# Embedding Hybrid Systems into Continuous Latent Vector Fields

arXiv: https://arxiv.org/abs/2606.10596 · HTML: https://mlsanity.com/paper/2606.10596/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Toward Safety-Aware Informative Motion Planning for Legged Robots](https://mlsanity.com/paper/2103.14252/) (2021)
- [GMKF: Generalized Moment Kalman Filter for Polynomial Systems with Arbitrary Noise](https://mlsanity.com/paper/2403.04712/) (2024)
- [Discrete-Time Hybrid Automata Learning: Legged Locomotion Meets Skateboarding](https://mlsanity.com/paper/2503.01842/) (2025)
- [Ego-Vision World Model for Humanoid Contact Planning](https://mlsanity.com/paper/2510.11682/) (2025)
- [Legged Robot State Estimation within Non-inertial Environments](https://mlsanity.com/paper/2403.16252/) (2024)
- [A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization](https://mlsanity.com/paper/2410.06233/) (2024)
- [Learning Hybrid Dynamics via Convex Optimizations](https://mlsanity.com/paper/2509.24157/) (2025)
- [MePoly: Max Entropy Polynomial Policy Optimization](https://mlsanity.com/paper/2602.17832/) (2026)
- [Robust Trajectory Tracking of Autonomous Surface Vehicle via Lie Algebraic Online MPC](https://mlsanity.com/paper/2511.18683/) (2025)
- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Stein Variational Ergodic Surface Coverage with SE(3) Constraints](https://mlsanity.com/paper/2603.09458/) (2026)
- [A Survey of Legged Robotics in Non-Inertial Environments: Past, Present, and Future](https://mlsanity.com/paper/2604.20990/) (2026)
- [Learning Neural Event Functions for Ordinary Differential Equations](https://mlsanity.com/paper/2011.03902/) (2020)

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

- [Learning Continuous Neural Representation of Stochastic Hybrid Systems](https://mlsanity.com/paper/2609.38893/) (2026)

## Abstract (arXiv)

This work proves that an n-dimensional hybrid system can be embedded into an m-dimensional Euclidean space equipped with a continuous vector field on its embedded image whenever m>2n. This result suggests that an intrinsically discontinuous hybrid system generically admits a continuous extrinsic representation that is well-posed for differentiable optimization. Building on this existence theorem, we show that a latent Neural ODE with consistency loss in both the latent and state space can accurately recover the flow of hybrid systems. Extensive experiments suggest the proposed method outperforms the existing method in learning hybrid systems with varying geometries from only time series data.