An official website of the United States government
Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent adversarial training methods have been effective at improving robustness to perturbed inputs (robust accuracy), often this benefit is accompanied by a decrease in accuracy on benign inputs (standard accuracy), leading to a tradeoff between often competing objectives. Complicating matters further, recent empirical evidence suggest that a variety of other factors (size and quality of training data, model size, etc.) affect this tradeoff in somewhat surprising ways. In this paper we provide a precise and comprehensive understanding of the role of adversarial training in the context of linear regression with Gaussian features. In particular, we characterize the fundamental tradeoff between the accuracies achievable by any algorithm regardless of computational power or size of the training data. Furthermore, we precisely characterize the standard/robust accuracy and the corresponding tradeoff achieved by a contemporary mini-max adversarial training approach in a high-dimensional regime where the number of data points and the parameters of the model grow in proportion to each other. Our theory for adversarial training algorithms also facilitates the rigorous study of how a variety of factors (size and quality of training data, model overparametrization etc.) affect the tradeoff between these two competing accuracies.
more »
« less
Precise Statistical Analysis of Classification Accuracies for Adversarial Training
Despite the wide empirical success of modern machine learning algorithms and models in a multitude of applications, they are known to be highly susceptible to seemingly small indiscernible perturbations to the input data known as \emph{adversarial attacks}. A variety of recent adversarial training procedures have been proposed to remedy this issue. Despite the success of such procedures at increasing accuracy on adversarially perturbed inputs or \emph{robust accuracy}, these techniques often reduce accuracy on natural unperturbed inputs or \emph{standard accuracy}. Complicating matters further, the effect and trend of adversarial training procedures on standard and robust accuracy is rather counter intuitive and radically dependent on a variety of factors including the perceived form of the perturbation during training, size/quality of data, model overparameterization, etc. In this paper we focus on binary classification problems where the data is generated according to the mixture of two Gaussians with general anisotropic covariance matrices and derive a precise characterization of the standard and robust accuracy for a class of minimax adversarially trained models. We consider a general norm-based adversarial model, where the adversary can add perturbations of bounded ellp norm to each input data, for an arbitrary p greater than one. Our comprehensive analysis allows us to theoretically explain several intriguing empirical phenomena and provide a precise understanding of the role of different problem parameters on standard and robust accuracies.
more »
« less
- PAR ID:
- 10339511
- Date Published:
- Journal Name:
- The annals of statistics
- ISSN:
- 2168-8966
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Low-dimensional structure of data can solve the adversarial robustness-accuracy conflict for machine learning systems. Modern machine learning systems have demonstrated breakthrough performance in a multitude of applications. However, they are known to be highly vulnerable to small perturbations to the input data, known as adversarial attacks. There are many well-documented examples of such behavior, for example small perturbations of an image, which is imperceptible to a human, can significantly degrade performance of modern classifiers. Adversarial training has been put forward as a way to improve robustness of learning algorithms to adversarial attacks. However, this benefit often comes at the cost of decreasing accuracy on natural unperturbed inputs, pointing to a potential conflict between adversarial robustness and standard accuracy. In “Adversarial robustness for latent models: Revisiting the robust-standard accuracies tradeoff,” Adel Javanmard and Mohammad Mehrabi develop a theory to show that when the data enjoys low-dimensional structure, then it is possible to train models that are nearly optimal with respect to both, the standard and robust accuracies.more » « less
-
Despite excellent performance on many tasks, NLP systems are easily fooled by small adversarial perturbations of inputs. Existing procedures to defend against such perturbations are either (i) heuristic in nature and susceptible to stronger attacks or (ii) provide guaranteed robustness to worst-case attacks, but are incompatible with state-of-the-art models like BERT. In this work, we introduce robust encodings (RobEn): a simple framework that confers guaranteed robustness, without making compromises on model architecture. The core component of RobEn is an encoding function, which maps sentences to a smaller, discrete space of encodings. Systems using these encodings as a bottleneck confer guaranteed robustness with standard training, and the same encodings can be used across multiple tasks. We identify two desiderata to construct robust encoding functions: perturbations of a sentence should map to a small set of encodings (stability), and models using encodings should still perform well (fidelity). We instantiate RobEn to defend against a large family of adversarial typos. Across six tasks from GLUE, our instantiation of RobEn paired with BERT achieves an average robust accuracy of 71.3% against all adversarial typos in the family considered, while previous work using a typo-corrector achieves only 35.3% accuracy against a simple greedy attack.more » « less
-
Despite excellent performance on many tasks, NLP systems are easily fooled by small adversarial perturbations of inputs. Existing procedures to defend against such perturbations are either (i) heuristic in nature and susceptible to stronger attacks or (ii) provide guaranteed robustness to worst-case attacks, but are incompatible with state-of-the-art models like BERT. In this work, we introduce robust encodings (RobEn): a simple framework that confers guaranteed robustness, without making compromises on model architecture. The core component of RobEn is an encoding function, which maps sentences to a smaller, discrete space of encodings. Systems using these encodings as a bottleneck confer guaranteed robustness with standard training, and the same encodings can be used across multiple tasks. We identify two desiderata to construct robust encoding functions: perturbations of a sentence should map to a small set of encodings (stability), and models using encodings should still perform well (fidelity). We instantiate RobEn to defend against a large family of adversarial typos. Across six tasks from GLUE, our instantiation of RobEn paired with BERT achieves an average robust accuracy of 71.3% against all adversarial typos in the family considered, while previous work using a typo-corrector achieves only 35.3% accuracy against a simple greedy attack.more » « less
-
Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small ℓ∞-noise). For other perturbations, these defenses offer no guarantees and, at times, even increase the model’s vulnerability. Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple perturbation types. We prove that a trade-off in robustness to different types of ℓp-bounded and spatial perturbations must exist in a natural and simple statistical setting. We corroborate our formal analysis by demonstrating similar robustness trade-offs on MNIST and CIFAR10. We propose new multi-perturbation adversarial training schemes, as well as an efficient attack for the ℓ1-norm, and use these to show that models trained against multiple attacks fail to achieve robustness competitive with that of models trained on each attack individually. In particular, we find that adversarial training with first-order ℓ∞, ℓ1 and ℓ2 attacks on MNIST achieves merely 50% robust accuracy, partly because of gradient-masking. Finally, we propose affine attacks that linearly interpolate between perturbation types and further degrade the accuracy of adversarially trained models.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
