# Control Disturbance Rejection in Neural ODEs

arXiv: https://arxiv.org/abs/2509.18034 · HTML: https://mlsanity.com/paper/2509.18034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [Overcoming Catastrophic Forgetting in Incremental Few-Shot Learning by Finding Flat Minima](https://mlsanity.com/paper/2111.01549/) (2021)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [Control in the spaces of ensembles of points](https://mlsanity.com/paper/1907.00905/) (2019)
- [A minimax optimal control approach for robust neural ODEs](https://mlsanity.com/paper/2310.17584/) (2023)
- [Control Theoretic Approach to Fine-Tuning and Transfer Learning](https://mlsanity.com/paper/2404.11013/) (2024)
- [Geometric Foundations of Tuning without Forgetting in Neural ODEs](https://mlsanity.com/paper/2509.03474/) (2025)

## Built on by (most cited first, 1 of 1)

- [Privacy Preserving Gossip Learning](https://mlsanity.com/paper/2609.14778/) (2026)

## Abstract (arXiv)

In this paper, we propose an iterative training algorithm for Neural ODEs that provides models resilient to control (parameter) disturbances. The method builds on our earlier work Tuning without Forgetting-and similarly introduces training points sequentially, and updates the parameters on new data within the space of parameters that do not decrease performance on the previously learned training points-with the key difference that, inspired by the concept of flat minima, we solve a minimax problem for a non-convex non-concave functional over an infinite-dimensional control space. We develop a projected gradient descent algorithm on the space of parameters that admits the structure of an infinite-dimensional Banach subspace. We show through simulations that this formulation enables the model to effectively learn new data points and gain robustness against control disturbance.