# Generalization Bound for a General Class of Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2508.18920 · HTML: https://mlsanity.com/paper/2508.18920/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 19 of 19)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Generalization bounds for deep convolutional neural networks](https://mlsanity.com/paper/1905.12600/) (2019)
- [Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data](https://mlsanity.com/paper/2402.14989/) (2024)
- [Generalization bounds for neural ordinary differential equations and deep residual networks](https://mlsanity.com/paper/2305.06648/) (2023)
- [Generalization Error Bounds for Deep Neural Networks Trained by SGD](https://mlsanity.com/paper/2206.03299/) (2022)
- [On the Generalization and Approximation Capacities of Neural Controlled Differential Equations](https://mlsanity.com/paper/2305.16791/) (2023)

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

- [Generalization Bounds of Spiking Neural Networks via Rademacher Complexity](https://mlsanity.com/paper/2605.02927/) (2026)

## Abstract (arXiv)

Neural ordinary differential equations (neural ODEs) are a popular type of deep learning model that operate with continuous-depth architectures. To assess how well such models perform on unseen data, it is crucial to understand their generalization error bounds. Previous research primarily focused on the linear case for the dynamics function in neural ODEs - Marion, P. (2023), or provided bounds for Neural Controlled ODEs that depend on the sampling interval Bleistein et al. (2023). In this work, we analyze a broader class of neural ODEs where the dynamics function is a general nonlinear function, either time dependent or time independent, and is Lipschitz continuous with respect to the state variables. We showed that under this Lipschitz condition, the solutions to neural ODEs have solutions with bounded variations. Based on this observation, we establish generalization bounds for both time-dependent and time-independent cases and investigate how overparameterization and domain constraints influence these bounds. To our knowledge, this is the first derivation of generalization bounds for neural ODEs with general nonlinear dynamics.