Adversarially robust knowledge distillation aims to compress a large-scale robust teacher model into a lightweight student counterpart while preserving adversarial robustness and natural performance. Previous methods primarily focused on aligning knowledge (e.g., predictions) between teacher and student models to transfer robustness. However, potentially incorrect predictions from the teacher can misguide the student, negatively impacting robustness transfer. To circumvent this, we propose a novel adversarially robust knowledge distillation scheme that promotes alignment towards more benign predictions rather than incorrect ones by refining inputs into so-called "inverse adversarial examples" via simply reversing the sign of adversarial perturbation. Through a comprehensive investigation of the properties of inverse adversaries, we provide new theoretical insights showing how mimicking the behavior of the teacher model on inverse adversaries facilitates reliable robustness transfer built upon the implicit connection between robustness and the input gradient information. We thus design a gradient matching mechanism between teacher and student models utilizing inverse adversaries to facilitate robust knowledge alignment. Furthermore, inspired by our analysis of the correlation between robustness and adversarial transferability, we propose a weight-space disruption strategy that jointly interacts with both teacher and student models to find a shared direction for better robustness transfer. Empirical evaluations across various datasets demonstrate that our method achieves state-of-the-art robustness and natural performance. Notably, on ImageNet, our approach outperforms prior methods by approximately 3.8% in both clean and robust accuracy. Moreover, we show that incorporating auxiliary generated data into distillation further boosts robustness. Our method can also be generalized to multimodal architectures.

Predicting human trajectories is essential for the safe operation of autonomous vehicles, yet current data-driven models often lack robustness in case of noisy inputs such as adversarial examples or imperfect observations. Although some trajectory prediction methods have been developed to provide empirical robustness, these methods are heuristic and do not offer guaranteed robustness. In this work, we propose a certification approach tailored for trajectory prediction that provides guaranteed robustness. To this end, we address the unique challenges associated with trajectory prediction, such as unbounded outputs and multi-modality. To mitigate the inherent performance drop through certification, we propose a diffusion-based trajectory denoiser and integrate it into our method. Moreover, we introduce new certified performance metrics to reliably measure the trajectory prediction performance. Through comprehensive experiments, we demonstrate the accuracy and robustness of the certified predictors and highlight their advantages over the non-certified ones. The code is available online: https://s-attack.github.io/

In this paper, we propose the *geometric invariance hypothesis (GIH)*, which argues that the input space curvature of a neural network remains invariant under transformation in certain architecture-dependent directions during training. We investigate a simple, non-linear binary classification problem residing on a plane in a high dimensional space and observe that—unlike MLPs—ResNets fail to generalize depending on the orientation of the plane. Motivated by this example, we define a neural network's **average geometry** and **average geometry evolution** as compact *architecture-dependent* summaries of the model's input-output geometry and its evolution during training. By investigating the average geometry evolution at initialization, we discover that the geometry of a neural network evolves according to the data covariance projected onto its average geometry. This means that the geometry only changes in a subset of the input space when the average geometry is low-rank, such as in ResNets. This causes an architecture-dependent invariance property in the input space curvature, which we dub GIH. Finally, we present extensive experimental results to observe the consequences of GIH and how it relates to generalization in neural networks.

Diffusion models have transformed image synthesis through iterative denoising, by defining trajectories from noise to coherent data. While their capabilities are widely celebrated, a critical challenge remains unaddressed: ensuring responsible use by verifying whether an image originates from a model's training set, its novel generations or external sources. We introduce a framework that analyzes diffusion trajectories for this purpose. Specifically, we demonstrate that temporal dynamics across the entire trajectory allow for more robust classification and challenge the widely-adopted "Goldilocks zone" conjecture, which posits that membership inference is effective only within narrow denoising stages. More fundamentally, we expose critical flaws in current membership inference practices by showing that representative methods fail under distribution shifts or when model-generated data is present. For model attribution, we demonstrate a first white-box approach directly applicable to diffusion. Ultimately, we propose the unification of data provenance into a single, cohesive framework tailored to modern generative systems.

Visual encoders have become fundamental components in modern computer vision pipelines. However, ensuring robustness against adversarial perturbations remains a critical challenge. Recent efforts have explored both supervised and unsupervised adversarial fine-tuning strategies. We identify two key limitations in these approaches: (i) they often suffer from instability, especially during the early stages of fine-tuning, resulting in suboptimal convergence and degraded performance on clean data, and (ii) they exhibit a suboptimal trade-off between robustness and clean data accuracy, hindering the simultaneous optimization of both objectives. To overcome these challenges, we propose **L**agrangian-**O**ptimized **R**obust **E**mbeddings (LORE), a novel unsupervised adversarial fine-tuning framework. LORE utilizes constrained optimization, which offers a principled approach to balancing competing goals, such as improving robustness while preserving nominal performance. By enforcing embedding-space proximity constraints, LORE effectively maintains clean data performance throughout adversarial fine-tuning. Extensive experiments show that LORE stabilizes training and significantly improves zero-shot adversarial robustness with minimal degradation in clean data accuracy. Furthermore, we demonstrate the effectiveness of the adversarially fine-tuned image encoder in out-of-distribution generalization and enhancing the interpretability of image embeddings. The code is available on [GitHub](https://github.com/Theborna/LORE-Lagrangian-Optimized-Robust-Embeddings).

Deep neural networks have been known to be vulnerable to adversarial examples, which are inputs that are modified slightly to fool the network into making incorrect predictions. This has led to a significant amount of research on evaluating the robustness of these networks against such perturbations. One particularly important robustness metric is the robustness to minimal $\ell_{2}$ adversarial perturbations. However, existing methods for evaluating this robustness metric are either computationally expensive or not very accurate. In this paper, we introduce a new family of adversarial attacks that strike a balance between effectiveness and computational efficiency. Our proposed attacks are generalizations of the well-known DeepFool (DF) attack, while they remain simple to understand and implement. We demonstrate that our attacks outperform existing methods in terms of both effectiveness and computational efficiency. Our proposed attacks are also suitable for evaluating the robustness of large models and can be used to perform adversarial training (AT) to achieve state-of-the-art robustness to minimal $\ell_{2}$ adversarial perturbations.

Although current deep learning techniques have yielded superior performance on various computer vision tasks, yet they are still vulnerable to adversarial examples. Adversarial training and its variants have been shown to be the most effective approaches to defend against adversarial examples. A particular class of these methods regularize the difference between output probabilities for an adversarial and its corresponding natural example. However, it may have a negative impact if a natural example is misclassified. To circumvent this issue, we propose a novel adversarial training scheme that encourages the model to produce similar output probabilities for an adversarial example and its “inverse adversarial” counterpart. Particularly, the counterpart is generated by maximizing the likelihood in the neighborhood of the natural example. Extensive experiments on various vision datasets and architectures demonstrate that our training method achieves state-of-the-art robustness as well as natural accuracy among robust models. Furthermore, using a universal version of inverse adversarial examples, we improve the performance of single-step adversarial training techniques at a low computational cost.

The transferability of adversarial examples is a key issue in the security of deep neural networks. The possibility of an adversarial example crafted for a source model fooling another targeted model makes the threat of adversarial attacks more realistic. Measuring transferability is a crucial problem, but the Attack Success Rate alone does not provide a sound evaluation. This paper proposes a new methodology for evaluating transferability by putting distortion in a central position. This new tool shows that transferable attacks may perform far worse than a black box attack if the attacker randomly picks the source model. To address this issue, we propose a new selection mechanism, called FiT, which aims at choosing the best source model with only a few preliminary queries to the target. Our experimental results show that FiT is highly effective at selecting the best source model for multiple scenarios such as single-model attacks, ensemble-model attacks and multiple attacks.

We investigate methods for manipulating classifier explanations while keeping the predictions unchanged. Our focus is on using a sparse attack, which seeks to alter only a minimal number of input features. We present an efficient and novel algorithm for computing sparse perturbations that alter the explanations but keep the predictions unaffected. We demonstrate that our algorithm, compared to PGD attacks with $\ell_{0}$ constraint, generates sparser perturbations while resulting in greater discrepancies between original and manipulated explanations. Moreover, we demonstrate that it is also possible to conceal the attribution of the k most significant features in the original explanation by perturbing fewer than k features of the input data. We present results for both image and tabular datasets, and emphasize the significance of sparse perturbation-based attacks for trustworthy model building in high-stakes applications. Our research reveals important vulnerabilities in explanation methods that should be taken into account when developing reliable explanation methods. Code can be found at https://github.com/ahmadajal/sparse_expl_attacks

Explanation methods highlight the importance of the input features in taking a predictive decision, and represent a solution to increase the transparency and trustworthiness in machine learning and deep neural networks (DNNs). However, explanation methods can be easily manipulated generating misleading explanations particularly under visually imperceptible adversarial perturbations. Recent work has identified the decision surface geometry of DNNs as the main cause of this phenomenon. To make explanation methods more robust against adversarially crafted perturbations, recent research has promoted several smoothing approaches. These approaches smooth either the explanation map or the decision surface.

Vehicle trajectory prediction is nowadays a fundamental pillar of self-driving cars. Both the industry and research communities have acknowledged the need for such a pillar by providing public benchmarks. While state-of-the-art methods are impressive, i.e., they have no off-road prediction, their generalization to cities outside of the benchmark remains unexplored. In this work, we show that those methods do not generalize to new scenes. We present a method that automatically generates realistic scenes causing state-of-the-art models to go off-road. We frame the problem through the lens of adversarial scene generation. The method is a simple yet effective generative model based on atomic scene generation functions along with physical constraints. Our experiments show that more than 60% of existing scenes from the current benchmarks can be modified in a way to make prediction methods fail (i.e., predicting off-road). We further show that the generated scenes (i) are realistic since they do exist in the real world, and (ii) can be used to make existing models more robust, yielding 30-40% reductions in the off-road rate. The code is available online: https://s-attack.github.io/.

Previous work has cast doubt on the general framework of uniform convergence and its ability to explain generalization in neural networks. By considering a specific dataset, it was observed that a neural network completely misclassifies a projection of the training data (adversarial set), rendering any existing generalization bound based on uniform convergence vacuous. We provide an extensive theoretical investigation of the previously studied data setting through the lens of infinitely-wide models. We prove that the Neural Tangent Kernel (NTK) also suffers from the same phenomenon and we uncover its origin. We highlight the important role of the output bias and show theoretically as well as empirically how a sensible choice completely mitigates the problem. We identify sharp phase transitions in the accuracy on the adversarial set and study its dependency on the training sample size. As a result, we are able to characterize critical sample sizes beyond which the effect disappears. Moreover, we study decompositions of a neural network into a clean and noisy part by considering its canonical decomposition into its different eigenfunctions and show empirically that for too small bias the adversarial phenomenon still persists.

For certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization, but for the networks used in practice, the empirical NTK only provides a rough first-order approximation. Still, a growing body of work keeps leveraging this approximation to successfully analyze important deep learning phenomena and design algorithms for new applications. In our work, we provide strong empirical evidence to determine the practical validity of such approximation by conducting a systematic comparison of the behavior of different neural networks and their linear approximations on different tasks. We show that the linear approximations can indeed rank the learning complexity of certain tasks for neural networks, even when they achieve very different performances. However, in contrast to what was previously reported, we discover that neural networks do not always perform better than their kernel approximations, and reveal that the performance gap heavily depends on architecture, dataset size and training task. We discover that networks overfit to these tasks mostly due to the evolution of their kernel during training, thus, revealing a new type of implicit bias.

Driven by massive amounts of data and important advances in computational resources, new deep learning systems have achieved outstanding results in a large spectrum of applications. Nevertheless, our current theoretical understanding of the mathematical foundations of deep learning lags far behind its empirical success. However, the field of adversarial robustness has recently become one of the main sources of explanations of our deep models. In this article, we provide an in-depth review of the field and give a self-contained introduction to its main notions. However, in contrast to the mainstream pessimistic perspective of adversarial robustness, we focus on the main positive aspects that it entails. We highlight the intuitive connection between adversarial examples and the geometry of deep neural networks and, eventually, explore how the geometric study of adversarial examples can serve as a powerful tool to understand deep learning. Furthermore, we demonstrate the broad applicability of adversarial robustness, providing an overview of the main emerging applications of adversarial robustness beyond security. The goal of this article is to provide readers with a set of new perspectives to understand deep learning and supply them with intuitive tools and insights on how to use adversarial robustness to improve it.

Adversarial examples are known as carefully perturbed images fooling image classifiers. We propose a geometric framework to generate adversarial examples in one of the most challenging black-box settings where the adversary can only generate a small number of queries, each of them returning the top-1 label of the classifier. Our framework is based on the observation that the decision boundary of deep networks usually has a small mean curvature in the vicinity of data samples. We propose an effective iterative algorithm to generate query-efficient black-box perturbations with small p norms which is confirmed via experimental evaluations on state-of-the-art natural image classifiers. Moreover, for p=2, we theoretically show that our algorithm actually converges to the minimal perturbation when the curvature of the decision boundary is bounded. We also obtain the optimal distribution of the queries over the iterations of the algorithm. Finally, experimental results confirm that our principled black-box attack algorithm performs better than state-of-the-art algorithms as it generates smaller perturbations with a reduced number of queries.

Important insights towards the explainability of neural networks reside in the characteristics of their decision boundaries. In this work, we borrow tools from the field of adversarial robustness, and propose a new perspective that relates dataset features to the distance of samples to the decision boundary. This enables us to carefully tweak the position of the training samples and measure the induced changes on the boundaries of CNNs trained on large-scale vision datasets. We use this framework to reveal some intriguing properties of CNNs. Specifically, we rigorously confirm that neural networks exhibit a high invariance to non-discriminative features, and show that the decision boundaries of a DNN can only exist as long as the classifier is trained with some features that hold them together. Finally, we show that the construction of the decision boundary is extremely sensitive to small perturbations of the training samples, and that changes in certain directions can lead to sudden invariances in the orthogonal ones. This is precisely the mechanism that adversarial training uses to achieve robustness.

In this work, we analyze the role of the network architecture in shaping the inductive bias of deep classifiers. To that end, we start by focusing on a very simple problem, i.e., classifying a class of linearly separable distributions, and show that, depending on the direction of the discriminative feature of the distribution, many state-of-the-art deep convolutional neural networks (CNNs) have a surprisingly hard time solving this simple task. We then define as neural anisotropy directions (NADs) the vectors that encapsulate the directional inductive bias of an architecture. These vectors, which are specific for each architecture and hence act as a signature, encode the preference of a network to separate the input data based on some particular features. We provide an efficient method to identify NADs for several CNN architectures and thus reveal their directional inductive biases. Furthermore, we show that, for the CIFAR-10 dataset, NADs characterize the features used by CNNs to discriminate between different classes.

Deep Neural Networks have achieved extraordinary results on image classification tasks, but have been shown to be vulnerable to attacks with carefully crafted perturbations of the input data. Although most attacks usually change values of many image's pixels, it has been shown that deep networks are also vulnerable to sparse alterations of the input. However, no computationally efficient method has been proposed to compute sparse perturbations. In this paper, we exploit the low mean curvature of the decision boundary, and propose SparseFool, a geometry inspired sparse attack that controls the sparsity of the perturbations. Extensive evaluations show that our approach computes sparse perturbations very fast, and scales efficiently to high dimensional data. We further analyze the transferability and the visual effects of the perturbations, and show the existence of shared semantic information across the images and the networks. Finally, we show that adversarial training can only slightly improve the robustness against sparse additive perturbations computed with SparseFool.

State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the geometry of the classification landscape and decision boundaries. We show in particular that adversarial training leads to a significant decrease in the curvature of the loss surface with respect to inputs, leading to a drastically more "linear" behaviour of the network. Using a locally quadratic approximation, we provide theoretical evidence on the existence of a strong relation between large robustness and small curvature. To further show the importance of reduced curvature for improving the robustness, we propose a new regularizer that directly minimizes curvature of the loss surface, and leads to adversarial robustness that is on par with adversarial training. Besides being a more efficient and principled alternative to adversarial training, the proposed regularizer confirms our claims on the importance of exhibiting quasi-linear behavior in the vicinity of data points in order to achieve robustness.

Despite the vast success neural networks have achieved in different application domains, they have been proven to be vulnerable to adversarial perturbations (small changes in the input), which lead them to produce the wrong output. In this paper, we propose a novel method, based on gradient projection, for generating universal adversarial perturbations for text; namely sequence of words that can be added to any input in order to fool the classifier with high probability. We observed that text classifiers are quite vulnerable to such perturbations: inserting even a single adversarial word to the beginning of every input sequence can drop the accuracy from 93% to 50%.

Deep neural networks have recently achieved tremendous success in image classification. Recent studies have however shown that they are easily misled into incorrect classification decisions by adversarial examples. Adversaries can even craft attacks by querying the model in black-box settings, where no information about the model is released except its final decision. Such decision-based attacks usually require lots of queries, while real-world image recognition systems might actually restrict the number of queries. In this paper, we propose qFool, a novel decision-based attack algorithm that can generate adversarial examples using a small number of queries. The qFool method can drastically reduce the number of queries compared to previous decision-based attacks while reaching the same quality of adversarial examples. We also enhance our method by constraining adversarial perturbations in low-frequency subspace, which can make qFool even more computationally efficient. Altogether, we manage to fool commercial image recognition systems with a small number of queries, which demonstrates the actual effectiveness of our new algorithm in practice.

In recent years Deep Neural Networks (DNNs) have been rapidly developed in various applications, together with increasingly complex architectures. The performance gain of these DNNs generally comes with high computational costs and large memory consumption, which may not be affordable for mobile platforms. Deep model quantization can be used for reducing the computation and memory costs of DNNs, and deploying complex DNNs on mobile equipment. In this work, we propose an optimization framework for deep model quantization. First, we propose a measurement to estimate the effect of parameter quantization errors in individual layers on the overall model prediction accuracy. Then, we propose an optimization process based on this measurement for finding optimal quantization bit-width for each layer. This is the first work that theoretically analyse the relationship between parameter quantization errors of individual layers and model accuracy. Our new quantization algorithm outperforms previous quantization optimization methods, and achieves 20-40% higher compression rate compared to equal bit-width quantization at the same model prediction accuracy.

The goal of this paper is to analyze the geometric properties of deep neural network image classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical study, we show that state-of-the-art deep nets learn connected classification regions, and that the decision boundary in the vicinity of datapoints is flat along most directions. We further draw an essential connection between two seemingly unrelated properties of deep networks: their sensitivity to additive perturbations of the inputs, and the curvature of their decision boundary. The directions where the decision boundary is curved in fact characterize the directions to which the classifier is the most vulnerable. We finally leverage a fundamental asymmetry in the curvature of the decision boundary of deep nets, and propose a method to discriminate between original images, and images perturbed with small adversarial examples. We show the effectiveness of this purely geometric approach for detecting small adversarial perturbations in images, and for recovering the labels of perturbed images.

Deep convolutional neural networks have been shown to be vulnerable to arbitrary geometric transformations. However, there is no systematic method to measure the invariance properties of deep networks to such transformations. We propose ManiFool as a simple yet scalable algorithm to measure the invariance of deep networks. In particular, our algorithm measures the robustness of deep networks to geometric transformations in a worst-case regime as they can be problematic for sensitive applications. Our extensive experimental results show that ManiFool can be used to measure the invariance of fairly complex networks on high dimensional datasets and these values can be used for analyzing the reasons for it. Furthermore, we build on ManiFool to propose a new adversarial training scheme and we show its effectiveness on improving the invariance properties of deep neural networks.

Given a state-of-the-art deep neural network classifier, we show the existence of a universal (image-agnostic) and very small perturbation vector that causes natural images to be misclassified with high probability. We propose a systematic algorithm for computing universal perturbations, and show that state-of-the-art deep neural networks are highly vulnerable to such perturbations, albeit being quasi-imperceptible to the human eye. We further empirically analyze these universal perturbations and show, in particular, that they generalize very well across neural networks. The surprising existence of universal perturbations reveals important geometric correlations among the high-dimensional decision boundary of classifiers. It further outlines potential security breaches with the existence of single directions in the input space that adversaries can possibly exploit to break a classifier on most natural images.

State-of-the-art deep neural networks have achieved impressive results on many image classification tasks. However, these same architectures have been shown to be unstable to small, well sought, perturbations of the images. Despite the importance of this phenomenon, no effective methods have been proposed to accurately compute the robustness of state-of-the-art deep classifiers to such perturbations on large-scale datasets. In this paper, we fill this gap and propose the DeepFool algorithm to efficiently compute perturbations that fool deep networks, and thus reliably quantify the robustness of these classifiers. Extensive experimental results show that our approach outperforms recent methods in the task of computing adversarial perturbations and making classifiers more robust.

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a semi-random noise regime that generalizes both the random and worst-case noise regimes. We propose the first quantitative analysis of the robustness of nonlinear classifiers in this general noise regime. We establish precise theoretical bounds on the robustness of classifiers in this general regime, which depend on the curvature of the classifier's decision boundary. Our bounds confirm and quantify the empirical observations that classifiers satisfying curvature constraints are robust to random noise. Moreover, we quantify the robustness of classifiers in terms of the subspace dimension in the semi-random noise regime, and show that our bounds remarkably interpolate between the worst-case and random noise regimes. We perform experiments and show that the derived bounds provide very accurate estimates when applied to various state-of-the-art deep neural networks and datasets. This result suggests bounds on the curvature of the classifiers' decision boundaries that we support experimentally, and more generally offers important insights onto the geometry of high dimensional classification problems.