1-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustness

The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on enhancing certifiable robustness guarantees by crafting 1-Lipschitz neural networks that leverage Lipschitz bounded dense and convolutional layers. Although different methods have been proposed in the literature to achieve this goal, understanding the performance of such methods is not straightforward, since different metrics can be relevant (e.g., training time, memory usage, accuracy, certifiable robustness) for different applications. For this reason, this work provides a thorough theoretical and empirical comparison between methods by evaluating them in terms of memory usage, speed, and certifiable robust accuracy. The paper also provides some guidelines and recommendations to support the user in selecting the methods that work best depending on the available resources. We provide code at https://github.com/berndprach/1LipschitzLayersCompared.

Robust-by-Design Classification via Unitary-Gradient Neural Networks

The use of neural networks in safety-critical systems requires safe and robust models, due to the existence of adversarial attacks. Knowing the minimal adversarial perturbation of any input x, or, equivalently, knowing the distance of x from the classification boundary, allows evaluating the classification robustness, providing certifiable predictions. Unfortunately, state-of-the-art techniques for computing such a distance are computationally expensive and hence not suited for online applications. This work proposes a novel family of classifiers, namely Signed Distance Classifiers (SDCs), that, from a theoretical perspective, directly output the exact distance of x from the classification boundary, rather than a probability score (e.g., SoftMax). SDCs represent a family of robust-by-design classifiers. To practically address the theoretical requirements of a SDC, a novel network architecture named Unitary-Gradient Neural Network is presented. Experimental results show that the proposed architecture approximates a signed distance classifier, hence allowing an online certifiable classification of x at the cost of a single inference.

Defending From Physically-Realizable Adversarial Attacks Through Internal Over-Activation Analysis

This work presents Z-Mask, a robust and effective strategy to improve the adversarial robustness of convolutional networks against physically-realizable adversarial attacks. The presented defense relies on specific Z-score analysis performed on the internal network features to detect and mask the pixels corresponding to adversarial objects in the input image. To this end, spatially contiguous activations are examined in shallow and deep layers to suggest potential adversarial regions. Such proposals are then aggregated through a multi-thresholding mechanism. The effectiveness of Z-Mask is evaluated with an extensive set of experiments carried out on models for both semantic segmentation and object detection. The evaluation is performed with both digital patches added to the input images and printed patches positioned in the real world. The obtained results confirm that Z-Mask outperforms the state-of-the-art methods in terms of both detection accuracy and overall performance of the networks under attack. Additional experiments showed that Z-Mask is also robust against possible defense-aware attacks.

On the Minimal Adversarial Perturbation for Deep Neural Networks with Provable Estimation Error

Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has opened an interesting research line on provable techniques capable of quantifying the robustness of a given input. In this regard, the Euclidean distance of the input from the classification boundary denotes a well-proved robustness assessment as the minimal affordable adversarial perturbation. Unfortunately, computing such a distance is highly complex due the non-convex nature of NNs. Despite several methods have been proposed to address this issue, to the best of our knowledge, no provable results have been presented to estimate and bound the error committed. This paper addresses this issue by proposing two lightweight strategies to find the minimal adversarial perturbation. Differently from the state-of-the-art, the proposed approach allows formulating an error estimation theory of the approximate distance with respect to the theoretical one. Finally, a substantial set of experiments is reported to evaluate the performance of the algorithms and support the theoretical findings. The obtained results show that the proposed strategies approximate the theoretical distance for samples close to the classification boundary, leading to provable robustness guarantees against any adversarial attacks.