Adversarial Pruning: A Survey and Benchmark of Pruning Methods for Adversarial Robustness

Recent work has proposed neural network pruning techniques to reduce the size of a network while preserving robustness against adversarial examples, i.e., well-crafted inputs inducing a misclassification. These methods, which we refer to as adversarial pruning methods, involve complex and articulated designs, making it difficult to analyze the differences and establish a fair and accurate comparison. In this work, we overcome these issues by surveying current adversarial pruning methods and proposing a novel taxonomy to categorize them based on two main dimensions: the pipeline, defining when to prune; and the specifics, defining how to prune. We then highlight the limitations of current empirical analyses and propose a novel, fair evaluation benchmark to address them. We finally conduct an empirical re-evaluation of current adversarial pruning methods and discuss the results, highlighting the shared traits of top-performing adversarial pruning methods, as well as common issues. We welcome contributions in our publicly-available benchmark at https://github.com/pralab/AdversarialPruningBenchmark

HO-FMN: Hyperparameter Optimization for Fast Minimum-Norm Attacks

Gradient-based attacks are a primary tool to evaluate robustness of machine-learning models. However, many attacks tend to provide overly-optimistic evaluations as they use fixed loss functions, optimizers, step-size schedulers, and default hyperparameters. In this work, we tackle these limitations by proposing a parametric variation of the well-known fast minimum-norm attack algorithm, whose loss, optimizer, step-size scheduler, and hyperparameters can be dynamically adjusted. We re-evaluate 12 robust models, showing that our attack finds smaller adversarial perturbations without requiring any additional tuning. This also enables reporting adversarial robustness as a function of the perturbation budget, providing a more complete evaluation than that offered by fixed-budget attacks, while remaining efficient. We release our open-source code at https://github.com/pralab/HO-FMN.

Over-parameterization and Adversarial Robustness in Neural Networks: An Overview and Empirical Analysis

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks' vulnerability to adversarial example -- input samples crafted ad-hoc to induce a desired misclassification. Relevant literature has claimed contradictory remarks in support of and against the robustness of over-parameterized networks. These contradictory findings might be due to the failure of the attack employed to evaluate the networks' robustness. Previous research has demonstrated that depending on the considered model, the algorithm employed to generate adversarial examples may not function properly, leading to overestimating the model's robustness. In this work, we empirically study the robustness of over-parameterized networks against adversarial examples. However, unlike the previous works, we also evaluate the considered attack's reliability to support the results' veracity. Our results show that over-parameterized networks are robust against adversarial attacks as opposed to their under-parameterized counterparts.

AttackBench: Evaluating Gradient-based Attacks for Adversarial Examples

Adversarial examples are typically optimized with gradient-based attacks. While novel attacks are continuously proposed, each is shown to outperform its predecessors using different experimental setups, hyperparameter settings, and number of forward and backward calls to the target models. This provides overly-optimistic and even biased evaluations that may unfairly favor one particular attack over the others. In this work, we aim to overcome these limitations by proposing AttackBench, i.e., the first evaluation framework that enables a fair comparison among different attacks. To this end, we first propose a categorization of gradient-based attacks, identifying their main components and differences. We then introduce our framework, which evaluates their effectiveness and efficiency. We measure these characteristics by (i) defining an optimality metric that quantifies how close an attack is to the optimal solution, and (ii) limiting the number of forward and backward queries to the model, such that all attacks are compared within a given maximum query budget. Our extensive experimental analysis compares more than 100 attack implementations with a total of over 800 different configurations against CIFAR-10 and ImageNet models, highlighting that only very few attacks outperform all the competing approaches. Within this analysis, we shed light on several implementation issues that prevent many attacks from finding better solutions or running at all. We release AttackBench as a publicly available benchmark, aiming to continuously update it to include and evaluate novel gradient-based attacks for optimizing adversarial examples.

Robustness-Congruent Adversarial Training for Secure Machine Learning Model Updates

Machine-learning models demand for periodic updates to improve their average accuracy, exploiting novel architectures and additional data. However, a newly-updated model may commit mistakes that the previous model did not make. Such misclassifications are referred to as negative flips, and experienced by users as a regression of performance. In this work, we show that this problem also affects robustness to adversarial examples, thereby hindering the development of secure model update practices. In particular, when updating a model to improve its adversarial robustness, some previously-ineffective adversarial examples may become misclassified, causing a regression in the perceived security of the system. We propose a novel technique, named robustness-congruent adversarial training, to address this issue. It amounts to fine-tuning a model with adversarial training, while constraining it to retain higher robustness on the adversarial examples that were correctly classified before the update. We show that our algorithm and, more generally, learning with non-regression constraints, provides a theoretically-grounded framework to train consistent estimators. Our experiments on robust models for computer vision confirm that (i) both accuracy and robustness, even if improved after model update, can be affected by negative flips, and (ii) our robustness-congruent adversarial training can mitigate the problem, outperforming competing baseline methods.

$σ$-zero: Gradient-based Optimization of $\ell_0$-norm Adversarial Examples

Evaluating the adversarial robustness of deep networks to gradient-based attacks is challenging. While most attacks consider $\ell_2$- and $\ell_\infty$-norm constraints to craft input perturbations, only a few investigate sparse $\ell_1$- and $\ell_0$-norm attacks. In particular, $\ell_0$-norm attacks remain the least studied due to the inherent complexity of optimizing over a non-convex and non-differentiable constraint. However, evaluating adversarial robustness under these attacks could reveal weaknesses otherwise left untested with more conventional $\ell_2$- and $\ell_\infty$-norm attacks. In this work, we propose a novel $\ell_0$-norm attack, called $\sigma$-zero, which leverages an ad hoc differentiable approximation of the $\ell_0$ norm to facilitate gradient-based optimization, and an adaptive projection operator to dynamically adjust the trade-off between loss minimization and perturbation sparsity. Extensive evaluations using MNIST, CIFAR10, and ImageNet datasets, involving robust and non-robust models, show that $\sigma$-zero finds minimum $\ell_0$-norm adversarial examples without requiring any time-consuming hyperparameter tuning, and that it outperforms all competing sparse attacks in terms of success rate, perturbation size, and scalability.

Raze to the Ground: Query-Efficient Adversarial HTML Attacks on Machine-Learning Phishing Webpage Detectors

Machine-learning phishing webpage detectors (ML-PWD) have been shown to suffer from adversarial manipulations of the HTML code of the input webpage. Nevertheless, the attacks recently proposed have demonstrated limited effectiveness due to their lack of optimizing the usage of the adopted manipulations, and they focus solely on specific elements of the HTML code. In this work, we overcome these limitations by first designing a novel set of fine-grained manipulations which allow to modify the HTML code of the input phishing webpage without compromising its maliciousness and visual appearance, i.e., the manipulations are functionality- and rendering-preserving by design. We then select which manipulations should be applied to bypass the target detector by a query-efficient black-box optimization algorithm. Our experiments show that our attacks are able to raze to the ground the performance of current state-of-the-art ML-PWD using just 30 queries, thus overcoming the weaker attacks developed in previous work, and enabling a much fairer robustness evaluation of ML-PWD.

Samples on Thin Ice: Re-Evaluating Adversarial Pruning of Neural Networks

Neural network pruning has shown to be an effective technique for reducing the network size, trading desirable properties like generalization and robustness to adversarial attacks for higher sparsity. Recent work has claimed that adversarial pruning methods can produce sparse networks while also preserving robustness to adversarial examples. In this work, we first re-evaluate three state-of-the-art adversarial pruning methods, showing that their robustness was indeed overestimated. We then compare pruned and dense versions of the same models, discovering that samples on thin ice, i.e., closer to the unpruned model's decision boundary, are typically misclassified after pruning. We conclude by discussing how this intuition may lead to designing more effective adversarial pruning methods in future work.

Improving Fast Minimum-Norm Attacks with Hyperparameter Optimization

Evaluating the adversarial robustness of machine learning models using gradient-based attacks is challenging. In this work, we show that hyperparameter optimization can improve fast minimum-norm attacks by automating the selection of the loss function, the optimizer and the step-size scheduler, along with the corresponding hyperparameters. Our extensive evaluation involving several robust models demonstrates the improved efficacy of fast minimum-norm attacks when hyper-up with hyperparameter optimization. We release our open-source code at https://github.com/pralab/HO-FMN.

Minimizing Energy Consumption of Deep Learning Models by Energy-Aware Training

Deep learning models undergo a significant increase in the number of parameters they possess, leading to the execution of a larger number of operations during inference. This expansion significantly contributes to higher energy consumption and prediction latency. In this work, we propose EAT, a gradient-based algorithm that aims to reduce energy consumption during model training. To this end, we leverage a differentiable approximation of the $\ell_0$ norm, and use it as a sparse penalty over the training loss. Through our experimental analysis conducted on three datasets and two deep neural networks, we demonstrate that our energy-aware training algorithm EAT is able to train networks with a better trade-off between classification performance and energy efficiency.