| Input: M (number of neurons at the output of feature extractor),Iimg (initial input), K (number of |
| procedure ATTACK(Iimg,F,T) | iteration), F (known feature extractor),α (step constant),T (the target model on attack): |
| 1: 2: | fori from 1 to M do |
| Y=0m |
| 3: 4: | |
| 5: | Y[𝑖] = 1000; >Any sufficiently large number |
| 6: | X=Iimg for j from 1 to K do |
| 7: | L = γ(F(X)[i])-Y[i])²+ β(∑t≠i relu(F(X)[l]-Y[[])²) |
| 8: | 8= |
| 9: | X=X-αδ |
| 10: | if T(X） bypasses the authentication then return X |
| return | |
+
+Algorithm Design. The brute force algorithm is shown in Algorithm 1. We first iterate through all neurons at the output of the feature extractor and set the target, $Y$ , such that at each iteration only one neuron is triggered. We set all elements of $Y$ to zero except for the $i ^ { t h }$ one which can be set to any sufficiently large number, e.g., 1000, in Algorithm 1. Note that $Y$ is a target of the feature extractor, not that of the entire re-trained model. In the case of the VGG face, there are 4096 neurons at this layer. So, we only try 4096 times at maximum. In fact, we will show in the next section that we only need to try a few times to trigger any class and we need way fewer than 4096 attempts to trigger all target classes at least once.
+
+Inside the second loop, we use the derivative of the loss with respect to an input and change the input gradually to decrease the loss. Note that in the loop we only use the pre-trained model and the re-trained target model is not needed. We find that typical MSE loss between Y and feature extractor is very inefficient. For the target activation vector where $i ^ { t h }$ neuron is large and all other neurons are close to zero, the modified loss is defined as follows:
+
+$$
+L = \gamma ( F ( x ) [ i ] ) - Y [ i ] ) ^ { 2 } + \beta ( \sum _ { l \neq i } r e l u ( F ( x ) [ l ] - Y [ l ] ) ^ { 2 } ) ,
+$$
+
+where $F ( X )$ is the output of feature extractor (i.e. activation vector) and $Y$ is the target activation vector. It is similar to the regular MSE loss with two minor changes: I) Because the importance of $i ^ { t h }$ neuron is greater than all other 4095 neurons to our attack, we use $\gamma$ and $\beta$ to control the influence of each part on the loss function. II) Because of the existence of relu function after each fully connected layer to provide non-linearity, any value on the $( - \infty , 0 ]$ range becomes 0. Hence, instead of crafting an image that has large value in $i ^ { t h }$ neuron and zero value in all other neurons, we aim to craft an image that has large value in $i ^ { t h }$ neuron and any non-positive value in all other neurons. Not only the original MSE might not converge to an adversary example, our revised loss function defined in (1) is much more efficient since the loss function only focuses on neurons that have positive value at each step and ignores the ones that are already negative. This goal is acheived by adding the relu function in the loss function.
+
+Implication. We call this type of attack target-agnostic because it does not exploit any information from target’s classes, model, or samples. In fact, if the same pre-trained model is used to re-train two different target tasks (models), $A$ and $B$ , the proposed target-agnostic attack crafts similar adversarial inputs for both $A$ and $B$ since it only uses the pre-trained model to craft inputs. The implication is that the attacker can craft a set of adversarial inputs with the source model using the proposed attack and use it effectively to attack all re-trained models that use the same pre-trained model. This means that the attack crafting time is not important and one can create a database of likely-to-trigger inputs for each popular pre-trained model, such as the VGG face or ResNet18. Given the simplicity, remarkable effectiveness, and target-agnostic feature of the proposed algorithm, it poses a huge security threat to transfer learning.
+
+# 5 EVALUATION
+
+In this section, we evaluate the effectiveness of our approach using two test cases: Face recognition and speech recognition (Appendix A.2). We use Keras with Tensorflow backend and a server with Intel Xeon W-2155 and Nvidia Titan Xp GPU using Ubuntu $1 6 . 0 4 ^ { 1 }$ . We use two metrics to evaluate the proposed attack model: 1) Number of attempts to break all classes (NABAC): Assuming that the number of target classes are known, this metric shows how many adversarial input instances are queried, on average, to trigger all target classes at least once with above $9 9 \%$ confidence. 2) Effectiveness $( X \% )$ : This metric shows the ratio of crafted inputs that trigger any target classes with $X \%$ confidence over the total number of crafted inputs. We use $9 5 \%$ and $9 9 \%$ confidence for effectiveness in this paper.
+
+# 5.1 CASE STUDY: FACE RECOGNITION
+
+In this case study, we use the VGG face model Parkhi et al. (2015) as a pre-trained model. We remove the last FC layer and the softmax (SM) layer to make a feature extractor. Then, we pair it with a new FC and SM layer, and re-train the model (while fixing feature extractor) with labeled faces of vision lab at UMass LWF (2016). During re-training, we train the model with Adam optimizer and cross entropy loss function. We set $K = 5 0 0 0 0$ , $\alpha = 0 . 1$ , $\beta = 0 . 0 1$ , and $\gamma = 1$ . In some experiments, we add more FC layers before the SM layer, as explained later.
+
+Number of Target Classes. Table 1 shows the impact of number of target classes on the attack performance. We use 20 classes with the highest number of samples from UMass dataset LWF (2016). The largest class is George W Bush with 530 samples and the smallest one is Alejandro Toledo with 39 samples. A blank image is used as an intial image. For 5, 10, and 15 classes, we randomly choose a set from 20 classes and re-train and attack the model 50 times and average the results. For 20 classes, we only re-train and attack once. That is the reason we do not show the standard deviation in the table. Table 2 shows the result when we use five images from each class for test set and all other images for training set. Hence, the re-training dataset is imbalanced. To balance the dataset, we undersample all classes to have an equal training size, shown in Table 1.
+
+As it is shown, the effectiveness of the attack on an imbalanced model is higher. However, the NABAC is slightly worse. We find out that on average the weights of SM layer for the class with larger training samples are slightly higher than the other classes. Hence, it is easier to trigger that class with the proposed method which increases the effectiveness. However, it is much harder to trigger the smallest class which makes the NABAC larger. The impact of imbalance re-training dataset is studied in more detail in Appendix A.1, where we show that the probability of triggering a target class directly associated with the number of training samples of that class during re-training. Moreover, the effectiveness and the NABAC improves when the number of target classes decreases, as expected. Note that in all scenarios, the effectiveness is greater than $7 5 \%$ . It means that the first crafted image has more than $7 5 \%$ chance of bypassing the authentication system (or any other application). It basically means that the traditional approach of limiting the number of queries to prevent brute-force-based attack does not work here.
+
+Number of Layers to Re-train. In previous experiments, we assume that the weights of the feature extractor transferred from the pre-trained model are fixed during re-training and only the last FC layer is changed. One can tune more layers during re-training. Fig. 3(a) shows the impact of tuning more layers on the effectiveness and accuracy. Note that we assume that attacker does not know anything about the target model. Hence, in this experiment, the attacker still uses the pre-trained feature extractor up until the last FC layer. That means the pre-trained feature extractor that the attacker uses is slightly different from the re-trained model. In Fig. 3(a), X axis represents the layer from which we start tuning up to the last FC layer. Due to the small re-training dataset, as the number of tuning layers increases the accuracy drops. However, by tuning more layers, the pre-trained model that the attacker has access to becomes more different from the re-trained model. That is why the effectiveness of the attack decreases. Similarly, NABAC increases, as shown in Fig. 3(b). Despite the difference between the re-trained model and the model the attacker has access to, the attack is still effective, which means that the pre-trained model cannot be changed dramatically during re-training process and re-training more layers is not an effective defense strategy.
+
+Table 1: Attack performance on balanced re-training dataset. Acc, NABAC, and $E f f$ stands for accuracy, number of attempts to break all classes, and effectiveness, respectively.
+
+ | Input: M (number of neurons at the output of feature extractor),Iimg (initial input), K (number of |
| procedure ATTACK(Iimg,F,T) | iteration), F (known feature extractor),α (step constant),T (the target model on attack): |
| 1: 2: | fori from 1 to M do |
| Y=0m |
| 3: 4: | |
| 5: | Y[𝑖] = 1000; >Any sufficiently large number |
| 6: | X=Iimg for j from 1 to K do |
| 7: | L = γ(F(X)[i])-Y[i])²+ β(∑t≠i relu(F(X)[l]-Y[[])²) |
| 8: | 8= |
| 9: | X=X-αδ |
| 10: | if T(X） bypasses the authentication then return X |
| return | |
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+ ],
+ "table_footnote": [],
+ "table_body": " | Input: M (number of neurons at the output of feature extractor),Iimg (initial input), K (number of |
| procedure ATTACK(Iimg,F,T) | iteration), F (known feature extractor),α (step constant),T (the target model on attack): |
| 1: 2: | fori from 1 to M do |
| Y=0m |
| 3: 4: | |
| 5: | Y[𝑖] = 1000; >Any sufficiently large number |
| 6: | X=Iimg for j from 1 to K do |
| 7: | L = γ(F(X)[i])-Y[i])²+ β(∑t≠i relu(F(X)[l]-Y[[])²) |
| 8: | 8= |
| 9: | X=X-αδ |
| 10: | if T(X） bypasses the authentication then return X |
| return | |
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| procedure ATTACK(Iimg,F,T) | iteration), F (known feature extractor),α (step constant),T (the target model on attack): |
| 1: 2: | fori from 1 to M do |
| Y=0m |
| 3: 4: | |
| 5: | Y[𝑖] = 1000; >Any sufficiently large number |
| 6: | X=Iimg for j from 1 to K do |
| 7: | L = γ(F(X)[i])-Y[i])²+ β(∑t≠i relu(F(X)[l]-Y[[])²) |
| 8: | 8= |
| 9: | X=X-αδ |
| 10: | if T(X） bypasses the authentication then return X |
| return | |
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| procedure ATTACK(Iimg,F,T) | iteration), F (known feature extractor),α (step constant),T (the target model on attack): |
| 1: 2: | fori from 1 to M do |
| Y=0m |
| 3: 4: | |
| 5: | Y[𝑖] = 1000; >Any sufficiently large number |
| 6: | X=Iimg for j from 1 to K do |
| 7: | L = γ(F(X)[i])-Y[i])²+ β(∑t≠i relu(F(X)[l]-Y[[])²) |
| 8: | 8= |
| 9: | X=X-αδ |
| 10: | if T(X） bypasses the authentication then return X |
| return | |
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