# Exchangeable Neural ODE for Set Modeling

arXiv: https://arxiv.org/abs/2008.02676 · HTML: https://mlsanity.com/paper/2008.02676/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2020.

## Built on by (most cited first, 19 of 19)

- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (2021)
- [Top-N: Equivariant set and graph generation without exchangeability](https://mlsanity.com/paper/2110.02096/) (2021)
- [NRTSI: Non-Recurrent Time Series Imputation](https://mlsanity.com/paper/2102.03340/) (2021)
- [Ab-initio study of interacting fermions at finite temperature with neural canonical transformation](https://mlsanity.com/paper/2105.08644/) (2021)
- [Phoneme Hallucinator: One-shot Voice Conversion via Set Expansion](https://mlsanity.com/paper/2308.06382/) (2023)
- [Deep Variational Free Energy Approach to Dense Hydrogen](https://mlsanity.com/paper/2209.06095/) (2022)
- [Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamics](https://mlsanity.com/paper/2305.14286/) (2023)
- [Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectives](https://mlsanity.com/paper/2309.00380/) (2023)
- [Partially Observed Exchangeable Modeling](https://mlsanity.com/paper/2102.06083/) (2021)
- [Transparent Single-Cell Set Classification with Kernel Mean Embeddings](https://mlsanity.com/paper/2201.07322/) (2022)
- [Correcting Auto-Differentiation in Neural-ODE Training](https://mlsanity.com/paper/2306.02192/) (2023)
- [Advances in Set Function Learning: A Survey of Techniques and Applications](https://mlsanity.com/paper/2501.14991/) (2025)
- [EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction with Exogenous Variables](https://mlsanity.com/paper/2208.01913/) (2022)
- [Towards Cost Sensitive Decision Making](https://mlsanity.com/paper/2410.03892/) (2024)
- [Enhancing Neural Subset Selection: Integrating Background Information into Set Representations](https://mlsanity.com/paper/2402.03139/) (2024)
- [Probabilistic Forecasting of Irregular Time Series via Conditional Flows](https://mlsanity.com/paper/2402.06293/) (2024)
- [PointODE: Lightweight Point Cloud Learning with Neural Ordinary Differential Equations on Edge](https://mlsanity.com/paper/2506.00438/) (2025)
- [Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning models](https://mlsanity.com/paper/2604.09769/) (2026)

## Abstract (arXiv)

Reasoning over an instance composed of a set of vectors, like a point cloud, requires that one accounts for intra-set dependent features among elements. However, since such instances are unordered, the elements' features should remain unchanged when the input's order is permuted. This property, permutation equivariance, is a challenging constraint for most neural architectures. While recent work has proposed global pooling and attention-based solutions, these may be limited in the way that intradependencies are captured in practice. In this work we propose a more general formulation to achieve permutation equivariance through ordinary differential equations (ODE). Our proposed module, Exchangeable Neural ODE (ExNODE), can be seamlessly applied for both discriminative and generative tasks. We also extend set modeling in the temporal dimension and propose a VAE based model for temporal set modeling. Extensive experiments demonstrate the efficacy of our method over strong baselines.