAug}}$ is detected by $f_{p}$ as a potentially poisoned image, the logits for optimising the objective in Equation 2 come from $f_{p}$; otherwise, $\mathbf{\hat{y}}=\mathbf{\hat{y}}_{r}$ for optimisation. In other words, optimising the objective in Equation 2 requires both $f_{p}$ and $f_{r}$ to contribute to the logits.

$$ $\min_{{\bm{\theta}}_{r}}\mathbb{E}_{\mathbf{x}\sim\mathcal{D}^{\text{tune}}}[ \ell(\mathbf{\hat{y}},\mathbf{y})]$ (2) $$

The unlearn set $\mathcal{D}^{\text{ul}}$ accumulates data until it has enough data for one batch containing potentially poisoned images $(\mathbf{x}^{\hat{p}},\mathbf{y}^{\hat{p}})$, which is then unlearned by $f_{p}$ during finetuning. Unlike the continuously decaying learning rate $lr^{\text{tune}}$ used for normal finetuning, the unlearning rate $lr^{\text{ul}}$ doesn’t depend on just the decay schedule. Given $lr^{\text{tune}}$ which follows the cosine annealing decay schedule, the $(k-1)^{\text{th}}$ batch with potentially poisoned images $(\mathbf{x}^{\hat{p}}_{k-1},\mathbf{y}^{\hat{p}}_{k-1})$, the number of classes in the dataset $N_{c}$, and the robust module $f_{r}(\cdot\,;{\bm{\theta}}_{r})$, the dynamic unlearning rate for the current batch $(\mathbf{x}^{\hat{p}}_{k},\mathbf{y}^{\hat{p}}_{k})$ is defined in Equation 3 and can be viewed as a function of cross entropy loss of the previous batch of potentially poisoned images $\ell(f_{r}(\mathbf{x}^{\hat{p}}_{k-1}\,;{\bm{\theta}}_{r}),\mathbf{y}^{\hat{p}
}_{k-1})$.

$$ $lr^{\text{ul}}_{k}=lr^{\text{tune}}\cdot\left(\bm{1}_{k>0}(k)\cdot\max\left[6- \exp\left[-\left(\ln(N_{c})-\ell(f_{r}(\mathbf{x}^{\hat{p}}_{k-1}\,;{\bm{ \theta}}_{r}),\mathbf{y}^{\hat{p}}_{k-1})\div\sqrt{2}\right)\right],0.2\right] +\bm{1}_{k=0}(k)\right)$ (3) $$

The two indicator functions ensure $lr^{\text{ul}}_{k}=lr^{\text{tune}}$ when $k=0$, which occurs at an epoch’s beginning. The term that scales $lr^{\text{tune}}$ in Equation 3 is an exponentially decreasing function with respect to increasing loss $\ell(f_{r}(\mathbf{x}^{\hat{p}}_{k-1}\,;{\bm{\theta}}_{r}),\mathbf{y}^{\hat{p}
}_{k-1})$, causing $lr^{\text{ul}}_{k}$ to be large when the previous batch $\mathbf{x}^{\hat{p}}_{k-1}$ produces low cross entropy loss on $f_{r}$. This keeps the backdoor from being learned by $f_{r}$. Although it is shown in Table 9 that using $lr^{\text{ul}}_{k}=c\cdot lr^{\text{tune}}$ for some $c\in\mathbb{R}^{+}$ performs better than using Equation 3, one benefit of defining $lr^{\text{ul}}_{k}$ using a fixed function is that $lr^{\text{ul}}_{k}$ is no longer a hyperparameter that needs to be tuned. In addition to solving Equation 2, finetuning during stage 2 also optimises for the objective in Equation 4, which is implemented using gradient ascent performed on $f_{r}$ given $(\mathbf{x}^{\hat{p}},\mathbf{y}^{\hat{p}})\in\mathcal{D}^{\text{ul}}$. See Algorithm 1 in Appendix B for a precise description of stage 2.

$$ $\max_{{\bm{\theta}}_{r}}\mathbb{E}_{\mathbf{x}^{\hat{p}}\sim\mathcal{D}^{\text {ul}}}[\ell(f_{r}(\mathbf{x}^{\hat{p}}\,;{\bm{\theta}}_{r}),\mathbf{y}^{\hat{p }})]$ (4) $$

### 3.2 Why Not a Fixed-Sized Unlearn Set?

In this subsection, we argue that our method of using $f_{p}$ to isolate poisoned data is orthogonal to similar methods used in ABL (Li et al., ) and is more suitable for our IEU. Authors in ABL isolates a fixed fraction (called “$r_{\text{isol}}$”) of the tuning set where $0\leq r_{\text{isol}}\leq 1$ (they used $r_{\text{isol}}=0.01$). In their method, images whose cross entropy loss rank amongst the lowest $r_{\text{isol}}$ fraction of $\mathcal{D}^{\text{tune}}$ is collected to form $\mathcal{D}^{\text{ul}}$ of size $\hat{\alpha}=r_{\text{isol}}$. ABL uses techniques such as Local Gradient Ascent (LGA) or loss Flooding on the defended model to encourage poisoned images to have low loss. Compared to using $r_{\text{isol}}$ (ABL), there are two main advantages for using $c_{\text{thresh}}$ (our method) to produce the unlearn set in our method: (a) the effectiveness (FPR or FNR) of our isolation method is not significantly affected by the value of the poisoning rate $\alpha$, which is unknown to the defender (Table 1), and (b) the unlearn set size varies as $\alpha$ varies, which increases defence success using IEU since a high proportion of poisoned data should be added to $\mathcal{D}^{\text{ul}}$ for low ASR and high CA ($\hat{\alpha}_{i}\div\alpha\in\{0.9,1.0\}$ in Table 2).

**Table 1: Performance of the two methods when evaluated on detecting poisoned finetuning data (CIFAR10). Five poisoned module ($f_{p}$) instances are pre-finetuned for 10 epochs at $2\cdot 10^{-4}$ learning rate with different poisoning rate $\alpha$; $c_{\text{thresh}}$ and $r_{\text{isol}}$ are fixed at $0.95$ and $0.1$, respectively. Each cell shows the FPR/FNR values as percentages (“positive” means “poisoned”).**
| Attack | Selection Method | $\alpha=0.02$ | 0.05 | 0.10 | 0.15 | 0.20 |
| --- | --- | --- | --- | --- | --- | --- |
| BadNets-white | $r_{\text{isol}}$ | 8.68/25.30 | 6.42/22.04 | 0.80/7.22 | 0.03/33.49 | 0.00/50.00 |
| $c_{\text{thresh}}$ | 9.16/24.90 | 5.67/22.84 | 5.62/5.30 | 6.09/10.25 | 4.71/5.17 |  |
| ISSBA | $r_{\text{isol}}$ | 8.59/21.00 | 5.60/6.44 | 0.62/5.54 | 0.00/33.33 | 0.00/50.00 |
| $c_{\text{thresh}}$ | 6.27/25.40 | 6.79/5.76 | 5.55/2.58 | 6.51/1.48 | 5.68/0.48 |  |

**Table 2: Performance of models that are defended during stage 2 using IEU with hand-crafted unlearn sets $\mathcal{D}^{\text{ul}}_{i}$ of varying sizes ($\hat{\alpha}_{i}$) as a fraction of the original finetune set $\mathcal{D}^{\text{tune}}$. The poisoning rate is fixed at $\alpha=0.1$ and the sizes of $\mathcal{D}^{\text{ul}}_{i}$ as a fraction of $\mathcal{D}^{\text{tune}}$ are $\hat{\alpha}_{i}\in(0.01,0.02,0.05,0.1,0.2)$. A hand-crafted unlearn set $\mathcal{D}^{\text{ul}}_{i}$ consists entirely of poisoned data if $\hat{\alpha}_{i}\div\alpha\leq 1$ and includes all poisoned data if $\hat{\alpha}_{i}\div\alpha\geq 1$. All values here are expressed in percentages.**
| Size ratio ($\hat{\alpha}_{i}\div\alpha$): | 0.1 | 0.2 | 0.5 | 0.9 | 1.0 | 2.0 |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Dataset | Attack | ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA |
| CIFAR10 | BadNets-white | 10.09 | 98.18 | 9.89 | 97.58 | 6.41 | 96.30 | 0.88 | 97.94 | 0.88 | 98.28 | 0.67 | 97.83 |
| ISSBA | 100.00 | 98.31 | 100.00 | 98.18 | 0.00 | 96.94 | 0.00 | 97.99 | 0.00 | 98.23 | 0.00 | 98.16 |  |
| Smooth | 95.32 | 98.24 | 82.28 | 97.93 | 0.06 | 97.00 | 0.77 | 97.98 | 0.94 | 98.24 | 0.11 | 97.90 |  |
| TinyImageNet | BadNets-white | 0.32 | 61.95 | 0.01 | 57.89 | 0.00 | 54.03 | 0.00 | 63.43 | 0.00 | 65.95 | 0.00 | 37.18 |
| ISSBA | 57.84 | 64.94 | 0.15 | 58.70 | 0.00 | 22.50 | 0.00 | 38.63 | 0.16 | 46.97 | 0.05 | 16.37 |  |
| Smooth | 93.51 | 68.37 | 77.33 | 64.84 | 0.00 | 55.93 | 0.00 | 61.95 | 0.01 | 66.28 | 0.00 | 38.86 |  |

Table 1 shows that the FPR/FNR are similar for both $r_{\text{isol}}$ and $c_{\text{thresh}}$ at low poisoning rate. However, as $\alpha$ increases, using $r_{\text{isol}}$ causes more poisoned data to be left out of $\mathcal{D}^{\text{ul}}$. For example, at $\alpha=0.2$ and $r_{\text{isol}}=0.1$ (meaning $\hat{\alpha}_{i}\div\alpha=0.1\div 0.2=0.5$), the FNR is $50\%$. This results in instability during defence and worse performance as shown in Table 2 (column 0.5) since a large fraction of poisoned data is not in $\mathcal{D}^{\text{ul}}$. As less poisoned data is included in $\mathcal{D}^{\text{ul}}$, our defence becomes less effective with ASR increasing and CA decreasing (Table 2). Since using a fixed $r_{\text{isol}}$ leaves many poisoned images outside of $\mathcal{D}^{\text{ul}}$ when $\alpha>r_{\text{isol}}$, we use $c_{\text{thresh}}$ to select a variable-sized $\mathcal{D}^{\text{ul}}$.

We show in Table 15 (Appendix C) that our shallow $f_{p}$ is not compatible with LGA/Flooding for isolating poisoned data; they are meant to be orthogonal methods.

## 4 Experiments

See Appendix A for more details regarding baselines, attacks, datasets and defence parameters.

Baselines. We use three baseline methods for comparison with our defence. Specifcally, we compare against I-BAU (Zeng et al., ), ABL (Li et al., ), and AttnBlock (Subramanya et al., ) which is a ViT-specific defence. We report results for AttnBlock in Section A.2 due to high ASR. I-BAU and ABL are state-of-the-art general defences not specifically designed for ViTs; authors in (Wang et al., ) suggest that I-BAU is the most competitive baseline compared to others. We attempt and fail to reproduce the RNP defence (Li et al., ) for ViTs despite following recommendations in Mo et al. () to mask features of linear layers instead of those of norm layers.

**Table 3: Performance of IEU compared to no defence, ABL (Li et al., ), I-BAU (Zeng et al., ) given as percentages. Averages of each column are given in the last row for that dataset and best/second-best values are bolded/underlined. See Section A.2 for AttnBlock results.**
| Dataset | Attack | No Defence | I-BAU | ABL | IEU (Ours) |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA |  |  |
| CIFAR10 | BadNets-white | 97.51 | 98.36 | 10.12 | 95.86 | 9.7 | 98.11 | 0.96 | 98.19 |
| BadNets-pattern | 100.0 | 98.23 | 91.84 | 92.16 | 100.0 | 97.4 | 0.0 | 98.22 |  |
| ISSBA | 100.0 | 98.13 | 9.46 | 92.96 | 100.0 | 37.62 | 0.33 | 98.35 |  |
| BATT | 100.0 | 98.28 | 21.68 | 95.86 | 90.05 | 97.94 | 0.02 | 98.23 |  |
| Blended | 100.0 | 98.39 | 21.0 | 93.92 | 25.04 | 97.82 | 0.0 | 98.27 |  |
| Trojan-WM | 99.99 | 98.32 | 79.94 | 94.16 | 99.91 | 97.97 | 0.0 | 98.15 |  |
| Trojan-SQ | 99.7 | 98.31 | 68.26 | 94.62 | 99.62 | 98.27 | 0.04 | 98.22 |  |
| Smooth | 99.76 | 98.24 | 16.26 | 94.0 | 9.31 | 97.12 | 0.09 | 97.77 |  |
| l0-inv | 100.0 | 98.34 | 10.28 | 93.24 | 0.04 | 97.12 | 0.0 | 98.19 |  |
| l2-inv | 99.98 | 98.41 | 9.98 | 93.4 | 8.62 | 98.1 | 0.44 | 98.24 |  |
| SIG | 98.49 | 88.75 | 9.16 | 94.38 | 97.94 | 88.44 | 0.0 | 87.67 |  |
| Average | 99.58 | 97.43 | 31.63 | 94.05 | 58.2 | 91.45 | 0.17 | 97.23 |  |
| GTSRB | BadNets-white | 95.7 | 95.63 | 5.48 | 99.1 | 4.09 | 92.83 | 0.93 | 82.07 |
| BadNets-pattern | 100.0 | 96.44 | 5.46 | 98.17 | 4.09 | 93.76 | 0.0 | 88.53 |  |
| ISSBA | 99.99 | 95.91 | 5.48 | 99.48 | 3.63 | 93.15 | 100.0 | 93.52 |  |
| BATT | 100.0 | 96.18 | 6.08 | 99.58 | 2.29 | 92.79 | 0.03 | 93.47 |  |
| Blended | 100.0 | 96.95 | 11.24 | 97.75 | 0.0 | 92.95 | 8.76 | 81.2 |  |
| Trojan-WM | 100.0 | 92.75 | 5.26 | 98.11 | 0.0 | 75.16 | 3.12 | 86.54 |  |
| Trojan-SQ | 99.85 | 94.91 | 5.48 | 99.61 | 99.6 | 81.99 | 0.07 | 77.29 |  |
| Smooth | 99.79 | 96.29 | 27.5 | 99.74 | 3.46 | 92.36 | 6.15 | 84.52 |  |
| l0-inv | 100.0 | 96.76 | 5.44 | 99.7 | 100.0 | 94.96 | 0.0 | 87.48 |  |
| l2-inv | 100.0 | 93.93 | 9.06 | 99.71 | 77.79 | 96.03 | 12.85 | 87.5 |  |
| SIG | 99.52 | 91.41 | 2.92 | 38.32 | 95.53 | 83.49 | 0.21 | 72.07 |  |
| Average | 99.53 | 95.2 | 8.13 | 93.57 | 35.5 | 89.95 | 12.01 | 84.93 |  |
| TinyImageNet | BadNets-white | 98.51 | 61.46 | 0.48 | 51.06 | 0.24 | 59.19 | 0.12 | 66.35 |
| BadNets-pattern | 100.0 | 62.72 | 75.72 | 55.04 | 0.25 | 60.59 | 0.0 | 66.62 |  |
| ISSBA | 99.62 | 63.1 | 87.18 | 0.66 | 0.08 | 57.56 | 0.05 | 40.6 |  |
| BATT | 99.98 | 66.66 | 89.8 | 60.16 | 0.02 | 62.36 | 3.07 | 64.15 |  |
| Blended | 100.0 | 70.21 | 65.22 | 61.38 | 0.0 | 64.06 | 0.0 | 66.41 |  |
| Trojan-WM | 99.96 | 69.89 | 90.68 | 60.9 | 99.31 | 68.92 | 0.0 | 67.33 |  |
| Trojan-SQ | 99.79 | 63.56 | 97.5 | 57.46 | 99.74 | 63.04 | 0.0 | 67.28 |  |
| Smooth | 99.35 | 68.58 | 4.62 | 60.68 | 0.03 | 61.74 | 0.17 | 66.03 |  |
| l0-inv | 100.0 | 63.14 | 99.76 | 54.48 | 99.99 | 44.29 | 0.0 | 65.89 |  |
| l2-inv | 99.82 | 65.43 | 0.44 | 59.32 | 0.04 | 57.92 | 0.01 | 64.5 |  |
| SIG | 67.99 | 71.65 | 19.04 | 63.58 | 83.67 | 59.04 | 7.77 | 71.71 |  |
| Average | 96.82 | 66.04 | 57.31 | 53.16 | 34.85 | 59.88 | 1.02 | 64.26 |  |

Attacks. We evaluate the performance of our design on 11 backdoor attacks. Specifically, we consider 9 out of 10 attacks in Wang et al. (): BadNets-white (white lower-right corner), BadNets-pattern (grid pattern in lower-right corner) (Gu et al., ), Blended (Chen et al., ), l0-inv, l2-inv (Li et al., ), Smooth (Zeng et al., ), Trojan-SQ, Trojan-WM (Liu et al., ), and a clean label attack, SIG (Barni et al., ). In addition, we consider the sample-specific invisible attack ISSBA (Li et al., ) and an image transformation-based attack BATT (Xu et al., ). Please refer to Section A.1 for visualisations of backdoored images. Although ViT-specific backdoor attacks exist in literature (Zheng et al., ; Lv et al., ), we did not include these attacks due to their focus on inference-time attacks. Moreover, they use threat models that are incompatible with ours. For example, Zheng et al. () injects a trigger at inference-time (which does not concern finetuning), while Lv et al. () modifies the finetuning procedure (which is controlled by the defender in our threat model) by using an attacker-specified loss function.

Datasets and default parameters. We used three datasets to evaluate our defence (CIFAR10 Krizhevsky (), GTSRB Houben et al. (), and TinyImageNet(^1^11Used in Stanford’s course CS231N. Download: [http://cs231n.stanford.edu/tiny-imagenet-200.zip](http://cs231n.stanford.edu/tiny-imagenet-200.zip)) Deng et al. ()). Defence parameters are shown in Section A.2.

### 4.1 Main Results

We show the results of our IEU compared to other baselines in Table 3. Our method’s ASR out-performs I-BAU by $31.46$ percentage points (pp) on CIFAR10 and out-performs ABL by $33.83$pp on TinyImageNet. In addition, our IEU’s CA for CIFAR10 and TinyImageNet are generally better than the corresponding values of the baselines. Our method has the lowest ASR in all attacks and 9 out of 11 attacks in CIFAR10 and TinyImageNet, respectively. Moreover, our method produces the highest CA for 9 out of 11 attacks for both CIFAR10 and TinyImageNet. We explore the limitations of IEU in Section 5 for weaker attacks and for the GTSRB dataset. Note that I-BAU uses the highest amount of GPU memory (39 GB on an NVIDIA A100) when compared to ABL and IEU ($\leq 20$ GB).

### 4.2 Ablation Study on Hyperparameters

The importance of logit masking is shown in Table 4, which demonstrates performance degradation of IEU when logit masking is not used. Without logit masking, $f_{r}$ both learns and unlearns $(\mathbf{x}^{\hat{p}},\mathbf{y}^{\hat{p}})\in\mathcal{D}^{\text{ul}}$, which by default is not learned in IEU. If the robust module performs poorly on potentially poisoned data because of asynchronous unlearning, the absence of logit masking allows the model to relearn the poisoned data during parameter updates for finetuning. Therefore, the model repeatedly learns and unlearns the same data, resulting in low performance on non-poisoned data. This reasoning also guides our decision to use $f_{p}$ instead of $f_{r}$ to isolate $\mathbf{x}^{\hat{p}}$ for Interleaved Unlearning.

**Table 4: Performance of IEU without applying logit masking during finetuning. Leaving out logit masking means that $\mathbf{\hat{y}}=\mathbf{\hat{y}}_{r}$ is used instead of using Equation 1. All values given in percentages.**
| Dataset | BATT | BadNets-white | ISSBA | Smooth |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA |  |
| CIFAR10 | 0.00 | 79.75 | 0.61 | 81.49 | 0.00 | 83.42 | 0.00 | 64.06 |
| TinyImageNet | 0.36 | 56.12 | 0.01 | 28.85 | 0.00 | 11.98 | 0.00 | 26.49 |

**Table 5: Performance of IEU when finetuned using $\mathcal{D}^{\text{tune}}$ with different poisoning rate values using CIFAR10, $\alpha=\{0.02,0.05,0.1,0.15,0.2\}$. All values given in percentages.**
| Attack | $\alpha=0.02$ | 0.05 | 0.10 | 0.15 | 0.20 |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA |  |
| BadNets-white | 1.30 | 88.27 | 1.22 | 94.05 | 0.96 | 98.19 | 0.81 | 97.14 | 1.16 | 97.85 |
| ISSBA | 0.04 | 91.78 | 0.00 | 96.78 | 0.33 | 98.35 | 0.16 | 98.15 | 0.00 | 98.10 |

Defence performance for varying poisoning rate is shown in Table 5. We test a wide range of poison rates to determine the effectiveness of IEU under different attack settings. Overall, our IEU is able to defend against backdoor attacks with both high and low poisoning rate. The decrease in CA when poisoning rate is low is due to the worse performance of $f_{p}$ at detecting potentially poisoned samples as shown in Table 1. We believe that better isolation methods for collating $\mathcal{D}^{\text{ul}}$ (Doan et al., ) will result in higher CA.

Effects of different confidence threshold values are shown in Table 6. As one of the important hyperparameters in our IEU, varying $c_{\text{thresh}}$ does not significantly affect model performance for both CIFAR10 and TinyImageNet. Looking at the “Poison” and “Clean” columns of Table 6, we generally see less data (ether poisoned or clean) having maximum class probability above the confidence threshold as $c_{\text{thresh}}$ increases. Based on this observation, we argue that the performance of IEU remains stable even as $\mathcal{D}^{\text{ul}}$ decreases in size.

**Table 6: Performance of IEU with $c_{\text{thresh}}\in\{0.9,0.95,0.99\}$. The values in the “Poison” and “Clean” columns correspond to the percentage of poisoned and clean data, respectively, that’s classified as poisoned data by $f_{p}$ for the corresponding $c_{\text{thresh}}$. Note that $c_{\text{thresh}}=0.95$ is the default setting. All values given in percentages.**
| Dataset | $c_{\text{thresh}}$ | BATT | BadNets-white | Smooth |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | Poison | Clean | ASR | CA | Poison | Clean | ASR | CA | Poison | Clean |  |  |
| CIFAR10 | 0.90 | 0.06 | 94.42 | 94.51 | 13.61 | 0.81 | 97.47 | 95.71 | 11.53 | 0.05 | 96.79 | 97.23 | 15.16 |
| 0.95 | 0.02 | 98.23 | 95.83 | 7.10 | 0.96 | 98.19 | 95.00 | 5.62 | 0.09 | 97.77 | 95.81 | 7.79 |  |
| 0.99 | 1.74 | 98.09 | 90.68 | 0.78 | 1.27 | 98.09 | 92.70 | 0.55 | 0.32 | 97.98 | 90.76 | 1.26 |  |
| TinyImageNet | 0.90 | 6.73 | 65.31 | 92.68 | 0.52 | 0.12 | 65.10 | 89.45 | 0.48 | 0.00 | 66.03 | 92.27 | 0.88 |
| 0.95 | 3.07 | 64.15 | 88.48 | 0.11 | 0.12 | 66.35 | 87.44 | 0.21 | 0.17 | 66.03 | 89.30 | 0.41 |  |
| 0.99 | 1.10 | 65.41 | 92.19 | 0.00 | 0.12 | 65.35 | 82.03 | 0.01 | 2.45 | 64.65 | 80.17 | 0.07 |  |

The complexity of the poisoned module as represented by the depth of $f_{p}$ significantly affects the defence performance of IEU as shown in Table 7. As the depth of $f_{p}$ increases, it becomes more complex and more adept at learning non-poisoned samples. Since $f_{p}$ is confident about a larger number of clean images, this causes the number of clean data in $\mathcal{D}^{\text{ul}}$ to become higher and reduces the amount of data learned by $f_{r}$. Therefore, as $f_{p}$ becomes deeper, CA decreases since the robust module unlearns more clean data (rows for CIFAR10 and TinyImageNet of Table 7). This effect is especially pronounced for simpler datasets (e.g., CIFAR10) because simpler datasets are more easily learned given the same model complexity, leading to more clean images being directed to $\mathcal{D}^{\text{ul}}$. Tuning $c_{\text{thresh}}$ for different depth leads to better performance as shown in the last two rows of Table 7.

**Table 7: Performance of IEU with varying poisoned module depth. The $c_{\text{thresh}}$ values used for the last three rows are chosen after inspecting the distribution of maximum class probability values $\max(\sigma(f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p}))$ using poisoned training data. All values given in percentages.**
|  | Depth ($c_{\text{thresh}}$) | BadNets-white | Blended | ISSBA |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
|  | ASR | CA | ASR | CA | ASR | CA |  |
| CIFAR10 | 1 (0.95) | 0.96 | 98.19 | 0.00 | 98.27 | 0.33 | 98.35 |
| 2 (0.95) | 1.30 | 56.09 | 0.00 | 86.49 | 0.00 | 87.90 |  |
| 3 (0.95) | 0.00 | 18.04 | 0.00 | 64.83 | 0.00 | 34.21 |  |
| TinyImagenet | 1 (0.95) | 0.12 | 66.35 | 0.00 | 66.41 | 0.05 | 40.60 |
| 2 (0.95) | 0.02 | 60.26 | 0.00 | 63.77 | 0.04 | 37.68 |  |
| 3 (0.95) | 0.01 | 59.11 | 0.00 | 61.80 | 0.12 | 36.50 |  |
| CIFAR10<br>(Variable $c_{\text{thresh}}$) | 2 (0.99) | 0.92 | 97.65 | 0.00 | 92.10 | 0.00 | 98.25 |
| 3 (0.998) | 0.82 | 92.79 | 0.00 | 98.20 | 0.00 | 98.02 |  |

### 4.3 Ablation Study on Defence Design

We demonstrate that IEU works well for Vision Transformer variants and CNN architectures in Table 8. We evaluate IEU where the following Vision Transformer variants are used as the robust module: CaiT-XXS (Touvron et al., ), DeiT-S (Touvron et al., ), PiT-XS (Heo et al., ), ViT-S (default architecture, Dosovitskiy et al. ()), and XCiT-Tiny (El-Nouby et al., ). In addition, we use ResNet-18 (He et al., ) and WideResNet-50-2 (Zagoruyko & Komodakis, ) to evaluate our defence on non-ViT architectures. The Interleaved Ensemble Unlearning framework generally performs well for most architectures. In addition, IEU trains high-performing models when $\alpha=0$ where $\mathcal{D}^{\text{tune}}$ is clean (see “No Attack” column of Table 8).

The effects of using constant unlearning rate is shown in Table 9. Our defence is slightly more effective when $lr^{\text{ul}}$ and $lr^{\text{tune}}$ differ by a small constant factor (first three rows of CIFAR10 & TinyImageNet in Table 9). However, on average there is only a small difference between the performance of Dynamic and constant $lr^{\text{ul}}$. For example, Dynamic $lr^{\text{ul}}$ on average achieves $65.97\%$ CA on TinyImageNet, only $2.48$pp lower than the best CA at $lr^{\text{ul}}=lr^{\text{tune}}$; ASR is comparable. To have fewer hyperparameters, we use Dynamic $lr^{\text{ul}}$ instead of $lr^{\text{ul}}=c\cdot lr^{\text{tune}}$ for hyperparameter $c$.

**Table 8: Performance of IEU with different model architectures using CIFAR10. The penultimate column showcases CA when applying IEU on clean $\mathcal{D}^{\text{tune}}$. The “No Defence” column uses BadNets-white as the attack and is tuned without defence. The first layer of ViT-S is used as the poisoned module for all models. We use $c_{\text{thresh}}=0.99$ for “No Attack” since this choice mounts an effective defence as shown in Table 6. All values given in percentages.**
| Variant | BATT | BadNets-white | ISSBA | Smooth | No Attack | No Defence |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA |  |
| CaiT-XXS | 0.01 | 97.01 | 0.98 | 97.07 | 0.76 | 97.11 | 1.20 | 97.09 | - | 97.40 | 96.80 | 97.09 |
| DeiT-S | 0.25 | 97.83 | 1.00 | 97.94 | 0.32 | 98.22 | 2.05 | 97.83 | - | 98.21 | 96.96 | 97.96 |
| PiT-XS | 0.09 | 96.44 | 1.14 | 96.62 | 4.73 | 96.74 | 3.53 | 96.66 | - | 96.78 | 96.70 | 96.66 |
| ViT-S | 0.02 | 98.14 | 0.93 | 97.95 | 0.06 | 98.15 | 0.09 | 97.61 | - | 97.87 | 97.34 | 98.12 |
| XCiT-Tiny | 0.96 | 87.72 | 0.99 | 87.67 | 1.04 | 85.47 | 4.66 | 83.96 | - | 92.48 | 95.07 | 91.79 |
| ResNet-18 | 0.35 | 90.99 | 7.22 | 91.68 | 6.37 | 91.00 | 6.38 | 91.45 | - | 92.45 | 94.25 | 91.73 |
| VGG-11 | 3.19 | 88.86 | 8.39 | 90.22 | 11.63 | 89.45 | 9.70 | 73.78 | - | 91.22 | 95.36 | 90.59 |

**Table 9: Performance of IEU using different ways of computing $lr^{\text{ul}}$. Average ASR/CA across rows are shown in the last column. Dynamic $lr^{\text{ul}}$ is computed using Equation 3. All values given in percentages.**
| Dataset | $lr^{\text{ul}}$ | BATT | BadNets-white | Smooth | Trojan-WM | l0-inv | Average |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA | ASR | CA |  |  |
| CIFAR10 | $1\cdot lr^{\text{tune}}$ | 0.02 | 98.02 | 0.72 | 97.97 | 0.05 | 98.01 | 0.00 | 93.84 | 0.00 | 97.76 | 0.20 | 96.96 |
| $2\cdot lr^{\text{tune}}$ | 0.01 | 93.95 | 0.72 | 93.16 | 0.04 | 93.56 | 0.00 | 85.59 | 0.00 | 88.57 | 0.19 | 91.56 |  |
| $4\cdot lr^{\text{tune}}$ | 0.00 | 79.37 | 0.63 | 83.16 | 0.01 | 70.43 | 0.00 | 70.50 | 0.00 | 76.45 | 0.16 | 75.87 |  |
| Dynamic | 0.02 | 98.23 | 0.96 | 98.19 | 0.09 | 97.77 | 0.00 | 98.15 | 0.00 | 98.19 | 0.27 | 98.09 |  |
| TinyImageNet | $1\cdot lr^{\text{tune}}$ | 2.47 | 67.21 | 0.15 | 68.72 | 0.03 | 68.79 | 0.00 | 69.07 | 0.00 | 68.04 | 0.66 | 68.45 |
| $2\cdot lr^{\text{tune}}$ | 0.02 | 66.87 | 0.05 | 63.68 | 0.02 | 63.66 | 0.00 | 67.04 | 0.00 | 60.93 | 0.02 | 65.31 |  |
| $4\cdot lr^{\text{tune}}$ | 0.00 | 63.38 | 0.07 | 47.53 | 0.00 | 51.10 | 0.00 | 49.08 | 0.00 | 29.72 | 0.02 | 52.77 |  |
| Dynamic | 3.07 | 64.15 | 0.12 | 66.35 | 0.17 | 66.03 | 0.00 | 67.33 | 0.00 | 65.89 | 0.84 | 65.97 |  |

## 5 Discussion and Limitations

The major finding is that the Interleaved Unlearning Framework is a high-performing defence for tuning benign models on backdoored datasets. The impact is that this framework is an improvement for ViTs in terms of stability and performance over existing unlearning-based methods that aim to cleanse models after tuning on backdoored data.

Figure: Figure 2: Maximum class probability $\max(\sigma(f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p}))$ CDF based on logits produced by the poisoned module on clean and poisoned data for the ISSBA attack on the three datasets. Dotted horizontal lines show percentages of clean/poisoned data whose $\max(\sigma(f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p}))$ lie below 0.95.
Refer to caption: x2.png

Weakness [a] Worse performance on less complex datasets (e.g., GTSRB). Our IEU fails against ISSBA when using the GTSRB dataset as shown in Table 3 (cell coloured red) and underperforms on GTSRB in general. We suggest that this happens because the GTSRB dataset is easily learnt by $f_{p}$. Evidence is shown in Figure 2, which plots the CDF of the maximum class probability values for poisoned/clean data for all three datasets using the ISSBA attack. Compared to CIFAR10 and TinyImageNet, clean images from the GTSRB dataset is only marginally more difficult to learn than backdoored GTSRB images. In Figure 2, a higher proportion of clean data has $\max(\sigma(f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p}))>0.95$ and a lower proportion of poisoned data has $\max(\sigma(f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p}))>0.95$ for GTSRB when compared to the other two datasets. Therefore, using a shallow ViT as the poisoned module is insufficient for discerning poisoned data from clean data for GTSRB.

Weakness [b] The weaker the attack, the worse the defender’s performance. We believe that defending/detecting weak attacks is as important as defending strong attacks. A key difficulty in designing performant unlearning-based backdoor defence methods is identifying and mitigating weak attacks. An example of a relatively weak attack is WaNet (Nguyen & Tran, ), and as shown in Table 10, the two unlearning-based methods (our IEU and ABL) we consider are less performant. Weakness [a] and [b] have a similar root cause. Both weaknesses are caused by a less effective $f_{p}$ for isolating backdoored data. This effect is also seen to a smaller extent against the clean label SIG attack (Barni et al., ) on TinyImageNet, where the ASR without defence is $\approx 68\%$. As shown in Table 3, although ASR for SIG when defended using IEU is the lowest when comparing across different defences, the ASR for SIG is higher compared to the ASR on other attacks when defending using our IEU.

Solutions for weaknesses [a] and [b]. A better isolation method can be used in place of $f_{p}$, such as in Doan et al. (). We surmise that using Doan et al. ()’s isolation method would make interleaved unlearning even more effective: although our IEU does not require poisoned data isolation rate to be close to 100% (see the ASR and CA values in Table 6 where adjacent “Poison” values are $\approx 0.8$ and Table 2 where $\hat{\alpha}_{i}\div\alpha\in\{0.5,0.9\}$), a more effective isolation method causes the robust module to learn less backdoored data and unlearn less clean data.

Table: Table 10: Performance of different backdoor defences on the WaNet attack (Nguyen & Tran, ) using the CIFAR10 dataset. Best and second-best values are bolded and underlined, respectively. All values are reported in percentages.

| No Defence | I-BAU | ABL | IEU |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA |
| 72.81 | 97.39 | 10.26 | 90.24 | 0.00 | 10.00 | 26.01 | 94.17 |

Figure: Figure 3: $\max(\sigma(f_{p}(\mathbf{x}\,;{\bm{\theta}}_{p}))$ CDF on clean/poisoned data for WaNet using CIFAR10.

Weakness [c] Instability during defence in stage 2 occurs when defending the VGG-11 model architecture against the Smooth attack. The instability causes NaN loss values during finetuning.

Potential solutions for weakness [c]: either (1) using $lr^{\text{ul}}=c\cdot lr^{\text{tune}}$ for hyperparameter $c$ instead of the Dynamic $lr^{\text{ul}}$ explained in Equation 3 or (2) replacing $\ell(f_{r}(\mathbf{x}^{\hat{p}}_{k-1}\,;{\bm{\theta}}_{r}),\mathbf{y}_{k-1})$ with a weighted moving average of successive cross entropy losses in Equation 3 may prevent instabilities from being introduced when alternating between finetuning and unlearning steps.

## 6 Conclusion

This work presents a novel and effective method for finetuning benign ViTs on backdoored datasets called Interleaved Ensemble Unlearning (IEU). We use a small and shallow ViT (the poisoned module) to distinguish between clean and backdoored images and show that alternating between learning clean data and unlearning poisoned data during defence is an effective way of preserving high clean accuracy whilst foiling the backdoor attack. We demonstrate that our defence is effective for complicated real-world datasets and discuss ways to make IEU more robust.

Impact. This paper’s impact goes beyond defending Vision Transformers against backdoor attacks. We believe that the Interleaved Ensemble Unlearning framework, which extends ABL (Li et al., ) and Denoised PoE (Liu et al., ), can be used to tune benign models with a great variety of different model architectures. In addition, we encourage future work to consider and remedy the weaknesses we point out in Section 5 for unlearning-based backdoor defences.

## Appendix A More Implementation Details

### A.1 Backdoor Attack Details

For SIG (Barni et al., ) we poison 100% of the chosen target class regardless of the dataset. We mostly base our data poisoning code on BackdoorBox’s attacks (Li et al., ); for attacks that are not available in BackdoorBox, we adapt our code from the attack authors’ source code. We modify the code for BATT (Xu et al., ) implemented in BackdoorBox by moving the attacker-specified transformation to before the data augmentation step. For ISSBA (Li et al., ), one encoder/decoder pair is trained for each of the three datasets. Figure 4 shows visualisations of backdoored images on CIFAR10. Throughout the paper, the target class used by the attacker is class 1.

Figure: Figure 4: Visualisation of backdoored images (CIFAR10).
Refer to caption: x4.png

### A.2 Backdoor Defence Details

The data augmentations used for finetuning without defence and in our method (IEU) are based on the augmentations in Atito et al. () where drop_perc and drop_replace are set to 0.3 and 0.0, respectively. Three views of each image are produced: an unaugmented image, a clean crop with only colour jitter, and a corrupted crop with colour jitter and patch-based corruption. We used the pretrained checkpoint in Atito et al. () for finetuning. Note that only the non-corrupted view is used to finetune models when demonstrating the effectiveness of IEU with different model architectures in Table 8. Each image’s spatial dimension is $224\times 224$ pixels. For all experiments except for those found in Table 8, ViT-S is used as the base architecture: patch size of the ViT is $16\times 16$; we use $\texttt{embed_dim}=384,\texttt{ num_heads}=6,\texttt{ mlp_ratio}=4$, and LayerNorm (Ba et al., ).

Finetuning without defence. On all datasets, the ViT is finetuned for 10 epochs using the Adam (Kingma & Ba, ) optimizer with initial learning rate $2\cdot 10^{-5}$ and a cosine annealing learning rate scheduler that terminates at $1\cdot 10^{-6}$, weight decay using a cosine annealing scheduler starting from $0.04$ and increasing to $0.1$, and effective batch size 128 (recall that the two augmented views of each image is used during finetuning).

**Table 11: Defence parameters used for CIFAR10/TinyImageNet and GTSRB. Parameters for CIFAR10/TinyImageNet have never been tuned (i.e., they were set to these values prior to running any experiments with IEU).**
| Dataset | Pre-finetuning Epochs/Warmup | Pre-finetuning lr | $c_{\text{thresh}}$ | lr decay |
| --- | --- | --- | --- | --- |
| GTSRB | 5/No | $1\cdot 10^{-3}$ | $0.998$ | No |
| CIFAR10/TinyImageNet | 10/Yes | $2\cdot 10^{-4}$ | $0.95$ | No |

Our method (IEU). For stage 1, the differences in the hyperparameters used for CIFAR10/TinyImageNet and GTSRB to pre-finetune the poisoned module are shown in Table 11. A weight decay of $0.0$ is applied to the poisoned module throughout stage 1 and no data augmentations are applied. If learning rate warmup is used, the learning rate scheduler performs a linear warmup for one epoch starting from $lr=0$. The batch size is 64. Recall that poisoned module is a shallow ViT of depth 1. For stage 2, we use the same parameters during finetuning as for finetuning without defence. Please refer to Section 3 and Equation 3 for an explanation of the unlearning rate $lr^{\text{ul}}$.

ABL. Since the model architecture we use is different compared to the architectures used in Li et al. (), we perform hyperparameter tuning using the BadNets-white attack on all three datasets. The isolation ratio $r_{\text{isol}}$ (fraction of $\mathcal{D}^{\text{tune}}$ to unlearn) is set to 0.01 and every image in $\mathcal{D}^{\text{ul}}$ is poisoned by default since we verify that LGA/Flooding can accurately select poisoned images on BadNets-white using CIFAR10. Table 12 shows the ABL hyperparameter tuning results for all three datasets. We choose $5\cdot 10^{-7},1\cdot 10^{-6},2\cdot 10^{-7}$ as the unlearning rate for CIFAR10, GTSRB, and TinyImageNet, respectively. In addition, we use the Adam optimiser.

**Table 12: Hyperparameter tuning for ABL on CIFAR10, GTSRB, and TinyImageNet. Bolded are reasonably good values that correspond to our choices for unlearning lr.**
| Unlearning lr | CIFAR10 | GTSRB | TinyImageNet |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA |  |
| $5.0\cdot 10^{-8}$ | 97.29 | 98.40 | - | - | 97.80 | 61.34 |
| $1.0\cdot 10^{-7}$ | 97.02 | 98.41 | - | - | 95.61 | 61.06 |
| $2.0\cdot 10^{-7}$ | 96.19 | 98.38 | 94.53 | 95.56 | 0.25 | 59.29 |
| $3.0\cdot 10^{-7}$ | 85.64 | 98.37 | 93.85 | 95.49 | 0.03 | 57.30 |
| $5.0\cdot 10^{-7}$ | 9.63 | 98.08 | 83.84 | 95.46 | 0.00 | 45.52 |
| $1.0\cdot 10^{-6}$ | 7.00 | 94.73 | 4.84 | 93.56 | 0.00 | 3.06 |
| $2.0\cdot 10^{-6}$ | - | - | 0.00 | 83.11 | - | - |
| $3.0\cdot 10^{-6}$ | - | - | 0.00 | 72.39 | - | - |
| $5.0\cdot 10^{-6}$ | 0.00 | 84.78 | 0.00 | 36.74 | 0.00 | 0.50 |
| $1.0\cdot 10^{-5}$ | 0.00 | 10.00 | 0.00 | 3.56 | 0.00 | 0.50 |
| $5.0\cdot 10^{-5}$ | 0.00 | 10.00 | 0.00 | 3.56 | 0.00 | 0.50 |
| $1.0\cdot 10^{-4}$ | 0.00 | 10.00 | 0.00 | 0.95 | 0.00 | 0.50 |

I-BAU. We also perform hyperparameter tuning for I-BAU (Zeng et al., ) for the same reasons above. Following suggestions in the appendix of Wang et al. (), we tune outer_lr $\in\{5\cdot 10^{-4},1\cdot 10^{-4},5\cdot 10^{-5},1\cdot 10^{-5},5\cdot 10^{-6}\}$ and inner_lr $\in\{0.1,1,5,10,20\}$ for CIFAR10 and TinyImageNet. GTSRB is not separately tuned since good eprformance is reached using CIFAR10’s hyperparameters. We choose as the hyperparameters $(\texttt{outer_lr},\texttt{inner_lr})=[(5\cdot 10^{-5},5),(5\cdot 10^{-5},5)
,(5\cdot 10^{-5},10)]$ for CIFAR10, GTSRB, and TinyImageNet, respectively. In addition, we use the Adam optimiser as the outer optimiser for I-BAU. For every dataset, $5000$ images from the testing set are used for the unlearning step (unlloader in their code). Note that $5000$ clean images taken from the testing set is the default setup in the defence code of I-BAU.

AttnBlock. This is the defence referred to as the “Attn Blocking” defence in Subramanya et al. (). We use GradRollout (Gildenblat, ) to compute the interpretation map on image $\mathbf{x}$ $\mathbf{I}_{\text{map}}(\mathbf{x})$ using the backdoored checkpoint and find the coordinates of the interpretation map’s maximum $\max(\mathbf{I}_{\text{map}}(\mathbf{x})$. A $30\times 30$ patch centred at the coordinates $\max(\mathbf{I}_{\text{map}})$ is zeroed out from the original image $\mathbf{x}$ to form $\mathbf{x}^{\prime}$. If this centred patch goes outside of the image, the patch is shifted so that it is on the image’s border. Then, the backdoored checkpoint is used to classify $\mathbf{x}^{\prime}$. The results for the test-time interpretation-informed defence proposed in Subramanya et al. () is shown in Table 13. Generally, the defence does not defend against the non-patch-based attacks evaluated in our work.

**Table 13: Performance of AttnBlock**
| Attack | CIFAR10 | GTSRB | TinyImageNet |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA |  |
| BadNets-white | 34.71 | 98.21 | 29.05 | 94.73 | 54.35 | 60.21 |
| BadNets-pattern | 12.61 | 98.06 | 22.03 | 94.2 | 7.55 | 61.2 |
| ISSBA | 100.0 | 97.93 | 100.0 | 94.13 | 99.27 | 61.82 |
| BATT | 99.99 | 98.0 | 100.0 | 94.63 | 99.99 | 65.42 |
| Blended | 99.99 | 98.15 | 100.0 | 94.8 | 100.0 | 68.94 |
| Trojan-WM | 99.98 | 98.13 | 99.98 | 91.35 | 99.97 | 68.82 |
| Trojan-SQ | 99.48 | 98.09 | 99.47 | 94.06 | 99.63 | 61.97 |
| Smooth | 99.72 | 97.99 | 99.71 | 94.66 | 99.17 | 67.54 |
| l0-inv | 100.0 | 98.1 | 100.0 | 95.14 | 100.0 | 62.1 |
| l2-inv | 99.99 | 98.2 | 100.0 | 92.77 | 99.78 | 64.33 |
| SIG | 98.35 | 88.53 | 99.43 | 90.42 | 68.36 | 70.41 |
| Average | 85.89 | 97.22 | 86.33 | 93.72 | 84.37 | 64.8 |

### A.3 Hardware Resources

Most experiments are conducted on one NVIDIA A100 GPU. A few experiments are (and can be) conducted on one NVIDIA Quadro RTX 6000 GPU. We did not reproduce I-BAU (Zeng et al., ) on the RTX 6000 GPU due to GPU memory constraints.

## Appendix B Algorithm for Stage 2

The steps for Stage 2 of IEU is shown in Algorithm 1.

Figure: Algorithm 1 Stage 2 of IEU: Defending $f_{r}$

## Appendix C Ablation Study (cont’d)

Noisy logits. Table 14 shows the effects of adding normally distributed zero-mean noise to $\mathbf{\hat{y}}_{p}$ when accumulating the unlearn set. Whether noise is added or not has almost no effect on the model performance.

**Table 14: Performance of IEU on CIFAR10 when adding normally distributed zero-mean noise with different variances to $\mathbf{\hat{y}}_{p}$ after computing $m_{{\bm{\theta}}_{p}}$, i.e., $m_{{\bm{\theta}}_{p}}$ is still defined according to Equation 1 but $\max(\sigma(\mathbf{\hat{y}}_{p}+\mathbf{n}))>c_{\text{thresh}}$ where $\mathbf{n}\sim{\mathcal{N}}(0,\sigma^{2})$ is used to determine whether $\mathbf{x}$ belongs in $\mathcal{D}^{\text{ul}}$. This creates a mismatch between the data added onto $\mathcal{D}^{\text{ul}}$ (unlearned by $f_{r}$) and the data learned by $f_{r}$.**
| Variance | BATT | BadNets-white | ISSBA | Smooth |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ASR | CA | ASR | CA | ASR | CA | ASR | CA |  |
| 0.0 | 0.02 | 98.23 | 0.96 | 98.19 | 0.33 | 98.35 | 0.09 | 97.77 |
| 0.1 | 0.02 | 98.09 | 0.93 | 98.23 | 0.10 | 98.43 | 0.08 | 97.85 |
| 0.5 | 0.02 | 98.21 | 0.88 | 98.13 | 0.35 | 98.36 | 0.04 | 97.64 |
| 1.0 | 0.01 | 98.15 | 0.95 | 98.09 | 0.05 | 98.30 | 0.05 | 97.91 |
| 2.0 | 0.02 | 96.82 | 0.94 | 98.17 | 0.46 | 98.30 | 0.06 | 97.95 |

The effect of using LGA/Flooding in conjunction with our poisoned module is shown in Table 15. The short-hand $f_{p}$ & $M$ means applying method $M$ when tuning $f_{p}$ during stage 1 of our method. Given the high FNR for most attacks with CIFAR10 and TinyImageNet when using LGA/Flooding together with our $f_{p}$, we argue that using poisoned module is orthogonal to LGA/Flooding for isolating poisoned data.

**Table 15: Comparison of the three methods’ (LGA, Flooding, no-method) ability to distinguish between poisoned and clean data when used in conjunction with our $f_{p}$ during prefinetuning. The $f_{p}$ is prefinetuned for 10 epochs using default parameters. The flooding/LGA parameter is set to $\gamma=1.5,\gamma=3.0$ for CIFRA10 and TinyImageNet, respectively. Each cell shows the FPR/FNR values as percentages (positive means “poisoned”).**
| Method | CIFAR10 | TinyImageNet |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| BadNets-white | ISSBA | Smooth | BadNets-white | ISSBA | Smooth |  |
| $f_{p}$ & Flooding | 0.00/99.98 | 0.00/57.76 | 0.00/99.54 | 0.03/20.07 | 0.01/64.66 | 0.12/15.89 |
| $f_{p}$ & LGA | 0.00/99.98 | 0.00/65.84 | 0.00/97.86 | 0.03/20.07 | 0.12/67.32 | 0.12/15.89 |
| $f_{p}$ & no-method | 5.62/5.30 | 5.58/2.10 | 7.90/3.14 | 0.21/11.97 | 0.15/22.59 | 0.42/9.83 |

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 5
presentation: 2
questions: Please see the weakness part.
soundness: 3
strengths: -	The two-stage method is reasonable, especially, using a shallow model to learn shortcuts in the dataset in the first stage. 
-	The experiments show that IEU performs better than existing methods, including I-BAU and ABL. Besides, the ablation studies are well-organized, illustrating the necessity of designs in IEU.
summary: This paper presented Interleaved Ensemble Unlearning (IEU), a method for finetuning
clean ViTs on backdoored datasets. IEU includes two stages, where the first one is designed to train a shallow ViT used to block potentially poisoned data and the second stage defends backdoor attacks utilizing unlearning. The experiments demonstrate that IEU out-performs existing defenses on diverse datasets and backdoor attacks.
weaknesses: -	The novelty is limited. The proposed IEU utilizes the unlearning strategy for backdoor defense. Compared to ABL, the main differences lie in using a shallow model to block potentially poisoned data and a confidence threshold to determine the unlearned samples rather than a fixed-sized unlearned set.

-	I am confused as to why IEU is tailored to ViTs. According to my understanding, there is no customized design in IEU for transformer-like architectures. Also, the authors evaluate CNN models in Table 8. Hence, if I am correct, I recommend the authors revise the writing to highlight the universality of the proposed IEU.

-	I suggest that Eq.2 could be further clarified in detail. If the logits for optimizing the objective in Equation 2 sometimes come from $f_p$, should the optimized parameters include $\theta_p$?

---

confidence: 4
contribution: 4
initial_rating: 8
presentation: 3
questions: - Could the authors elaborate on the architectural choices for the shallow ViT used as the poisoned module?

- How does IEU perform on deeper ViT architectures for the 'poisoned module' not covered in the study?

I notice some sharp drops in ASR in Table 2. For Example, for ISSBA-CIFAR-10, the ASR is 100.00 for 0.2 and 0.0 for 0.5. Similar results can be for Smooth and Tiny ImageNet. Can the authors provide some insights on the sharp drops? This could provide better insights for future works to reproduce the results (or even improve).
soundness: 3
strengths: - IEU provides a novel approach to mitigating backdoor attacks in ViTs by implementing a layered defense strategy that separates poisoned data using a shallow 'poisoned module'.

- The method’s two-stage process of alternating between learning and unlearning adds robustness against various backdoor attacks without relying on a pre-identified clean set.

- The paper provides comprehensive empirical evaluation against a wide array of backdoor attacks across multiple datasets (CIFAR10, GTSRB, and TinyImageNet), showcasing improvements in ASR reduction and maintenance of high clean accuracy on CIFAR10 and TinyImageNet.

- IEU demonstrates practical value, particularly in domains where ViTs are deployed for security-sensitive tasks, making it a valuable contribution to backdoor defense for ViTs.

- The paper also discusses the method's limitations (e.g., simple dataset, weak attacks, and instability) to provide insights into how to improve the method further in future works.
summary: This paper introduces Interleaved Ensemble Unlearning (IEU), a defense strategy designed to protect Vision Transformers (ViTs) (or any model in general) from backdoor attacks during the fine-tuning process.

The IEU approach uses a shallow ViT model as a 'poisoned module' to detect backdoored data and protect the main 'robust module,' which is fine-tuned on clean data sorted through the 'poisoned module'.
IEU operates in two stages: the first trains the poisoned module on backdoored data, while the second uses it to isolate potentially poisoned samples for unlearning by the robust module. By alternating between learning and unlearning, the IEU method mitigates the effects of poisoned images, maintaining high accuracy on clean data while effectively defending against backdoor attacks. 

Evaluation results on three datasets (CIFAR10, GTSRB, and TinyImageNet) demonstrate its competitive performance against other state-of-the-art backdoor defenses, especially for CIFAR10 and TinyImageNet.
weaknesses: - **Limited Explanations for reproducibility:** The article provides limited clarity in the explanations of the technical details, particularly in the specific architectures and configurations used for the 'poisoned module' and 'robust module', respectively. This provides limited insight into understanding the 'poisoned module,' which is the most important component of the proposed approach. 

- **Generalizability to Complex Architectures:** It is unclear whether the proposed approach is generalizable to more complex ViT Architectures or is limited to standard ViT architectures. Further, while the approach is proposed specifically for the ViT, in theory, it can be applied to non-ViT-based models, improving the applicability of the proposed defense. 

- **Limited insight on the limitations:** The article highlights the limitations and discusses them, providing insights on why the approach underperforms in certain cases. I am not strongly convinced that this is the only reason for underperformance (though it is minimal underperformance). For example, the authors argue that the GTSRB dataset is less complex than the other datasets evaluated, which is why underperformance happens. However, it is a failure case of a 'poisoned module' not to learn well enough to distinguish (as evidenced by Fig 2).
Moreover, the Clean Accuracy is also lower, suggesting that $m_{\theta_p}$, which is directly related to the logits calculated by $f_p$, also affects the performance. 
Further, no insights have been provided as to why the poisoned module learn differently for the GTSRB dataset, nor have any suggestions on improving the training of the 'poisoned module' to prevent these failure cases. While I do not state that the approach should perform better for the GTSRB dataset natively, I think there is an oversight in identifying and discussing why the 'poisoned module' gives high enough logits for the poisoned images, which affects both Clean Accuracy as well as ASR directly.

---

confidence: 3
contribution: 2
initial_rating: 3
presentation: 1
questions: 1. The proposed method heavily relies on the prediction of the poisoned module. What if the poisoned module itself is attacked by malicious users? How can the proposed method address this scenario?

2. The proposed method appears to be sensitive to the heuristic threshold $c_{thresh}$. How do the authors determine the value of the threshold?
soundness: 2
strengths: 1. The paper proposes a unique ensemble-based strategy specifically tailored for ViTs, addressing the scarcity of ViT-targeted backdoor defenses.

2. IEU is evaluated on diverse datasets (CIFAR10, GTSRB, TinyImageNet) and multiple backdoor attacks, providing extensive empirical data on performance improvements.
summary: The paper presents Interleaved Ensemble Unlearning (IEU), a method aimed at defending Vision Transformers (ViTs) from backdoor attacks during fine-tuning on backdoored datasets. IEU employs a two-stage approach, using a shallow "poisoned module" ViT to filter potentially poisoned data and a "robust module" to learn clean data. In stage one, the poisoned module is trained to confidently predict backdoor-labeled data, while stage two involves using this module to identify and remove potentially backdoored data. This dynamic unlearning technique is tested on multiple datasets and against various attacks, showcasing IEU’s ability to improve attack success rate (ASR) and clean accuracy (CA).
weaknesses: 1. The presentation quality falls significantly short of the standards expected at a prestigious conference like ICLR. Readers without a strong background in vision transformers and backdoor attacks will likely struggle to follow the manuscript. Key background information, such as the concept of "unlearning", is notably absent. Additionally, Figure 1 presents mathematical notations to illustrate the proposed method, yet these notations lack sufficient explanation. For example, the symbol $\mathcal{D}^{ul}$ is used without clarifying its meaning.

2. Although the paper claims that IEU enhances ViT robustness against backdoor attacks, it lacks clarity on which specific design elements are tailored to address vulnerabilities unique to the ViT architecture.

3. This paper lacks novelty. The ensemble strategy primarily relies on heuristic thresholds rather than introducing innovative designs. Additionally, Stage 1 does not present any novel contributions.

---

confidence: 3
contribution: 3
initial_rating: 5
presentation: 3
questions: Listed in the weakness of the paper.

Score can be improved if concerns listed above are resolved.
soundness: 3
strengths: - This paper explores a method for finetuning clean ViTs on backdoored datasets, Interleaved Ensemble Unlearning (IEU), giving a good reference to the research on this aspect.

- The proposed method IEU is simple but effective to achieve the defense, and the good performance obtained by the experiments strongly supports this point.

- The ablation study is organized well to clearly demonstrate the whole proposed method. And it makes the paper easy to follow.
summary: Vision Transformers (ViTs) are increasingly used in computer vision tasks but are vulnerable to backdoor attacks that can compromise their performance, especially in security-sensitive applications. Existing backdoor defenses for Convolutional Neural Networks (CNNs) are not as effective for ViTs, and tailored solutions are limited.

To address this, the paper proposes Interleaved Ensemble Unlearning (IEU), a method for fine-tuning clean ViTs on backdoored datasets. In the first stage, a shallow ViT is fine-tuned to exhibit high confidence on backdoored data while maintaining low confidence on clean data. In the second stage, this shallow ViT serves as a "gate" to filter out potentially poisoned data from the defended ViT, which is then added to an unlearn set and asynchronously unlearned via gradient ascent.

The paper demonstrates IEU's effectiveness across three datasets against 11 state-of-the-art backdoor attacks and highlight its versatility by applying it to various model architectures.
weaknesses: - I have some concerns regarding **the fairness of comparison with previous defense methods,** particularly due to the inclusion of the additional poisoned module, which involves an extra network for defense.

- The authors propose an effective framework of backdoor defense on ViT. It would be beneficial to consider a more realistic scenerio, where the attacker knows the existence of IEU and can generate a poisoned dataset to perform adaptive attacks. **It would be wonderful if the authors can design an adaptive attack for IEU and provide some experimental results.**

- I recommend conducting further experiments to assess whether BSD can successfully defend against backdoor attacks **with different target labels.** This could provide valuable insights into the robustness of the defense mechanism across various scenarios.

- There are existing backdoor defenses that focus on training clean models using poisoned datasets [1, 2], which could provide useful context for this research.

[1] Backdoor Defense via Adaptively Splitting Poisoned Dataset. CVPR, 2023.

[2] Backdoor Defense via Deconfounded Representation Learning. CVPR, 2023.