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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09613 |
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| _version_ | 1866911437530595328 |
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| author | Wöhrer, Tobias Kuehn, Christian |
| author_facet | Wöhrer, Tobias Kuehn, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs Wöhrer, Tobias Kuehn, Christian Dynamical Systems Machine Learning 37M25, 68T07, 37N99 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. |
| title | Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs |
| topic | Dynamical Systems Machine Learning 37M25, 68T07, 37N99 |
| url | https://arxiv.org/abs/2602.09613 |