# fast_advprop__8342f305.pdf

Published as a conference paper at ICLR 2022

FAST ADVPROP

Jieru Mei1, Yucheng Han2, Yutong Bai1, Yixiao Zhang1, Yingwei Li1, Xianhang Li3

Alan Yuille1 & Cihang Xie3

1Johns Hopkins University 2Nanyang Technological University 3UC Santa Cruz

Adversarial Propagation (Adv Prop) is an effective way to improve recognition models, leveraging adversarial examples. Nonetheless, Adv Prop suffers from the extremely slow training speed, mainly because: a) extra forward and backward passes are required for generating adversarial examples; b) both original samples and their adversarial counterparts are used for training (i.e., 2 data). In this paper, we introduce Fast Adv Prop, which aggressively revamps Adv Prop s costly training components, rendering the method nearly as cheap as the vanilla training. Speciﬁcally, our modiﬁcations in Fast Adv Prop are guided by the hypothesis that disentangled learning with adversarial examples is the key for performance improvements, while other training recipes (e.g., paired clean and adversarial training samples, multi-step adversarial attackers) could be largely simpliﬁed. Our empirical results show that, compared to the vanilla training baseline, Fast Adv Prop is able to further model performance on a spectrum of visual benchmarks, without incurring extra training cost. Additionally, our ablations ﬁnd Fast Adv Prop scales better if larger models are used, is compatible with existing data augmentation methods (i.e., Mixup and Cut Mix), and can be easily adapted to other recognition tasks like object detection. The code is available here: https://github.com/meijieru/fast_advprop.

1 INTRODUCTION

Deep neural networks are highly successful for visual recognition. As fueled by powerful computational resources and massive amounts of data, deep networks achieve compelling, sometimes even superhuman, performance on a wide range of visual benchmarks. However, when testing out of the box, these exemplary models are usually get criticized for lacking generalization/robustness an increasing amount of works point out that deep neural networks are brittle at handling out-of-domain situations like natural image corruptions (Hendrycks & Dietterich, 2018), images with shifted styles (Geirhos et al., 2018; Hendrycks et al., 2020), etc.

Adversarial propagation (Adv Prop) (Xie et al., 2020), which additionally feeds networks with adversarial examples during training, emerged as one of the most effective ways to train not only accurate but also robust deep neural networks. The key in Adv Prop is to apply separate batch normalization (BN) layers (Ioffe & Szegedy, 2015) to clean training samples and adversarial training samples, as they come from different underlying distributions. Later works further explore the potential of Adv Prop on other learning tasks, including object detection (Chen et al., 2021b; Xu et al., 2021), contrastive learning (Jiang et al., 2020; Ho & Vasconcelos, 2020; Xu & Yang, 2020) and large-batch training (Liu et al., 2022).

However, the beneﬁts brought by Adv Prop do not come for free Adv Prop introduces a signiﬁcant amount of additional training cost, which is mainly incurred by generating and augmenting adversarial training samples. For instance, compared to the vanilla training baseline (where only clean images are involved), the default setting in Adv Prop (Xie et al., 2020) increase the total computational cost by factor of 7, i.e., 5/7 from generating adversarial examples, 1/7 from training adversarial examples, 1/7 from training clean images. This extremely high training cost not only limits the further explorations of Adv Prop on larger networks (Xie et al., 2019; Brock et al., 2021; Dosovitskiy et al., 2020), with larger datasets (Sun et al., 2017; Kuznetsova et al., 2020), and for different learning tasks, but also makes the direct comparisons against other low-cost learning algorithms (Zhang et al., 2018; De Vries & Taylor, 2017; Yun et al., 2019; Cubuk et al., 2019b;a) seemingly unfair.

Published as a conference paper at ICLR 2022

Sampled Batch

Model Input

Free operation

Heavy operation

Clean Image

Adversarial Image

Image w/ Noise

Sampled Batch

Model Input

(a) Adv Prop (b) Fast Adv Prop

Figure 1: Comparison between Adv Prop and Fast Adv Prop. (a) Adv Prop generates a paired adversarial image (with color orange) for each clean image (with color blue) in the sampled batch, therefore incurring heavy training cost. Moreover, in addition to clean images, adversarial images are also fed into networks for training, therefore further increasing the total training cost, i.e., 2x data is used here compared to the vanilla training. (b) Different from Adv Prop, Fast Adv Prop only uses a small portion of the sampled batch to generate adversarial examples. Moreover, during the generation of adversarial images, the gradient calculation of input images and the gradient calculation of network parameters are merged into the same forward and backward pass as in (Shafahi et al., 2019; Zhang et al., 2019), therefore making generating adversarial examples for free .

In this paper, we present Fast Adv Prop, which can run as cheaply as the vanilla training baseline in practice. In particular, noting the most costly training components in Adv Prop are (1) generating adversarial examples where multiple forward passes and backward passes are additionally required, and (2) training with both clean samples and their adversarial counterparts therefore the size of training data gets doubled, Fast Adv Prop revamps the original training pipeline as the following:

Firstly, though both clean training samples and their adversarial counterparts are default components in traditional adversarial training (Goodfellow et al., 2015; Kurakin et al., 2017), we argue such pairing behavior is not a fundamental request by Adv Prop. Speciﬁcally, in Fast Adv Prop, we reposition adversarial examples solely as a bonus part for network training, i.e., networks now are expected to train with a mixture of a large portion of clean images and a small portion of adversarial examples. This adjustment on training data helps lower down training cost. Though the total number of adversarial training examples is reduced, our empirical results verify this strategy is sufﬁcient to let networks gain robust feature representations. Secondly, we integrate the recent techniques on accelerating adversarial training (Wong et al., 2020; Zhang et al., 2019; Shafahi et al., 2019) into Adv Prop, mainly for reducing the complexity of generating adversarial examples. However, this is non-trivial naively adopting these fast adversarial training techniques will collapse the training, resulting in suboptimal model performance. We identify such failure is caused by the label leaking effect (Kurakin et al., 2017), which largely weakens the regularization power imposed by adversarial training samples. We further note this leakage comes from the intra-batch communication among training samples in the same mini-batch, and resolve it via shufﬂing BN (He et al., 2020). Additionally, we ﬁnd a) re-balancing the importance between clean training samples and adversarial training samples and b) synchronizing parameter updating speed are the other two key ingredients for ensuring Fast Adv Prop s improvements.

Our empirical results demonstrate that Fast Adv Prop can successfully improve recognition models for free . For instance, without incurring any extra training cost, Fast Adv Prop helps Res Net-50 (He et al., 2016) outperforms its vanilla counterpart by 0.3% on Image Net, 2.1% on Image Net-C, 1.9% on Image Net-R and 0.5% on Stylized-Image Net. Furthermore, such free lunch can consistently be observed when Fast Adv Prop is applied to networks at different scales, combined with various data augmentation strategies, and adapted to other recognition tasks. By easing the computational barriers, we hope this work can encourage the community to further explore the potential of Adv Prop (or adversarial learning in general) on developing better deep learning models.

Published as a conference paper at ICLR 2022

2 RELATED WORK

Adversarial training. Adversarial training (Szegedy et al., 2014; Goodfellow et al., 2015), which trains networks with adversarial examples that are generated on the ﬂy, is one of the most effective ways for defending against adversarial attacks. Nonetheless, compared to vanilla training, adversarial training signiﬁcantly increases the computational overhead, mainly due to the high complexity of generating adversarial examples.

To this end, many efforts have been devoted to accelerating adversarial training. Both (Shafahi et al., 2019) and (Zhang et al., 2019) propose to merge the gradient for adversarial attacks and the gradient for network parameter updates into a single forward and backward pass to reduce computations. Wong et al. (Wong et al., 2020) alternatively argue that the cheapest adversarial attacker, Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2015), actually can train robust classiﬁers, if combined with random initialization. This work is further enhanced by (Andriushchenko & Flammarion, 2020) to explicitly maximizing the gradient alignment inside the perturbation set for enhancing the quality of the FGSM solution. In this work, we aim to integrate these fast adversarial training techniques into Adv Prop, for reducing the overhead of generating adversarial training samples.

Adversarial propagation. It is generally believed that adversarial training hurts generalization (Raghunathan et al., 2019). Adversarial propagation (Adv Prop) (Xie et al., 2020), a special form of adversarial training, challenges this belief by showing training with adversarial examples actually can improve recognition models. The key is to utilize an additional set of batch normalization layers exclusively for the adversarial images (or more importantly, as suggested in (Chen et al., 2021a), by applying a different set of rescaling parameters in batch normalization layers), as they have different underlying distributions to clean examples. Later works further explore the potential of Adv Prop on other recognition tasks (Chen et al., 2021b; Xu et al., 2021; Shu et al., 2020; Chen et al., 2021a; Xie & Yuille, 2020; Wang et al., 2020; Gong et al., 2021), under different learning paradigms (Jiang et al., 2020; Ho & Vasconcelos, 2020; Xu & Yang, 2020), with different adversarial data (Merchant et al., 2020; Li et al., 2020; Herrmann et al., 2021), enabling extremely large-batch training (Liu et al., 2022), etc. In this paper, rather than furthering performance, we aim to make Adv Prop free .

Data augmentation. Data augmentation, which effectively increases the size and the diversity of the training dataset, is crucial for the success of deep neural networks (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015; Szegedy et al., 2015; He et al., 2016). Popular ways for augmenting data include geometric transformations (e.g., translation, rotation), color jittering (e.g., brightness, contrast), mixing images (Zhang et al., 2018; Yun et al., 2019; De Vries & Taylor, 2017), etc.

Training with adversarial examples (Goodfellow et al., 2015; Xie et al., 2020; Chen et al., 2021b) can be regarded as a special way to augment data different from traditional data augmentation strategies which are usually ﬁxed and model agnostic, the policy of generating adversarial examples is jointly evolved with the model updating throughout the whole training process. This behavior ensures the augmentation policy of adversarial examples stays current and relevant. Nonetheless, a signiﬁcant drawback of augmenting adversarial examples is that the introduced computational overhead is much more expensive than that of traditional augmentation strategies. We hereby aim to make training with adversarial examples as cheap as other data augmentation strategies.

3 FAST ADVPROP

We hereby present Fast Adv Prop, which aggressively revamps the costly components in Adv Prop. Particularly, our modiﬁcations mainly focus on reducing the computational overheads stemmed from adversarial examples, meanwhile (empirically) still attempt to retain the beneﬁts brought by Adv Prop.

3.1 REVISITING ADVPROP

Adv Prop (Xie et al., 2020) demonstrates adversarial examples can improve recognition models. By noticing adversarial images and clean images have different underlying distributions, Adv Prop bridges such distribution mismatch by using two BN scheme the original BN layers are applied exclusively for clean images, and the auxiliary BN layers are applied exclusively for adversarial images. This scheme ensures each BN layer is executed on a single data source (i.e., either clean images or adversarial images). More concretely, in each iteration,

Published as a conference paper at ICLR 2022

Table 1: The performance of vanilla training, Adv Prop, same-budget Adv Prop, and Fast Adv Prop on various datasets. / indicate the higher/lower the better.

IMAGENET IMAGENET-C IMAGENET-R S-IMAGENET TRAINING BUDGET

Vanilla Training 76.2 58.5 36.3 7.8 1

PGD-5 Adv Prop 77.0 52.0 42.3 12.0 7 15-epoch PGD-5 Adv Prop 66.8 66.2 31.7 8.6 1 PGD-1 Adv Prop 77.5 54.3 39.5 8.6 3 35-epoch PGD-1 Adv Prop 73.9 59.6 36.5 9.3 1

Fast-Adv Prop (ours) 76.5 56.4 38.2 8.3 1

Step 1: After randomly sampling a subset of the training data, Adv Prop applies the adversarial attack to these clean images for generating the corresponding adversarial images, using the auxiliary BN layers.

Step 2: The clean images and their adversarial counterparts are then fed into the network as a pair. Speciﬁcally, the original BN layers are applied exclusively on the clean images, and the auxiliary BN layers are applied exclusively on the adversarial images.

Step 3: The loss from adversarial images and clean images are jointly optimized for updating network parameters.

As shown in (Xie et al., 2020), Adv Prop substantially improves both the clean images accuracy, as well as the model robustness. We conﬁrm it in our re-implementation as shown in the second row of Table 1, Adv Prop, using PGD-5 attacker, helps Res Net-50 beats its vanilla counterpart by 0.8% on Image Net (Russakovsky et al., 2015), 6.5% on Image Net-C (Hendrycks & Dietterich, 2018), 6.0% on Image Net-R (Hendrycks et al., 2020) and 4.2% on Stylized-Image Net (Geirhos et al., 2018).

But meanwhile, we note Adv Prop signiﬁcantly increases the training cost. For example, our Adv Prop re-implementation requires 7 more forward and backward passes than the vanilla baseline. Such heavy training cost not only limits the broader exploration with Adv Prop, but also makes the comparisons to other learning strategies (which are usually free , e.g., (Yun et al., 2019; Zhang et al., 2018; Cubuk et al., 2019a)) seemly unfair.

To reduce the computational cost, we ﬁrst give a naive attempt to simplify Adv Prop s training pipeline. Speciﬁcally, given PGD-5 Adv Prop here is 7 more expensive than the vanilla baseline, we directly cut its total training epochs by a factor of 7 (i.e., from 105 epochs to 15 epochs). As shown in the third row of Table 1, this 15-epoch PGD-5 Adv Prop severely degrades the original Adv Prop s performance (i.e., 66.8% vs. 77.0% on Image Net), even making the resulted model attains much lower performance than the vanilla training baseline. Moreover, we verify that applying the cheapest PGD-1 training (i.e., FGSM + random initialization as in (Wong et al., 2020)) to Adv Prop still leads to inferior performance. These results demonstrate that the task of accelerating Adv Prop is non-trivial, therefore motivate us to explore more sophisticated solutions next.

3.2 LIGHTENING ADVPROP

We hereby carefully diagnose the design choices of Adv Prop, aiming to simplify/purge its costly training components. Note that in our ablations, we always keep the disentangled learning behavior with adversarial training samples unchanged (i.e., keep separate BN layers for adversarial samples and clean samples), as we assume this is the key for gaining robust features from adversarial examples.

3.2.1 UNPAIRING TRAINING SAMPLES IN ADVPROP

Let s consider the training cost of one epoch. We denote the cost of a single forward and backward pass for one image as 1 1, and the dataset size as N. Then the cost of vanilla training for one epoch is

cost(Vanilla) = N. (1)

1During a standard training step, we compute the gradient for all parameters used in the forward process; while for attacking the network, we only compute the gradient with respect to the input images (therefore less computations). Nonetheless, we ignore such differences for simpliﬁcation in cost calculation.

Published as a conference paper at ICLR 2022

Table 2: The performance of Adv Prop with different settings. +ADVPROP denotes the original Adv Prop. +1 ITER denotes the Adv Prop with PGD-1 attacker. +DECOUPLED denotes the decoupled training where only a small portion (e.g., 20% here) of training images are used for generating adversarial examples. The last column reports the corresponding training budget in one epoch.

+ADVPROP +1 ITER +DECOUPLED IMAGENET IMAGENET-C TRAINING BUDGET

76.2 58.5 N 77.0 51.9 7N 77.5 54.3 3N 76.6 56.8 1.2N

Similarly, the cost of Adv Prop using PGD-K attack (Madry et al., 2018) for one epoch is:

cost(Adv Prop) = N + K N + N = (K + 2) N, (2)

where the ﬁrst part (i.e., N) refers to the training cost of clean samples, the second part (i.e., K N) refers to the cost of generating adversarial examples, and the third part (i.e., N) refers to the training cost of adversarial examples. Note Adv Prop by default use K = 5 (Xie et al., 2020), therefore increasing the training cost by a factor of 7 compared to the vanilla training baseline. This high training cost makes further scaling Adv Prop to the large-computing settings (Xie et al., 2019; Mahajan et al., 2018; Dosovitskiy et al., 2020) challenging.

PGD-1 attack. Firstly, rather than using K = 5, we use K = 1 as the default setting to reduce the training cost from 7N to 3N. Note this change simplify the PGD attacker to the FGSM attacker (Goodfellow et al., 2015) with random noise initialization. As shown in Table 2, compared to the default Adv Prop, this simpliﬁcation increases the top-1 accuracy by 0.5% on Image Net, but at the cost of sacriﬁcing the robustness on Image Net-C (i.e., 2.4 higher m CE).

Decoupled training. Secondly, Adv Prop implicitly introduces a constraint that, for each clean image, we should generate a paired adversarial image for jointly training. Though such paired training behavior is popular and standard in adversarial training (Goodfellow et al., 2015), interestingly, we empirically ﬁnd this is not necessarily needed, i.e., models can still be beneﬁted from training with non-paired clean images and adversarial images. Moreover, if we choose to break such pairing behavior, the training cost will be reduced to:

cost(Fast Adv Prop) = pclean N + padv (K + 1) N (3)

where pclean is the percentages of training images used as clean examples, and padv is the percentages of training images used as adversarial examples. Note Adv Prop by default sets pclean = padv = 1. While for Fast Adv Prop, we exclusively set padv of the training samples for generating adversarial examples and keep the rest as clean examples. The training cost now is

cost(Fast Adv Prop) = (1 padv) N + padv (K + 1) N = (padv K + 1) N (4)

As shown in Table 2, by setting padv = 0.2 and apply PGD-1 attacker, our Fast Adv Prop not only largely reduces the training cost to 1.2N, but also beats the vanilla training baseline by 0.4% top-1 accuracy on Image Net and by 1.7 m CE on Image Net-C.

3.2.2 INCORPORATING FREE ADVERSARIAL TRAINING TECHNIQUES

Though decoupled training (using Equation 4) enables Adv Prop to use the same number of training images as the vanilla setting, the resulted strategy still incurs extra training cost. This is because additional forward-backward passes are exclusively reserved for generating adversarial examples.

Inspired by the recent works on accelerating adversarial training by recycling the gradient (Shafahi et al., 2019; Zhang et al., 2019), we aim to improve the gradient utilization in generating adversarial examples, i.e., such gradients will also be used for updating network parameters. In this way, we are able to let networks additionally train with the samples that are in the intermediate state of generating adversarial examples (e.g., clean image with random noise), and more importantly, for free . Note that, following Shafahi et al. (2019), in order to re-using gradient, we need to switch the attack mode from targeted attack to untargeted attack in Fast Adv Prop.

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Algorithm 1: Pseudo code of Fast Adv Prop for T epochs, given some radius ϵ, importance re-weight parameter β, learning rate γ, and ratio of adversarial examples padv. Data: A set of clean images with labels; Result: Network parameter θ for epoch = 1, . . . , T/(padv + 1) do

Sample a clean image mini-batch X with label Y Split X into X1, X2 with the ratio 1 padv and padv, respectively Generate the adversarial examples Xadv using X2 δ U( ϵ, ϵ) gδ δl(x + δ, y, θ) δ δ + ϵ sign(gδ) Xadv = X2 + clip(δ , ϵ, ϵ) Calculate gradients for X1, X2, Xadv, note gnoise θ and gδ could be compute simultaneously gclean θ Ex X1[ θl(x, y, θ)] gnoise θ Ex X2[ θl(x + δ, y, θ)] gadv θ Ex Xadv[ θl(x, y, θ)] Re-balance the gradients gθ gclean θ + β gnoise θ + β gadv θ Update θ using gradient descent θ θ γgθ end

As analyzed by Equation 4, the training cost of Fast Adv Prop now is (padv K + 1) N for one epoch. To let the training cost of Fast Adv Prop exactly match the training cost of the vanilla setting, we further calibrate the training by reducing the total number of epochs by a factor of (padv K + 1).

Following the design principles above, interestingly, we found naively recycling the gradients makes the training of Fast Adv Prop unstable. Next, as summarized in Algorithm 1, we stabilize the network training using the following techniques:

Bridging the gap between the running/batch statistics in BN. Adversarial attackers by default attack models using their testing mode, e.g., the running statistics is applied in BN. Nonetheless, we observe unstable training with Na N loss if we reuse the gradient and using BN s running statistics at the same time. We conjecture this comes from the inconsistent gradient paths we use the batch statistics for training with the clean examples and adversarial examples, but use the running statistics for generating adversarial examples. To remove that inconsistency, we now use the batch statistics for generating adversarial examples.

0 10 20 30 40 50 Epoch

Train Acc for adversarial examples(%)

w/o Shuffling BN w/ Shuffling BN

Figure 2: Illustration of the information leakage.

Shufﬂing BN for dealing with information leakage When attacking using batch statistics, we observe the training accuracy is unreasonably high, as shown in Figure 2. The network could classify images by cheating since we use the same batch for attacking and training, and the intra-batch information exchange introduced by BN leaks information. We use shufﬂing BN (He et al., 2020) to resolve this problem. Before feeding the adversarial images on each GPU into the network, we shufﬂe the generated adversarial examples across the multiple GPUs. This ensures the batch statistics for the images with random noise and the adversarial images come from different subsets, therefore preventing information leakage.

Published as a conference paper at ICLR 2022

Re-balancing training samples. By reusing the gradient, the images used for adversarial attack involve two forward and backward passes (i.e., one for generating adversarial examples, and one for training with adversarial examples), while the clean images involve only one forward and backward pass. With the intuition that each image within the batch should have the same importance, we propose to halve the importance of the images used for adversarial attack. In another perspective, the adversarial images and their intermediate products (i.e., the images with random noise) are two kinds of augmentations on the original images. Based on the argument in (Hoffer et al., 2020) that the overall importance of an image should be the same w/ or w/o the repeated augmentations, we therefore need to adjust the importance of the images with random noise and the importance of the adversarial examples accordingly (i.e., setting β = 0.5 in Algorithm 1).

Synchronizing parameter updating speed. The decoupled training strategy enables us to substantially reduce the training cost. Nonetheless, it causes problems when combining with the auxiliary BNs scheme. Speciﬁcally, the parameters of original BNs only receive the gradients from clean images, the parameters of auxiliary BNs only receive the gradients from images with random noise and adversarial examples, while the parameters of the shared layers receive gradients from all examples. The ratio between the gradient magnitude of shared layers/original BNs/auxiliary BNs is 1 : (1 padv) : padv. The inconsistent updating speed of network parameters harms the performance. To solve this problem, we re-scale the gradient to ensure the similar parameter updating speed.

4 EXPERIMENTS

4.1 EXPERIMENTS SETUP

Dataset. We evaluate model performance on Image Net classiﬁcation, and the robustness on different specialized benchmarks including Image Net-C, Image Net-R, and Stylized Image Net. Image Net dataset contains 1.2 million training images and 50000 images for validation of 1000 classes. Image Net-C measures the network robustness on 15 common corruption types, each with 5 severity. Image Net-R contains stylish renditions like cartoons, art, and sketches of 200 Image Net classes resulting in 30000 images. Stylized-Image Net dataset keeps the global shape information while removing the local texture information using the Ada IN style transfer (Huang & Belongie, 2017).

Implementation Details We use the renowned Res Net family (He et al., 2016) as our default architectures. We use a SGD optimizer with momentum 0.9 and train for 105 epochs. The learning rate starts from 0.1 and decays at 30, 60, 90, 100 epochs by 0.1. We use a batch size of 64 per GPU for vanilla training. For decoupled training setting, we use a batch size of 64/(1 padv) per GPU, keeping the same 64 batch size per GPU for the original BNs. padv is set to 0.2 if not speciﬁed.

For a strictly fair comparison, we scale the total epochs and decay epochs by the relative training cost to vanilla training (i.e., padv K + 1 in Fast Adv Prop, K + 2 in Adv Prop) in the same budget setting. To generate adversarial images, we using the PGD attacker with random initialization. We attack for one step (K = 1) and set the perturbation size to 1.0. As discussed in Section 3.2.2, to ensure the same importance of each example within a batch, we set β = 0.5 for halving the importance of the images with random noise and the adversarial images. Additionally, we re-scale the gradient to achieve the 1 : 1 : 1 ratio for ensuring similar updating speed of all parameters.

4.2 MAIN RESULTS

Table 1 compares our method with Adv Prop and the vanilla training using Res Net-50. Firstly, our re-implementation of Adv Prop achieves 77.0% top-1 accuracy on Image Net, 0.8% higher than the vanilla training baseline. We also evaluate robustness generalization on Image Net-C, Image Net R, Stylized-Image Net; Adv Prop also substantially outperforms the vanilla training baseline here. However, the comparison is unfair as Adv Prop using 7 training budget. In the fair comparison setting, the performance of 15-epoch Adv Prop (dividing the total epochs by 7) degrades signiﬁcantly, i.e., its Image Net accuracy is only 66.8%, which is 9.4% lower than the vanilla training baseline.

On the contrary, using exactly the same training budget as the vanilla setting, Fast Adv Prop achieves 76.5% accuracy on Image Net, which is 0.3% higher than the vanilla training baseline and signiﬁcantly higher than the 15-epoch Adv Prop. As shown in Table 1, our Fast Adv Prop also shows stronger robustness than both the vanilla training baseline and the 15-epochs Adv Prop.

Published as a conference paper at ICLR 2022

Table 3: The Image Net accuracy and robustness generalization of vanilla training and Fast Adv Prop.

IMAGENET IMAGENET-C IMAGENET-R S-IMAGENET

Res Net-50 76.2 58.5 36.3 7.8 + 15-epoch PGD-5 Adv Prop 66.8 66.2 31.7 8.6 + Fast Adv Prop 76.5 56.4 38.2 8.3

Res Net-101 77.8 54.7 40.1 9.1 + 15-epoch PGD-5 Adv Prop 68.6 61.8 34.0 12.3 + Fast Adv Prop 77.8 51.7 41.0 10.8

Res Net-152 78.3 52.3 40.5 10.5 + 15-epoch PGD-5 Adv Prop 69.0 59.6 36.2 13.2 + Fast Adv Prop 78.6 49.8 42.0 12.4

Additionally, our method scales better with larger networks. As shown in Table 3, Fast Adv Prop helps the large Res Net-152 achieve 78.6% top-1 accuracy on Image Net, 49.8 m CE on Image Net-C, 42.0% top-1 accuracy on Image Net-R and 12.4% top-1 accuracy on Stylized-Image Net, beating its vanilla counterpart by 0.3% on Image Net, 2.5% on Image Net-C, 1.5% on Image Net-R and 1.9% on Stylized-Image Net, respectively. This observation also holds when comparing Fast Adv Prop to the 15-epoch Adv Prop baseline (which has the same training cost as ours). Table 3 shows that, for all Res Net models, Fast Adv Prop attains much higher performance than the 15-epoch Adv Prop baseline on Image Net, Image Net-C and Image Net-R. The only exception is Stylized-Image Net, where 15-epoch Adv Prop always attains the best performance. We conjecture this is mainly due to a larger percentage of adversarial data is used during training, therefore letting the learned feature representation be biased towards shape cues (Geirhos et al., 2018; Zhang & Zhu, 2019).

4.3 ABLATION STUDY

The importance of decoupled training. In Table 4, we take a close look at the effect of padv. We can draw a clear conclusion that the larger the padv, the more inferior top-1 accuracy we achieved. Speciﬁcally, using 50% images as adversarial examples only gets 75.4% accuracy, which is 0.9% lower than the vanilla training. This comes from the fact that as padv increases, the training cost in one epoch increases (calculated using Equation 4), therefore the total training epoch needs to be reduced for keeping the training cost unchanged. In addition, reducing padv from 0.20 to 0.11 does not further decrease the model accuracy, suggesting its value is fairly robust in a certain range. If we further decrease padv to 0, then our method degenerates to the vanilla training baseline.

The decoupled training strategy enables us to train the networks with a mixture of a large portion of clean images and a small portion of adversarial examples, which helps the network go through the dataset with enough epochs. Based on Table 4, we choose padv = 0.2 as our default setup.

Table 4: Ablation study on the inﬂuence of the percentage of the adversarial images.

padv IMAGENET EPOCHS

0.00 76.2 105 0.11 76.5 94 0.20 76.5 87 0.33 76.0 79 0.50 75.4 70

The importance of example re-balancing and updating speed synchronization. In the default setting, the weight ratio between the clean/noise/adversarial examples is 1 : 1 : 1 without adjustment. With padv = 0.2, the ratio of updating speed between the shared/clean only/adversarial only parameters therefore is 1 : 0.8 : 0.2. We cannot observe any performance gain in this setting as shown in Table 5, i.e., its Image Net accuracy is 76.2%, almost the same as the vanilla training.

We ﬁnd it is important to simultaneously adopt those two strategies, which achieves 76.53% Image Net accuracy. Ignoring the re-balancing for the examples hurts the accuracy by 0.18%; this may because some examples now are more important than the others, therefore violating the assumption that the overall importance for each example should be the same (Hoffer et al., 2020). Removing the updating speed synchronization hurts the performance as well, leading to 76.27% Image Net accuracy, which is 0.26% lower than the setting with consistent parameter updating speed.

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Table 5: Ablation study of the effects on re-balancing samples and synchronizing updating speed.

SYNCHRONIZING THE UPDATE SPEED SAME IMPORTANCE IMAGENET

76.20 76.27 76.35 76.53

Information leakage problem. We ﬁnd that shufﬂing BN is important for gradient reusing. Without shufﬂing BN, the training accuracy on the adversarial images reaches 88.0%, even higher than the training accuracy on the clean images (73.3%). This observation is counter-intuitive, as the adversarial images are much more difﬁcult than the clean images. The shufﬂing BN technique resolves this problem effectively we observe a smooth and reasonable training curve in Figure 2. In addition, the validation accuracy boosts from 74.5% to 75.1%.

Combining with other data augmentations. Adv Prop could be viewed as a data augmentation method from the perspective of increasing the size and diversity of the dataset using adversarial examples. We next combine Fast Adv Prop with common data augmentation methods including Mixup (Zhang et al., 2018) and Cut Mix (Yun et al., 2019). Speciﬁcally, compared with the vanilla training baseline, Mixup and Cut Mix require extra training epochs to fully cope with their strong regularization. For Mixup, we train 180 epochs and decay the learning rate by 0.1 every 60 epochs. For Cut Mix, we train for 210 epochs and decay the learning rate at 75, 150 and 180, respectively. To properly integrate them with Fast Adv Prop, we apply the extra data augmentations on clean images only. Note that the training cost is the same w/ or w/o our method.

Fast Adv Prop achieves comparable performance on Image Net but much better robustness. As shown in Table 6, when combining with Cut Mix, our method beats the baseline by 2.1% on Image Net-C, 1.3% on Image Net-R, 2.5% on Stylized-Image Net. These results suggest Fast Adv Prop is compatible with existing data augmentations for furthering the network performance and robustness.

Table 6: Robustness when combining our Fast Adv Prop with existing data augmentation methods.

IMAGENET-C IMAGENET-R S-IMAGENET

Cut Mix 58.9 35.2 5.5 + Fast Adv Prop 55.0 36.5 7.0

Mix Up 53.4 41.0 10.0 + Fast Adv Prop 52.2 41.7 10.9

Object detection results. We implement Fast Adv Prop on object detection and evaluate it on COCO dataset (Lin et al., 2014). We adopt Retina Net (Lin et al., 2020) as the detection framework without freezing the BN s running statistics. We train 24 epochs for the baseline and 20 epochs for Fast Adv Prop. We benchmark both the standard performance on COCO and the robustness on COCO-C with 15 common corruption types (Michaelis et al., 2019). As shown in Table 7, compared to the baseline, our method achieves the similar performance on COCO detection, but much better robustness (i.e., +1.4%) in COCO-C.

Table 7: Object detection m AP(%) and robustness measurements on COCO and COCO-C.

COCO (m AP clean) COCO-C (m AP corr.)

Vanilla Training 35.8 17.6 + Fast-Adv Prop 35.8 19.0

5 CONCLUSION

Adv Prop is an effective method to get accurate and robust networks. However, it suffers from extremely high training costs. We propose the decoupled training where networks are expected to train with only a small portion of adversarial examples but a large portion of clean images, therefore reducing the training cost signiﬁcantly. In addition, we succeed in reusing the gradient when generating adversarial examples. Empirically, our Fast Adv Prop effectively and efﬁciently helps network gain better performance without incurring extra training cost. We believe our method will speed up the iteration of future works and accelerating the research on adversarial learning.

Published as a conference paper at ICLR 2022

ACKNOWLEDGEMENTS

This work was supported by ONR N00014-21-1-2812. Cihang Xie was supported by a gift grant from Open Philanthropy.

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A.1 DO WE NEED RANDOM INITIALIZATION IN PGD ATTACK?

Here we focus on ablating the effects of the random initialization in PGD attacker on Fast Adv Prop. Note that removing the random initialization simpliﬁes the PGD-1 attacker to the FGSM attacker. Though, as discussed in (Wong et al., 2020), the random initialization is the key step for enabling successful adversarial training, we observe Fast Adv Prop behaves robustly under such situation it achieves 76.46% top-1 Image Net accuracy (using FGSM), which closely matches the situation when random initialization is applied (i.e., 76.53% top-1 Image Net accuracy, using PGD-1).