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新论文 · v1arXiv:2611.08457

大步长对抗训练:隐式偏置、优化与锐度

Adversarial Training with Large Step Sizes: Implicit Bias, Optimization, and Sharpness

Yi Feng, Andrea Paudice

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该论文研究确定性梯度下降在大恒定步长下对抗训练的动力学,分析隐式偏置、优化收敛与损失锐度的演化,并指出其与标准训练的三点关键差异。

cs.LG · math.OC

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Adversarial Training (AT) is an important method for improving model robustness. We study the dynamics of deterministic Gradient Descent (GD) in AT. Most existing works in this direction focus on the small or vanishing step sizes regime, where GD resembles a continuous-time flow. However, such step sizes can make training inefficient and are rarely used in practice. In this paper, we study the AT dynamics of GD with large constant step sizes. We first study GD in adversarial linear logistic regression, focusing on two aspects: where the model parameters converge (implicit bias) and how quickly the losses decrease (optimization). We then turn to neural networks training and study how the sharpness of losses evolve during AT. Our results advance the understanding of the behaviors of GD with large step sizes in AT and highlight three key differences from its behavior in Standard Training (ST): (i) the implicit bias gap between AT and ST, previously established only for small step sizes, persists for arbitrarily large constant step sizes, (ii) different from ST, there is no uniform rate of convergence for the optimization error in AT, and (iii) sharpness can exhibit two-stage dynamics that differ from the Edge-of-Stability behavior observed in ST.