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Title: Extreme Values are Accurate and Robust in Deep Networks

Paper content:
Recent evidence shows that convolutional neural networks (CNNs) are biased towards textures so that CNNs are non-robust to adversarial perturbations over textures, while traditional robust visual features like SIFT (scale-invariant feature transforms) are designed to be robust across a substantial range of affine distortion, addition of noise, etc with the mimic of human perception nature.
This paper aims to leverage good properties of SIFT to renovate CNN architectures towards better accuracy and robustness.
We borrow the scale-space extreme value idea from SIFT, and propose EVPNet (extreme value preserving network) which contains three novel components to model the extreme values: (1) parametric differences of Gaussian (DoG) to extract extrema, (2) truncated ReLU to suppress non-stable extrema and (3) projected normalization layer (PNL) to mimic PCA-SIFT like feature normalization.
Experiments demonstrate that EVPNets can achieve similar or better accuracy than conventional CNNs, while achieving much better robustness on a set of adversarial attacks (FGSM,PGD,etc) even without adversarial training.
Convolutional neural networks (CNNs) evolve very fast ever since AlexNet (Krizhevsky & Hinton, 2012 ) makes a great breakthrough on ImageNet image classification challenge (Deng et al., 2009 ) in 2012.
Various network architectures have been proposed to further boost classification performance since then, including VGGNet (Simonyan & Zisserman, 2015) , GoogleNet , ResNet (He et al., 2016) , DenseNet (Huang et al., 2017) and SENet , etc.
Recently, people even introduce network architecture search to automatically learn better network architectures (Zoph & Le, 2017; Liu et al., 2018) .
However, state-of-the-art CNNs are challenged by their robustness, especially vulnerability to adversarial attacks based on small, human-imperceptible modifications of the input (Szegedy et al., 2014; Goodfellow et al., 2015) .
thoroughly study the robustness of 18 well-known ImageNet models using multiple metrics, and reveals that adversarial examples are widely existent.
Many methods are proposed to improve network robustness, which can be roughly categorized into three perspectives: (1) modifying input or intermediate features by transformation (Guo et al., 2018) , denoising Jia et al., 2019) , generative models (Samangouei et al., 2018; Song et al., 2018) ; (2) modifying training by changing loss functions (Wong & Kolter, 2018; Elsayed et al., 2018; , network distillation (Papernot et al., 2016) , or adversarial training (Goodfellow et al., 2015; Tramer et al., 2018 ) (3) designing robust network architectures Svoboda et al., 2019; Nayebi & Ganguli, 2017) and possible combinations of these basic categories.
For more details of current status, please refer to a recent survey (Akhtar & Mian, 2018) .
Although it is known that adversarial examples are widely existent , some fundamental questions are still far from being well studied like what causes it, and how the factor impacts the performance, etc.
One of the interesting findings in is that model architecture is a more critical factor to network robustness than model size (e.g. number of layers).
Some recent works start to explore much deeper nature.
For instance, both (Geirhos et al., 2019; Baker et al., 2018) show that CNNs are trained to be strongly biased towards textures so that CNNs do not distinguish objects contours from other local or even noise edges, thus perform poorly on shape dominating object instances.
On the contrary, there are no statistical difference for human behaviors on both texture rich objects and global shape dominating objects in psychophysical trials.
Ilyas et al. (2019) further analyze and show that deep convolutional features can be categorized into robust and non-robust features, while non-robust features may even account for good generalization.
However, non-robust features are not expected to have good model interpretability.
It is thus an interesting topic to disentangle robust and non-robust features with certain kinds of human priors in the network designing or training process.
In fact, human priors have been extensively used in handcraft designed robust visual features like SIFT (Lowe, 2004) .
SIFT detects scale-space (Lindeberg, 1994) extrema from input images, and selects stable extrema to build robust descriptors with refined location and orientation, which achieves great success for many matching and recognition based vision tasks before CNN being reborn in 2012 (Krizhevsky & Hinton, 2012) .
The scale-space extrema are efficiently implemented by using a difference-of-Gaussian (DoG) function to search over all scales and image locations, while the DoG operator is believed to biologically mimic the neural processing in the retina of the eye (Young, 1987) .
Unfortunately, there is (at least explicitly) no such scale-space extrema operations in all existing CNNs.
Our motivation is to study the possibility of leveraging good properties of SIFT to renovate CNN networks architectures towards better accuracy and robustness.
In this paper, we borrow the scale-space extrema idea from SIFT, and propose extreme value preserving networks (EVPNet) to separate robust features from non-robust ones, with three novel architecture components to model the extreme values: (1) parametric DoG (pDoG) to extract extreme values in scale-space for deep networks, (2) truncated ReLU (tReLU) to suppress noise or non-stable extrema and (3) projected normalization layer (PNL) to mimic PCA-SIFT (Ke et al., 2004) like feature normalization.
pDoG and tReLU are combined into one block named EVPConv, which could be used to replace all k × k (k > 1) conv-layers in existing CNNs.
We conduct comprehensive experiments and ablation studies to verify the effectiveness of each component and the proposed EVPNet.
Figure 1 illustrates a comparison of responses for standard convolution + ReLU and EVPConv in ResNet-50 trained on ImageNet, and shows that the proposed EVPConv produces less noises and more responses around object boundary than standard convolution + ReLU, which demonstrates the capability of EVPConv to separate robust features from non-robust ones.
Our major contribution are:
• To the best of our knowledge, we are the first to explicitly separate robust features from non-robust ones in deep neural networks from an architecture design perspective.
• We propose three novel network architecture components to model extreme values in deep networks, including parametric DoG, truncated ReLU, and projected normalization layer, and verify their effectiveness through comprehensive ablation studies.
• We propose extreme value preserving networks (EVPNets) to combine those three novel components, which are demonstrated to be not only more accurate, but also more robust to a set of adversarial attacks (FGSM, PGD, etc) even for clean model without adversarial training.
This paper mimics good properties of robust visual feature SIFT to renovate CNN architectures with some novel architecture components, and proposes the extreme value preserving networks (EVPNet).
Experiments demonstrate that EVPNets can achieve similar or better accuracy over conventional CNNs, while achieving much better robustness to a set of adversarial attacks (FGSM, PGD, etc) even for clean model without any other tricks like adversarial training.
top-1 accuracy to near zero, while the EVP-ResNet variants keep 6∼10% top-1 accuracy.
The gap in FGSM attacks is even larger.
This improvement is remarkable considering that it is by clean model without adversarial training.
For the MobileNet case, we also observe notable accuracy and robustness improvement.
Please refer to Table 4 for more details.
In summary, our solid results and attempts may inspire future new ways for robust network architecture design or even automatic search.

assistant: text: This paper aims to leverage good properties of robust visual features like SIFT to renovate CNN architectures towards better accuracy and robustness.