Unrolled gradients in disguise: bridging interpolation-based and Jacobian regularization for stable neural dynamics
Abstract
Hybrid models and neural differential equations (NDEs) are becoming increasingly important for modelling physical systems; however, they often encounter stability and accuracy issues during long-term integration. Training on unrolled trajectories is known to limit these divergences but quickly becomes too computationally expensive due to the need to compute gradients over an iterative process, making this method impractical for large-scale physical systems (e.g. weather and climate forecasting). Two popular paradigms for improving the stability of learned dynamics are to train on interpolated or noisy samples or to regularize the Jacobian of the learned representation. In this work, we demonstrate that these paradigms can be understood under a common lens and that they both correspond to an approximation of the gradients obtained in an unrolled learning strategy. Building on this understanding, we derive a principled and complete approach to regularize training and demonstrate its impact on the stability of learned dynamical systems.
Related
- Jacobian-Free Unrolling: memory efficient unrolled network for 3D SPECT Reconstruction
- Deeply unrolled alternating projections for phase retrieval
- Are trees really just butterflies in disguise?
- On the Adversarial Vulnerability of Neural Receivers with Unrolled LDPC Decoders
- Gauss-Manin Connection in Disguise: Holomorphic Anomaly Equations and Higher Genus Real Gromov-Witten Invariants
BibTeX
@misc{janvier2026unrolled,
title = {{Unrolled gradients in disguise: bridging interpolation-based and Jacobian regularization for stable neural dynamics}},
author = {Maya Janvier and Etienne Meunier},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03461},
eprint = {2611.03461},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03461},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unrolled gradients in disguise: bridging interpolation-based and Jacobian regularization for stable neural dynamics
AU - Maya Janvier
AU - Etienne Meunier
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03461
UR - https://arxiv.org/abs/2611.03461
AB - Hybrid models and neural differential equations (NDEs) are becoming increasingly important for modelling physical systems; however, they often encounter stability and accuracy issues during long-term integration. Training on unrolled trajectories is known to limit these divergences but quickly becomes too computationally expensive due to the need to compute gradients over an iterative process, making this method impractical for large-scale physical systems (e.g. weather and climate forecasting). Two popular paradigms for improving the stability of learned dynamics are to train on interpolated or noisy samples or to regularize the Jacobian of the learned representation. In this work, we demonstrate that these paradigms can be understood under a common lens and that they both correspond to an approximation of the gradients obtained in an unrolled learning strategy. Building on this understanding, we derive a principled and complete approach to regularize training and demonstrate its impact on the stability of learned dynamical systems.
ER -