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Rethinking Adversarial Training with Neural Tangent Kernel (2312.02236v1)

Published 4 Dec 2023 in cs.LG and cs.AI

Abstract: Adversarial training (AT) is an important and attractive topic in deep learning security, exhibiting mysteries and odd properties. Recent studies of neural network training dynamics based on Neural Tangent Kernel (NTK) make it possible to reacquaint AT and deeply analyze its properties. In this paper, we perform an in-depth investigation of AT process and properties with NTK, such as NTK evolution. We uncover three new findings that are missed in previous works. First, we disclose the impact of data normalization on AT and the importance of unbiased estimators in batch normalization layers. Second, we experimentally explore the kernel dynamics and propose more time-saving AT methods. Third, we study the spectrum feature inside the kernel to address the catastrophic overfitting problem. To the best of our knowledge, it is the first work leveraging the observations of kernel dynamics to improve existing AT methods.

Summary

  • The paper demonstrates that adversarial training exhibits distinct NTK evolution phases which significantly affect model robustness and accuracy.
  • The methodology uncovers the impact of data normalization and spectral kernel characteristics on catastrophic overfitting during training.
  • The study proposes enhanced training strategies using optimized batch normalization and clean data integration to improve both efficiency and robustness.

In the arena of machine learning security, adversarial training (AT) is a critical defense mechanism that trains models using examples specifically designed to fool them, thus improving their resilience to such attacks. However, the intricacies of AT and the techniques for understanding and improving it have remained partially shrouded. A paper delves deeper into analyzing the properties and the process of AT, leveraging a powerful analytic tool known as the Neural Tangent Kernel (NTK).

NTK has become increasingly popular for its ability to map and predict the behavior of neural networks. The novel research in question makes use of NTK to dissect the evolution of AT with intriguing revelations. It unveils three previously overlooked aspects: the influence of data normalization on AT, kernel dynamics (how kernels change over the course of training), and the spectral characteristics of the kernel that might cause what is termed 'catastrophic overfitting' where a model suddenly loses its adversarial robustness.

The paper posited a cutting-edge theory analyzing why adversarial training could detrimentally impact a model's performance on original, non-adversarial data. Their findings focus on how the neural network's output concerning adversarial inputs can deviate from the expected course, hinting at an underlying kernel shift – a notion that might help us understand the perplexing trade-off AT makes between model robustness and accuracy on clean data.

Most notably, the research discovers kernel dynamics' vital role in AT. Surprisingly, during the training process, the kernel undergoes three distinct evolution phases - a swift 'kernel learning' phase, a 'lazy training' phase where changes to the kernel flatline, and a second 'kernel learning' phase towards the end of training. This insight into the nature of kernel evolution has significant implications, especially in developing time-efficient training methods without undermining model performance.

The implications of these findings go beyond mere academic interest. For instance, by understanding NTK evolution, researchers can propose new training paradigms that significantly reduce the computational expense of AT, making it more accessible and efficient. Moreover, by studying the spectral features within the kernel, they offer strategies to mitigate catastrophic overfitting issues in single-step AT.

A key takeaway from this investigation is the proposed techniques for enhancing AT. Through empirical exploration, the researchers suggest optimizing batch normalization strategies and incorporating clean data during the initial training stage to expedite the training process. Such insights can lead to robust models that are still efficient to train, striking a balance that is of great interest in practical applications.

The paper also provides lessons on the interplay between clean and robust accuracies, underscoring that models may rely on different features to predict adversarial and non-adversarial inputs. While robust models tend to consider features across various classes when classifying adversarial examples, non-robust models may only focus on class-related features when predicting clean samples.

In conclusion, by rethinking adversarial training through the lens of Neural Tangent Kernel, this paper sheds light on hidden aspects of the training process, offering a path to optimize and understand AT better. This research represents a step toward creating models that maintain high performance while being resilient to adversarial attacks, moving us closer to more secure and reliable AI systems.

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