追踪有限时间Lyapunov指数以增强神经ODE的鲁棒性
Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs
AI总结：
通过FTLE正则化提升神经ODE的鲁棒性，利用FTLEs增强模型的输入输出动态可解释性与对抗鲁棒性。
摘要：
我们研究了深度神经网络在连续深度神经ODE框架内的有限时间Lyapunov指数（FTLEs），这是一种衡量输入扰动指数分离的指标。我们证明FTLEs是输入输出动态的强大组织者，允许更好的可解释性和不同模型架构的比较。我们建立了Lyapunov指数与对抗脆弱性之间的直接联系，并提出了一种新的训练算法，通过FTLE正则化提高鲁棒性。关键思想是抑制输入动态早期阶段远离零的指数。这种方法相比全区间正则化增强了鲁棒性并减少了计算成本，因为它避免了完整的``双''反向传播。
英文摘要：
We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks within the framework of continuous-depth neural ODEs. We demonstrate that FTLEs are powerful organizers for input-output dynamics, allowing for better interpretability and the comparison of distinct model architectures. We establish a direct connection between Lyapunov exponents and adversarial vulnerability, and propose a novel training algorithm that improves robustness by FTLE regularization. The key idea is to suppress exponents far from zero in the early stage of the input dynamics. This approach enhances robustness and reduces computational cost compared to full-interval regularization, as it avoids a full ``double'' backpropagation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
