CHyLL: Learning Continuous Neural Representations of Hybrid Systems
Sangli Teng, Hang Liu, Jingyu Song, Koushil Sreenath
TL;DR
CHyLL introduces a novel neural approach to model hybrid systems' continuous flows without segmentation, effectively capturing system topology and dynamics in a unified, smooth latent space.
Contribution
It proposes a continuous neural representation method that models hybrid systems without mode segmentation, leveraging differential topology for improved accuracy.
Findings
Accurately predicts hybrid system flows
Identifies topological invariants
Applies to stochastic optimal control
Abstract
Learning the flows of hybrid systems that have both continuous and discrete time dynamics is challenging. The existing method learns the dynamics in each discrete mode, which suffers from the combination of mode switching and discontinuities in the flows. In this work, we propose CHyLL (Continuous Hybrid System Learning in Latent Space), which learns a continuous neural representation of a hybrid system without trajectory segmentation, event functions, or mode switching. The key insight of CHyLL is that the reset map glues the state space at the guard surface, reformulating the state space as a piecewise smooth quotient manifold where the flow becomes spatially continuous. Building upon these insights and the embedding theorems grounded in differential topology, CHyLL concurrently learns a singularity-free neural embedding in a higher-dimensional space and the continuous flow in it. We…
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
(1) I find paper generally well written, besides few minor issues listed bellow. I like the clarity of motivation, transparency of novelties and appreciate the balance in presenting both intuition and technical complexity. (2) Up to my knowledge, CHyLL appears genuinely novel in its topological formulation of hybrid system learning. The reinterpretation of mode switches as gluing operations forming a quotient manifold and the learned embedding that makes hybrid flows continuous is non-standard
(1) Presentation: - Section 3: I find that introduction of main concepts like guards and resets should be smoother. Before jumping to formal Definitions, authors can use Figure 2 to introduce these concept first informally to build the intuition. e.g. in simple terms, what is the role of $q$. - Section 2: I feel that related work section would be easier to parse after the intuition and notation on hybrid systems is current Section 3. - Levenberg-Marquardt: Due to unclear Experimental conclusions
This article is quite abstract, drawing on profound mathematical theories to guide the methodology design. It addresses a very practical problem and has achieved promising results in the selected experimental examples.
1. Although this article cites many theorems and employs sophisticated mathematical frameworks, its contributions are primarily concentrated on methodological design, with the theoretical contributions not being sufficiently sound. Perhaps the authors could further incorporate theoretical analysis or proofs regarding their methods (such as the design of the loss Eq. 4). 2. The experiments in the paper all use simulated data from simple examples. There is an absence of benchmarking on publicly av
The paper is clear and well-motivated, and the pipeline and objectives are easy to follow. The route explored is worthwhile as a method to modeling hybrid dynamics that generalizes across systems. The proposal of learning a glued quotient manifold for hybrids via gluing + conformal losses is nice, and the training setup seems sensible (e.g. curriculum, anti-collapse, LM projection).
1. Although latent encoding for ODEs is not a new avenue, the quotient/gluing idea is a nice addition, but as the authors hint at in the paper, learning the correct 'glued' space might be hard in principle, and the lack of guarantees can be concerning. 2. The experimental scope is a little narrow, with toy problems/examples, and only a few comparative methods. The results for the ball juggling with MPPI experiment also show a deep Koopman baseline achieving a lower mean tracking cost, without
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Taxonomy
TopicsReinforcement Learning in Robotics · Model Reduction and Neural Networks · Gaussian Processes and Bayesian Inference