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Register a new userFeature Purification: How Adversarial Training Performs Robust Deep Learning
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Zeyuan Allen-Zhu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Despite the empirical success of using Adversarial Training to defend deep learning models against adversarial perturbations, so far, it still remains rather unclear what the principles are behind the existence of adversarial perturbations, and what adversarial training does to the neural network to remove them. In this paper, we present a principle that we call Feature Purification, where we show one of the causes of the existence of adversarial examples is the accumulation of certain small dense mixtures in the hidden weights during the training process of a neural network; and more importantly, one of the goals of adversarial training is to remove such mixtures to purify hidden weights. We present both experiments on the CIFAR-10 dataset to illustrate this principle, and a theoretical result proving that for certain natural classification tasks, training a two-layer neural network with ReLU activation using randomly initialized gradient descent indeed satisfies this principle. Technically, we give, to the best of our knowledge, the first result proving that the following two can hold simultaneously for training a neural network with ReLU activation. (1) Training over the original data is indeed non-robust to small adversarial perturbations of some radius. (2) Adversarial training, even with an empirical perturbation algorithm such as FGM, can in fact be provably robust against ANY perturbations of the same radius. Finally, we also prove a complexity lower bound, showing that low complexity models such as linear classifiers, low-degree polynomials, or even the neural tangent kernel for this network, CANNOT defend against perturbations of this same radius, no matter what algorithms are used to train them.
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How does a 110-layer ResNet learn a high-complexity classifier using relatively few training examples and short training time? We present a theory towards explaining this in terms of Hierarchical Learning. We refer hierarchical learning as the learner learns to represent a complicated target function by decomposing it into a sequence of simpler functions to reduce sample and time complexity. We formally analyze how multi-layer neural networks can perform such hierarchical learning efficiently and automatically by applying SGD. On the conceptual side, we present, to the best of our knowledge, the FIRST theory result indicating how deep neural networks can still be sample and time efficient using SGD on certain hierarchical learning tasks, when NO KNOWN existing algorithm is efficient. We establish a new principle called backward feature correction, where training higher-level layers in the network can improve the features of lower-level ones. We believe this is the key to understand the deep learning process in multi-layer neural networks. On the technical side, we show for regression and even binary classification, for every input dimension $d>0$, there is a concept class of degree $omega(1)$ polynomials so that, using $omega(1)$-layer neural networks as learners, SGD can learn any function from this class in $mathsf{poly}(d)$ time and sample complexity to any $frac{1}{mathsf{poly}(d)}$ error, through learning to represent it as a composition of $omega(1)$ layers of quadratic functions. In contrast, we do not know any other simple algorithm (including layer-wise training or applying kernel method sequentially) that can learn this concept class in $mathsf{poly}(d)$ time even to any $d^{-0.01}$ error. As a side result, we prove $d^{omega(1)}$ lower bounds for several non-hierarchical learners, including any kernel methods, neural tangent or neural compositional kernels.
Adversarial training (AT) is among the most effective techniques to improve model robustness by augmenting training data with adversarial examples. However, most existing AT methods adopt a specific attack to craft adversarial examples, leading to the unreliable robustness against other unseen attacks. Besides, a single attack algorithm could be insufficient to explore the space of perturbations. In this paper, we introduce adversarial distributional training (ADT), a novel framework for learning robust models. ADT is formulated as a minimax optimization problem, where the inner maximization aims to learn an adversarial distribution to characterize the potential adversarial examples around a natural one under an entropic regularizer, and the outer minimization aims to train robust models by minimizing the expected loss over the worst-case adversarial distributions. Through a theoretical analysis, we develop a general algorithm for solving ADT, and present three approaches for parameterizing the adversarial distributions, ranging from the typical Gaussian distributions to the flexible implicit ones. Empirical results on several benchmarks validate the effectiveness of ADT compared with the state-of-the-art AT methods.
The common self-supervised pre-training practice requires collecting massive unlabeled data together and then trains a representation model, dubbed textbf{joint training}. However, in real-world scenarios where data are collected in a streaming fashion, the joint training scheme is usually storage-heavy and time-consuming. A more efficient alternative is to train a model continually with streaming data, dubbed textbf{sequential training}. Nevertheless, it is unclear how well sequential self-supervised pre-training performs with streaming data. In this paper, we conduct thorough experiments to investigate self-supervised pre-training with streaming data. Specifically, we evaluate the transfer performance of sequential self-supervised pre-training with four different data sequences on three different downstream tasks and make comparisons with joint self-supervised pre-training. Surprisingly, we find sequential self-supervised learning exhibits almost the same performance as the joint training when the distribution shifts within streaming data are mild. Even for data sequences with large distribution shifts, sequential self-supervised training with simple techniques, e.g., parameter regularization or data replay, still performs comparably to joint training. Based on our findings, we recommend using sequential self-supervised training as a textbf{more efficient yet performance-competitive} representation learning practice for real-world applications.
Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. There is an emerging literature on tackling this problem by minimizing the worst-case risk over an uncertainty set. However, existing methods mostly construct ambiguity sets by treating all variables equally regardless of the stability of their correlations with the target, resulting in the overwhelmingly-large uncertainty set and low confidence of the learner. In this paper, we propose a novel Stable Adversarial Learning (SAL) algorithm that leverages heterogeneous data sources to construct a more practical uncertainty set and conduct differentiated robustness optimization, where covariates are differentiated according to the stability of their correlations with the target. We theoretically show that our method is tractable for stochastic gradient-based optimization and provide the performance guarantees for our method. Empirical studies on both simulation and real datasets validate the effectiveness of our method in terms of uniformly good performance across unknown distributional shifts.
Deep Learning (DL) has shown potential in accelerating Magnetic Resonance Image acquisition and reconstruction. Nevertheless, there is a dearth of tailored methods to guarantee that the reconstruction of small features is achieved with high fidelity. In this work, we employ adversarial attacks to generate small synthetic perturbations, which are difficult to reconstruct for a trained DL reconstruction network. Then, we use robust training to increase the networks sensitivity to these small features and encourage their reconstruction. Next, we investigate the generalization of said approach to real world features. For this, a musculoskeletal radiologist annotated a set of cartilage and meniscal lesions from the knee Fast-MRI dataset, and a classification network was devised to assess the reconstruction of the features. Experimental results show that by introducing robust training to a reconstruction network, the rate of false negative features (4.8%) in image reconstruction can be reduced. These results are encouraging, and highlight the necessity for attention to this problem by the image reconstruction community, as a milestone for the introduction of DL reconstruction in clinical practice. To support further research, we make our annotations and code publicly available at https://github.com/fcaliva/fastMRI_BB_abnormalities_annotation.
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