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Title: Fortified Networks: Improving the Robustness of Deep Networks by Modeling the Manifold of Hidden Representations

Paper content:
Deep networks have achieved impressive results across a variety of important tasks.
However, a known weakness is a failure to perform well when evaluated on data which differ from the training distribution, even if these differences are very small, as is the case with adversarial examples.
We propose \emph{Fortified Networks}, a simple transformation of existing networks, which “fortifies” the hidden layers in a deep network by identifying when the hidden states are off of the data manifold, and maps these hidden states back to parts of the data manifold where the network performs well.
Our principal contribution is to show that fortifying these hidden states improves the robustness of deep networks and our experiments (i) demonstrate improved robustness to standard adversarial attacks in both black-box and white-box threat models; (ii) suggest that our improvements are not primarily due to the problem of deceptively good results due to degraded quality in the gradient signal (the gradient masking problem) and (iii) show the advantage of doing this fortification in the hidden layers instead of the input space.
We demonstrate improvements in adversarial robustness on three datasets (MNIST, Fashion MNIST, CIFAR10), across several attack parameters, both white-box and black-box settings, and the most widely studied attacks (FGSM, PGD, Carlini-Wagner).
We show that these improvements are achieved across a wide variety of hyperparameters.
The success of deep neural networks across a variety of tasks has also driven applications in domains where reliability and security are critical, including self-driving cars BID6 , health care, face recognition BID25 , and the detection of malware BID17 .
Security concerns arise when an agent using such a system could benefit from the system performing poorly.
Reliability concerns come about when the distribution of input data seen during training can differ from the distribution on which the model is evaluated.Adversarial examples BID11 result from attacks on neural network models, applying small perturbations to the inputs that change the predicted class.
Such perturbations can be small enough to be unnoticeable to the naked eye.
It has been shown that gradient-based methods allow one to find modifications of the input that often change the predicted class BID26 BID11 .
More recent work demonstrated that it is possible to create modifications such that even when captured through a camera, they change the predicted class with high probability BID7 .Some
of the most prominent classes of defenses against adversarial examples include feature squeezing BID29 , adapted encoding of the input (Jacob BID14 , and distillation-related approaches BID20 . Existing
defenses provide some robustness but most are not easy to deploy. In addition
, many have been shown to be providing the illusion of defense by lowering the quality of the gradient signal, without actually providing improved robustness BID1 . Still others
require training a generative model directly in the visible space, which is still difficult today even on relatively simple datasets.Our work differs from the approaches using generative models in the input space in that we instead employ this robustification on the distribution of the learned hidden representations, which makes the The plot on the right shows direct experimental evidence for this hypothesis: we added fortified layers with different capacities to MLPs trained on MNIST, and display the value of the total reconstruction errors for adversarial examples divided by the total reconstruction errors for clean examples. A high value
indicates success at detecting adversarial examples. Our results
support the central motivation for fortified networks: that off-manifold points can much more easily be detected in the hidden space (as seen by the relatively constant ratio for the autoencoder in hidden space) and are much harder to detect in the input space (as seen by this ratio rapidly falling to zero as the input-space autoencoder's capacity is reduced).identification
of off-manifold examples easier. We do this by
training denoising autoencoders on top of the hidden layers of the original network. We call this
method Fortified Networks.We demonstrate that Fortified Networks (i) can be generically
added into an existing network; (ii) robustify the network
against adversarial attacks and (iii) provide a reliable signal
of the existence of input data that do not lie on the manifold on which it the network trained.In the sections that follow, we discuss the intuition behind the fortification of hidden layers and lay out some of the method's salient properties. Furthermore, we evaluate our proposed
approach on MNIST, Fashion-MNIST, CIFAR10 datasets against whitebox and blackbox attacks.
Protecting against adversarial examples could be of paramount importance in mission-critical applications.
We have presented Fortified Networks, a simple method for the robustification of existing deep neural networks.
Our method is practical, as fortifying an existing network entails introducing DAEs between the hidden layers of the network, which can be automated.
Furthermore, the DAE reconstruction error at test time is a reliable signal of distribution shift, which can result in examples unlike those encountered during training.
High error can signify either adversarial attacks or significant domain shift; both are important cases for the analyst or system to be aware of.
Moreover, fortified networks are efficient: since not every layer needs to be fortified to achieve improvements, fortified networks are an efficient way to improve robustness to adversarial examples.
For example, we have shown improvements on ResNets where only two fortified layers are added, and thus the change to the computational cost is very slight.
Finally, fortified networks are effective, as they improve results on adversarial defense on three datasets (MNIST, Fashion MNIST, and CIFAR10), across a variety of attack parameters (including the most widely used ε values), across three widely studied attacks (FGSM, PGD, Carlini-Wagner L2), and in both the black-box and white-box settings.A EXPERIMENTAL SETUP All attacks used in this work were carried out using the Cleverhans BID21 ) library.A.1
WHITE-BOX ATTACKS Our convolutional models (Conv, in the tables) have 2 strided convolutional layers with 64 and 128 filters followed by an unstrided conv layer with 128 filters.
We use ReLU activations between layers then followed by a single fully connected layer.
The convolutional and fully-connected DAEs have a single bottleneck layer with leaky ReLU activations with some ablations presented in the table below.With white-box PGD attacks, we used only convolutional DAEs at the first and last conv layers with Gaussian noise of σ = 0.01 whereas with FGSM attacks we used a DAE only at the last fully connected layer.
The weight on the reconstruction error λ rec and adversarial cost λ adv were set to 0.01 in all white-box attack experiments.
We used the Adam optimizer with a learning rate of 0.001 to train all models.The table below lists results a few ablations with different activation functions in the autoencoder Our black-box results are based on a fully-connected substitute model (input-200-200-output) , which was subsequently used to attack a fortified convolutional network.
The CNN was trained for 50 epochs using adversarial training, and the predictions of the trained CNN were used to train the substitute model.
6 iterations of Jacobian data augmentation were run during training of the substitute, with λ = 0.1.
The test set data holdout for the adversary was fixed to 150 examples.
The learning rate was set to 0.003 and the Adam optimizer was used to train both models.
TAB0 : More attack steps to uncover gradient masking effects.

assistant: text: Better adversarial training by learning to map back to the data manifold with autoencoders in the hidden states.