Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs

2026-02-10

AI Summary

This work addresses the vulnerability of neural ODE models to adversarial attacks under input perturbations and their lack of interpretable input–output dynamics. It establishes, for the first time, a direct link between finite-time Lyapunov exponents (FTLE) and adversarial fragility, proposing an efficient regularization strategy that suppresses non-zero FTLE only during the early phase of input dynamics. This approach avoids the high computational cost of full-interval backward-backward propagation by characterizing the exponential divergence induced by perturbations, thereby organizing and stabilizing the dynamical evolution of neural ODEs. Experimental results demonstrate that the proposed FTLE-based regularization significantly enhances adversarial robustness while outperforming conventional full-interval regularization methods, achieving a superior trade-off between computational efficiency and model performance.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Adversarial Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

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.

Problem

• Neural ODEs
• adversarial vulnerability
• robustness
• Lyapunov exponents
• input perturbations

Innovation

• Finite-Time Lyapunov Exponents
• Neural ODEs
• Adversarial Robustness
• FTLE Regularization
• Input-Output Dynamics