Title: ADVERSARIALLY ROBUST FEW-SHOT LEARNING: A META-LEARNING APPROACH

Abstract: Previous work on adversarially robust neural networks for image classification requires large training sets and computationally expensive training procedures. On the other hand, few-shot learning methods are highly vulnerable to adversarial examples. The goal of our work is to produce networks which both perform well at few-shot classification tasks and are simultaneously robust to adversarial examples. We develop an algorithm for producing adversarially robust meta-learners, and we thoroughly investigate factors which contribute to adversarial vulnerability. Moreover, our method achieves far superior robust performance on few-shot image classification tasks, such as Mini-ImageNet and CIFAR-FS, than robust transfer learning.

1. INTRODUCTION:

For safety-critical applications like facial recognition, traffic sign detection, and copyright control, adversarial attacks pose an actionable threat (Zhao et al., 2018; Eykholt et al., 2017; Saadatpanah et al., 2019) . Conventional adversarial training and pre-processing defenses aim to produce networks that resist attack (Madry et al., 2017; Zhang et al., 2019; Samangouei et al., 2018) , but such defenses rely heavily on the availability of large training data sets. In applications that require few-shot learning, such as face recognition from few images, recognition of a video source from a single clip, or recognition of a new object from few example photos, the conventional robust training pipeline breaks down.

When data is scarce or new classes arise frequently, neural networks must adapt quickly (Duan et al., 2017; Kaiser et al., 2017; Pfister et al., 2014; Vartak et al., 2017) . In these situations, metalearning methods conduct few-shot learning by creating networks that learn quickly from little data and with computationally cheap fine-tuning. While state-of-the-art meta-learning methods perform well on benchmark few-shot classification tasks, these naturally trained neural networks are highly vulnerable to adversarial examples. In fact, even adversarially trained feature extractors fail to resist attacks in the few-shot setting (see Section 4.1).

We propose a new approach, called adversarial querying, in which the network is exposed to adversarial attacks during the query step of meta-learning. This algorithm-agnostic method produces a feature extractor that is robust, even without adversarial training during fine-tuning. In the few-shot setting, we show that adversarial querying outperforms other robustness techniques by a wide margin in terms of both clean accuracy and adversarial robustness (see Table 1 ). We solve the following minimax problem:

EQUATION

where S and (x, y) are data sampled from the training distribution, A is a fine-tuning algorithm for the model parameters, θ, and is a p-norm bound for the attacker. In Section 4, we further motivate adversarial querying and exhibit a wide range of experiments. To motivate the necessity for adversarial querying, we test methods, such as adversarial fine-tuning and pre-processing defenses, which if successful, would eliminate the need for expensive adversarial training routines. We find that these methods are far less effective than adversarial querying. Before the emergence of meta-learning, a number of approaches existed to cope with few-shot problems. One simple approach is transfer learning, in which pre-trained feature extractors are trained on large data sets and fine-tuned on new tasks (Bengio, 2012) . Metric learning methods avoid overfitting to the small number of training examples in new classes by instead performing classification using nearest-neighbors in feature space with a feature extractor that is trained on a large corpus of data and not re-trained when classes are added (Snell et al., 2017; Gidaris & Komodakis, 2018; Mensink et al., 2012) . Metric learning methods are computationally efficient when adding new classes at inference, since the feature extractor is not re-trained.

Meta-learning algorithms create a "base" model that quickly adapts to new tasks by fine-tuning. This model is created using a set of training tasks {T i } that can be sampled from a task distribution.

Each task comes with support data, T s i , and query data, T q i . Support data is used for fine-tuning, and query data is used to measure the performance of the resulting network. In practice, each task is taken to be a classification problem involving only a small subset of classes in a large many-class data set. The number of examples per class in the support set is called the shot, so that fine-tuning on five support examples per class is 5-shot learning.

An iteration of training begins by sampling tasks {T i } from the task distribution. In the "inner loop" of training, the base model is fine-tuned on the support data from the sampled tasks. In the "outer loop" of training, the fine-tuned network is used to make predictions on the query data, and the base model parameters are updated to improve the accuracy of the resulting fine-tuned model. The outer loop requires backpropagation through the fine-tuning steps. A formal treatment of the prototypical meta-learning routine can be found in Algorithm 1.

Algorithm 1: The meta-learning framework Require: Base model, F θ , fine-tuning algorithm, A, learning rate, γ, and distribution over tasks, p(T ). Initialize θ, the weights of F ; while not done do Sample batch of tasks, {T i } n i=1 , where T i ∼ p(T ) and T i = (T s i , T q i ). for i = 1, ..., n do Fine-tune model on T i (inner loop). New network parameters are written

θ i = A(θ, T s i ). Compute gradient g i = ∇ θ L(F θi , T q i ). Update base model parameters (outer loop): θ ← θ -γ n i g i

Note that the fine-tuned parameters, θ i = A(θ, T s i ), in Algorithm 1, are a function of the base model's parameters so that the gradient computation in the outer loop may backpropagate through A. For validation after training, the base model is fine-tuned on the support set of hold-out tasks, and accuracy on the query set is reported. In this work, we report performance on Omniglot, Mini-ImageNet, and CIFAR-FS (Lake et al., 2015; Vinyals et al., 2016; Bertinetto et al., 2018) .

We focus on four meta-learning algorithms: MAML, R2-D2, MetaOptNet, and ProtoNet (Finn et al., 2017; Bertinetto et al., 2018; Lee et al., 2019; Snell et al., 2017) . During fine-tuning, MAML uses SGD to update all parameters, minimizing cross-entropy loss. Since unrolling SGD steps into a deep computation graph is expensive, first-order variants have been developed to avoid computing second-order derivatives. We use the original MAML formulation. R2-D2 and MetaOptNet, on the other hand, only update the final linear layer during fine-tuning, leaving the "backbone network" that extracts these features frozen at test time. R2-D2 replaces SGD with a closed-form differentiable solver for regularized ridge regression, while MetaOptNet achieves its best performance when replacing SGD with a solver for SVM. Because the objective of these linear problems is convex, differentiable convex optimizers can be efficiently deployed to find optima, and differentiate these optima with respect to the backbone parameters at train time. ProtoNet takes an approach inspired by metric learning. It constructs class prototypes as centroids in feature space for each task. These centroids are then used to classify the query set in the outer loop of training. Because each class prototype is a simple geometric average of feature representations, it is easy to differentiate through the fine-tuning step.

2.2. ADVERSARIAL ATTACKS AND DEFENSES:

Following standard practices, we assess the robustness of models by attacking them with ∞bounded perturbations. We craft adversarial perturbations using the projected gradient descent attack (PGD) since it has proven to be one of the most effective algorithms both for attacking as well as for adversarial training (Madry et al., 2017) . A detailed description of the PGD attack can be found in Algorithm 2. We consider perturbations with ∞ bound 8/255 and a step size of 2/255 as described by Madry et al. (2017) .

Adversarial training is the industry standard for creating robust models that maintain good cleanlabel performance (Madry et al., 2017) . This method involves replacing clean examples with adversarial examples during the training routine. A simple way to harden models to attack is adversarial training, which solves the minimax problem

EQUATION

where L θ (x + δ, y) is the loss function of a network with parameters θ, x is an input image with label y, and δ is an adversarial perturbation. Adversarial training finds network parameters which maintain low loss (and correct class labels) even when adversarial perturbations are added.

Algorithm 2: PGD Attack Require: network, F θ , input data, (x, y), number of steps, n, step size, γ, and attack bound, . Initialize δ ∈ B (x) randomly;

for i = 1, ..., n do Compute g = sign (∇ δ L θ (x + δ, y)). Update δ = δ + γg. If δ p > , then project δ onto the surface of B (x). return perturbed image x + δ 2.3 ROBUST LEARNING WITH LESS DATA

Several authors have tried to learn robust models in the data scarce regime. The authors of Shafahi et al. (2019) study robustness properties of transfer learning. They find that retraining earlier layers of the network during fine-tuning impairs the robustness of the network, while only retraining later layers can largely preserve robustness. ADML is the first attempt at achieving robustness through meta-learning. ADML is a MAML variant, specifically designed for robustness, which employs adversarial training (Yin et al., 2018) . However, this method for robustness is only compatible with MAML, an outdated meta-learning algorithm. Moreover, ADML is computationally expensive, and the authors only test their method against a weak attacker. We implement ADML and test it against a strong attacker. We show that our method simultaneously achieves higher robustness and higher natural accuracy.

3. NATURALLY TRAINED META-LEARNING METHODS ARE NOT ROBUST:

In this section, we benchmark the robustness of existing meta-learning methods. Similarly to classically trained classifiers, we expect that few-shot learners are highly vulnerable to attack when adversarial defenses are not employed. We test prominent meta-learning algorithms against a 20-step PGD attack as in Madry et al. (2017) . Table 2 contains natural and robust accuracy on the Mini-ImageNet and CIFAR-FS 5-shot tasks (Vinyals et al., 2016; Bertinetto et al., 2018) . Experiments in the 1-shot setting can be found in Appendix A.1.

Model:

A We find that these algorithms are completely unable to resist the attack. Interestingly, MetaOptNet uses SVM for fine-tuning, which is endowed with a wide margins property. The failure of even SVM to express robustness during testing suggests that using robust fine-tuning methods (at test time) on naturally trained meta-learners is insufficient for robust performance. To further examine this, we consider MAML, which updates the entire network during fine-tuning. We use a naturally trained MAML model and perform adversarial training during fine-tuning (see Table 3 ). Adversarial training is performed with 7-PGD as in (Madry et al., 2017) While clean trained MAML models with adversarial fine-tuning are slightly more robust than their naturally fine-tuned counterparts, they achieve almost no robustness on Mini-ImageNet. Omniglot is an easier data set, and the performance of adversarially fine-tuned MAML on the 5-shot version is below a reasonable tolerance for robustness. We conclude from these experiments that naturally trained meta-learners are vulnerable to adversarial examples, and robustness techniques specifically for few-shot learning are required.

4. ADVERSARIAL QUERYING: A META-LEARNING ALGORITHM FOR ADVERSARIAL ROBUSTNESS:

We now introduce adversarial querying (AQ), an adversarial training algorithm for meta-learning. Let A(θ, S) denote a fine-tuning algorithm. Then, A is a map from support data set, S, and network parameters, θ, to parameters for the fine-tuned network. Then, we seek to solve the following minimax problem (Equation 1 revisited):

min θ E S,(x,y) max δ p < L(F A(θ,S) , x + δ, y) ,

where S and (x, y) are support and query data, respectively, sampled from the training distribution, and is a p-norm bound for the attacker. Thus, the objective is to find a central parameter vector which, when fine-tuned on support data, minimizes the expected query loss against an attacker. We approach this minimax problem with an alternating algorithm consisting of the following steps:

1. Sample support and query data 2. Fine-tune on the support data (inner loop)

3. Perturb query data to maximize loss 4. Minimize query loss, backpropagating through the fine-tuning algorithm (outer loop)

A formal treatment of this method is presented in Algorithm 3. We test adversarial querying across multiple data sets and meta-learning protocols. It is important to note that adversarial querying is algorithm-agnostic. We test this method on the ProtoNet, R2-D2, and MetaOptNet algorithms on CIFAR-FS and Mini-ImageNet (see Table 4 and Table 5 ).

Algorithm 3: Adversarial Querying Require: Base model, F θ , fine-tuning algorithm, A, learning rate, γ, and distribution over tasks, p(T ). Initialize θ, the weights of F ; while not done do Sample batch of tasks, {T i } n i=1 , where T i ∼ p(T ) and T i = (T s i , T q i ). for i = 1, ..., n do Fine-tune model on T i . New network parameters are written θ i = A(θ, T s i ). Construct adversarial query data, T q i , by maximizing L(F θi , T q i ) constrained to x q j -x q j p < for query examples, x q j , and their associated adversaries, x q j . Compute gradient In our tests, R2-D2 outperforms MetaOptNet in robust accuracy despite having a less powerful backbone architecture. In Section 4.5, we dissect the effects of backbone architecture and classification head on robustness of meta-learned models. In Section 4.7, we verify that adversarial querying generates networks robust to a wide array of strong attacks.

g i = ∇ θ L(F θi , T q i ). Update base model parameters: θ ← θ -γ n i g i Model A nat 1-Shot A adv 1-Shot A nat 5-

4.1. ADVERSARIAL QUERYING IS MORE ROBUST THAN TRANSFER LEARNING FROM ADVERSARIALLY TRAINED MODELS:

We observe above that few-shot learning methods with a non-robust feature extractor break under attack. But what if we use a robust feature extractor? In the following section, we consider both transfer learning and meta-learning with a robust feature extractor.

In order to compare robust transfer learning and meta-learning, we train the backbone networks from meta-learning algorithms on all training data simultaneously in the fashion of standard adversarial training using 7-PGD (not meta-learning). We then fine-tune using the head from a meta-learning algorithm on top of the transferred feature extractor. We compare the performance of these feature extractors to that of those trained using adversarially queried meta-learning algorithms with the same backbones and heads. This experiment provides a direct comparison of feature extractors produced by robust transfer learning and robust meta-learning (see In the adversarial querying procedure detailed in Algorithm 3, we only attack query data. Consider that the loss value on query data represents performance on testing data after fine-tuning on the support data. Thus, low loss on perturbed query data represents robust accuracy on testing data after fine-tuning. Simply put, minimizing loss on adversarial query data moves the parameter vector towards a network with high robust test accuracy. It follows that attacking only support data is not an option for achieving robust meta-learners. Attacking support data but not query data can be seen as maximizing clean test accuracy when fine-tuned in a robust manner, but since we want to maximize robust test accuracy, this would be inappropriate. One question remains: should we attack both query and support data?

One reason to perturb only query data is computational efficiency. The bulk of computation in adversarial training is spent computing adversarial attacks since perturbing each batch requires an iterative algorithm. Perturbing support data doubles the number of adversarial attacks computed during training. Thus, only attacking query data significantly accelerates training.

Another reason to avoid attacking support data is that some meta-learning fine-tuning algorithms based on metric learning, such as ProtoNet, do not involve loss minimization during fine-tuning, so it is not clear what loss the attacker would maximize during the inner loop. But if attacking support data during the inner loop of training were to significantly improve robust performance, we would like to know.

We now compare adversarial querying to a variant in which support data is also perturbed during training. We use MAML to conduct this comparison on the Omniglot and Mini-ImageNet data sets. Additional experiments on 1-shot tasks can be found in Appendix A.3.

In these experiments, we find that adversarially attacking the support data during the inner loop of meta-learning does not improve performance over adversarial querying. Furthermore, networks trained in this fashion require adversarial fine-tuning during test time or else they suffer a massive loss in robust test accuracy. Following these results and the significant reasons to avoid attacking support data, we subsequently only attack query data. Adversarial querying can also be used to construct meta-learning analogues for other variants of adversarial training. We explore this by using the TRADES loss function in the querying step of AQ (Zhang et al., 2019) . We refer to this method as meta-TRADES. While meta-TRADES can marginally outperform our initial adversarial querying method in robust accuracy with a careful hyperparameter choice, λ, we find that networks trained with meta-TRADES severely sacrifice natural accuracy (see Table 9 ). Additional experiments on 1-shot tasks can be found in Appendix A.4. High performing meta-learning models, like MetaOptNet and R2-D2, fix their feature extractor and only update their last linear layer during fine-tuning. In the setting of transfer learning, robustness is a feature of early convolutional layers, and re-training these early layers leads to a significant drop in robust test accuracy (Shafahi et al., 2019) . We verify that re-training only the last layer leads to improved natural and robust accuracy in adversarially queried meta-learners by training a MAML model but only updating the final fully-connected layer during fine-tuning including during the inner loop of meta-learning. We find that the AQ model trained by fine-tuning only the last layer during the inner loop decisively outperforms the standard AQ MAML algorithm in both natural and robust accuracy (see The naturally trained R2-D2 algorithm performs worse than MetaOptNet in natural accuracy, but previous research has found that performance discrepancies between meta-learning algorithms might be an artifact of different backbone networks (Chen et al., 2019) . We confirm that MetaOpt-Net with the R2-D2 backbone performs similarly to R2-D2 in the natural meta-learning setting (see Table 11 ). However, we find that the performance discrepancy in the adversarial setting is not explained by differences in backbone architecture. In our adversarial querying experiments, we see that MetaOptNet is less robust than R2-D2. This discrepancy remains when we train MetaOptNet with the R2-D2 backbone (see Table 12 ). We conclude that MetaOptNet's backbone is not responsible for its inferior robustness. These experiments suggest that ridge regression may be a more effective fine-tuning technique than SVM for robust performance. ProtoNet with R2-D2 backbone also performs worse than the other two adversarially queried models with the same backbone architecture. et al., 2019) . Feature denoising blocks pair classical denoising operations with learned 1 × 1 convolutions to reduce the feature noise in feature maps at various stages of a network, and thus reduce the success of adversarial attacks. Massive architectures with these blocks have achieved state-of-theart robustness against targeted adversarial attacks on ImageNet. However, when deployed on small networks for meta-learning, we find that denoising blocks do not improve robustness. We deploy denoising blocks identical to those in Xie et al. ( 2019) after various layers of the R2-D2 network.



The best results for the denoising experiments are achieved by adding a denoising block after the fourth layer in the R2-D2 embedding network (see Table 13 ).

after training the generator on all CIFAR-100 classes, we find that DefenseGAN with a naturally trained R2-D2 meta-learner performs significantly worse in both natural and robust accuracy than an adversarially queried meta-learner of the same architecture. Similarly, the superresolution defense achieves little robustness. The results of these experiments can be found in 

6. DISCUSSION & CONCLUSION:

Naturally trained networks for few-shot image classification are vulnerable to adversarial attacks, and existing robust transfer learning methods do not perform well on few-shot tasks. Even, when adversarially fine-tuned, naturally trained networks suffer from adversarial vulnerability. We thus identify the need for few-shot methods for adversarial robustness. In particular, we study robustness in the context of meta-learning. We develop an algorithm-agnostic method, called adversarial querying, for hardening meta-learning models. We find that meta-learning models are most robust when the feature extractor is fixed and only the last layer is retrained during fine-tuning. We further identify that choice of classification head significantly impacts robustness. We believe that this paper is a starting point for developing adversarially robust methods for few-shot applications.

:



Figures and Tables:

Adversarially trained transfer learning, R2-D2(Bertinetto et al., 2018),ADML (Yin et al.,  2018), and our adversarially queried (AQ) R2-D2 model on 5-shot Mini-ImageNet. Natural accuracy is denoted A nat , and robust accuracy, A adv , is computed with a 20-step PGD attack as inMadry et al. (2017) with = 8/255. A description of our training regime can be found in Appendix A.5.

Table content: <table><tr><td>Model</td><td>A nat</td><td>A adv</td></tr><tr><td colspan="3">AT transfer learning (R2-D2 backbone) 39.13% 25.33%</td></tr><tr><td>Naturally Trained R2-D2</td><td colspan="2">73.01% 0.00%</td></tr><tr><td>ADML</td><td colspan="2">47.75% 18.49%</td></tr><tr><td>AQ R2-D2 (ours)</td><td colspan="2">57.87% 31.52%</td></tr><tr><td>2 RELATED WORK</td><td/><td/></tr><tr><td>2.1 LEARNING WITH LESS DATA</td><td/><td/></tr></table>

nat MI A adv MI A nat FS A adv FS 5-shot MiniImageNet (MI) and CIFAR-FS (FS) results comparing naturally trained metalearners. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack.

Table content: <table><tr><td>ProtoNet</td><td>70.23%</td><td>0.00%</td><td>79.66%</td><td>0.00%</td></tr><tr><td>R2-D2</td><td>73.02%</td><td>0.00%</td><td>82.81%</td><td>0.00%</td></tr><tr><td colspan="2">MetaOptNet 78.12%</td><td>0.00%</td><td>84.11%</td><td>0.00%</td></tr></table>

MAML models on Mini-ImageNet and Omniglot. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack.

Table content: <table><tr><td>Model</td><td>A nat</td><td>A adv</td><td colspan="2">A nat(AT ) A adv(AT )</td></tr><tr><td colspan="3">1-shot Mini-ImageNet 45.04% 0.03%</td><td>33.18%</td><td>0.20%</td></tr><tr><td colspan="3">5-shot Mini-ImageNet 60.25% 0.03%</td><td>32.45%</td><td>1.55%</td></tr><tr><td>1-shot Omniglot</td><td colspan="3">91.50% 68.46% 91.60%</td><td>74.66%</td></tr><tr><td>5-shot Omniglot</td><td colspan="3">97.12% 82.28% 97.71%</td><td>87.94%</td></tr></table>

Comparison of adversarially queried (AQ) meta-learners on 1-shot and 5-shot CIFAR-FS. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack. Top 1-shot and 5-shot robust accuracy is bolded.

Table content: <table><tr><td>Shot A adv 5-Shot</td></tr></table>

Table6). Meta-learning exhibits far superior robustness than transfer learning for all algorithms we test. Additional experiments on CIFAR-FS and on 1-shot Mini-ImageNet can be found in Appendix A.2.ModelA nat Transfer A adv Transfer A nat Meta A adv Adversarially trained transfer learning and adversarially queried meta-learning on 5-shot Mini-ImageNet. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack. Top natural and robust accuracy for each architecture is bolded.

Table content: <table><tr><td>Meta</td></tr></table>

Performance on 5-shot Omniglot. Robust accuracy, A adv , is computed with respect to a 20-step PGD attack. A nat(AT ) and A adv(AT ) are natural and robust test accuracy with 7-PGD training during fine-tuning. Top robust accuracy with and without adversarial fine-tuning is bolded.

Table content: <table><tr><td/><td>A nat</td><td>A adv</td><td colspan="2">A nat(AT ) A adv(AT )</td></tr><tr><td>MAML (naturally trained)</td><td colspan="3">97.12% 82.28% 97.71%</td><td>87.94%</td></tr><tr><td>MAML adv. query</td><td colspan="3">97.27% 95.85% 97.51%</td><td>96.14%</td></tr><tr><td colspan="4">MAML adv. query and support 95.61% 77.73% 97.46%</td><td>95.65%</td></tr><tr><td>ADML</td><td colspan="3">97.31% 94.19% 97.56%</td><td>94.82%</td></tr><tr><td>Model</td><td>A nat</td><td>A adv</td><td colspan="2">A nat(AT ) A adv(AT )</td></tr><tr><td>MAML (naturally trained)</td><td colspan="2">60.25% 0.03%</td><td>32.45%</td><td>1.55%</td></tr><tr><td>MAML adv. query</td><td colspan="3">33.45% 23.07% 33.03%</td><td>23.29%</td></tr><tr><td colspan="4">MAML adv. query and support 29.98% 22.55% 30.44%</td><td>23.03%</td></tr><tr><td>ADML</td><td colspan="3">47.75% 18.49% 47.27%</td><td>20.23%</td></tr></table>

Performance on 5-shot Mini-ImageNet. Robust accuracy, A adv , is computed with respect to a 20-step PGD attack. A nat(AT ) and A adv(AT ) are natural and robust test accuracy with 7-PGD training during fine-tuning. Top robust accuracy with and without adversarial fine-tuning is bolded.

Table content: <table/>

A nat MI A adv MI A nat FS A 5-shot Mini-ImagNet (MI) and CIFAR-FS (FS) results comparing meta-TRADES to adversarial querying. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack. 4.4 FOR BETTER NATURAL AND ROBUST ACCURACY, ONLY FINE-TUNE THE LAST LAYER.

Table content: <table><tr><td>adv FS</td></tr></table>

Table 10). Adversarially queried MAML compared with a MAML variant where only the last layer is re-trained during fine-tuning on 5-shot Mini-ImageNet. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack. A nat(AT ) and A adv(AT ) are natural and robust test accuracy, respectively with 7-PGD training during fine-tuning. Layers are fine-tuned for 10 steps with a learning rate of 0.01.

Table content: <table><tr><td colspan="2">Layers updated A nat</td><td>A adv</td><td>A nat(AT ) A adv(AT )</td></tr><tr><td>All layers</td><td colspan="3">33.45% 23.07% 33.03%</td><td>23.29%</td></tr><tr><td>FC only</td><td colspan="3">40.06% 25.15% 39.94%</td><td>25.32%</td></tr><tr><td colspan="4">4.5 THE R2-D2 HEAD, NOT EMBEDDING, IS RESPONSIBLE FOR SUPERIOR ROBUST</td></tr><tr><td>PERFORMANCE.</td><td/><td/></tr></table>



Table content: <table><tr><td>Model</td><td>A nat</td><td>A adv</td></tr><tr><td>R2-D2</td><td colspan="2">82.81% 0.00%</td></tr><tr><td>R2-D2 AQ (ours)</td><td colspan="2">69.25% 44.80%</td></tr><tr><td>R2-D2 with SR defense</td><td colspan="2">35.15% 23.00%</td></tr><tr><td colspan="3">R2-D2 with DefenseGAN 35.15% 28.05%</td></tr></table>

5-shot CIFAR-FS results comparing the superresolution defense (SR defense) and De-fenseGAN. A nat and A adv are natural and robust test accuracy, respectively, where robust accuracy is computed with respect to a 20-step PGD attack. Both methods perform worse than their adversarially queried counterpart. Top robust accuracy is bolded.

Table content: <table/>

Peer review (iclr2020):
Summary: This paper presents a method that enhances the robustness of few-shot learning by introducing adversarial query data attack in the inner-task fine-tuning phase of a meta-learning algorithm (e.g. MAML). Extensive experimental results are reported to demonstrate the robustness of the proposed approach on benchmarks. Strong points: -S1. The problem of robust meta-learning is interesting. The proposed solution is well motivated and extensively evaluated with promise. -S2. The paper is clearly presented and easy to follow in general. Weak points: -W1. The degree of novelty in methodology is limited. In my opinion, the proposed method is an adaptation of PGD to optimization-based meta-learning. Although the idea is somewhat interesting and it comes up with a thorough numerical study, the value-added beyond a direct combination of traditional adversarial learning techniques and meta-learning seems not sufficient enough to represent a significant contribution to the addressed topic. -W2. The method is (over) extensively evaluated but short of justification in principle. The core idea of the proposal is introducing adversarial attack in the query data for task-level training. However, it is not clear why introducing adversarial attack on the query data should work better than on the support data or both query and support data? The principle/intuition behind the idea needs to be more clearly explained in theory and/or experiment. -W3. Numerical study is misleading in some places. The goal of this paper is to show the effectiveness of introducing the adversarial attack during query steps to enhance the robustness of few-shot learning. However, some reported experimental results are less relevant to this theme. For an instance, Table 6 shows that by replacing the loss, AQ-MAML can achieve better performance. These results seem not very interesting for the core method evaluation; they just demonstrate that changing the loss function can effectively improve the performance. The experiment reported in section 4.1 also gives the reader a similar impression that the results are weakly related to what the paper is really about. To make the contents in Section 4 more concentrated, I suggest moving some of the less relevant experiments presented in Section 4 to Section 3 as the motivation of adversarial meta-learning, or to the appendix. Overall, the main Section 4 should be more focused on the experimental/theoretical comparison against prior approaches, rather than exploring the effects of different model structures or loss functions. Minor issues: - M1. The concepts of ``AQ MAML’’ (at the end of Section 3.1) and ``robust meta-learning’’ (above Table 4) are not defined or referenced in the context. - M2. On the table citation in section 4.2, the Table 8 and Table 9 are wrongly cited as Table 4.2.