ML Security PapersTracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs
Christian Kuehn 1, Tobias Wöhrer 2
Published on arXiv
2602.09613
Input Manipulation Attack
OWASP ML Top 10 — ML01
Key Finding
FTLE suppression during the early stage of input dynamics enhances adversarial robustness while reducing computational cost by avoiding full double backpropagation compared to full-interval regularization.
FTLE Regularization
Novel technique introduced
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.
Key Contributions
- Establishes a direct theoretical connection between finite-time Lyapunov exponents and adversarial vulnerability in neural ODEs
- Proposes FTLE regularization that suppresses exponents far from zero in the early stage of input dynamics to improve robustness
- Demonstrates that early-stage FTLE suppression reduces computational cost by avoiding full double backpropagation compared to full-interval regularization
🛡️ Threat Analysis
Directly addresses adversarial vulnerability by establishing a theoretical link between Lyapunov exponents and input perturbation sensitivity, then proposes FTLE regularization as a training-time defense that reduces adversarial vulnerability at inference time.