# V-MORALS: Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space

arXiv: https://arxiv.org/abs/2602.23524 · HTML: https://mlsanity.com/paper/2602.23524/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Mastering Visual Continuous Control: Improved Data-Augmented Reinforcement Learning](https://mlsanity.com/paper/2107.09645/) (2021)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Robot Motion Planning in Learned Latent Spaces](https://mlsanity.com/paper/1807.10366/) (2018)
- [Latent Space Roadmap for Visual Action Planning of Deformable and Rigid Object Manipulation](https://mlsanity.com/paper/2003.08974/) (2020)
- [Latent Action Diffusion for Cross-Embodiment Manipulation](https://mlsanity.com/paper/2506.14608/) (2025)
- [Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systems](https://mlsanity.com/paper/1611.00122/) (2016)
- [Learning Region of Attraction for Nonlinear Systems](https://mlsanity.com/paper/2110.00731/) (2021)
- [Learning to Get Up](https://mlsanity.com/paper/2205.00307/) (2022)
- [Safety with Agency: Human-Centered Safety Filter with Application to AI-Assisted Motorsports](https://mlsanity.com/paper/2504.11717/) (2025)
- [Latent Space Planning for Multi-Object Manipulation with Environment-Aware Relational Classifiers](https://mlsanity.com/paper/2305.10857/) (2023)
- [Latent Representations for Control Design with Provable Stability and Safety Guarantees](https://mlsanity.com/paper/2505.23210/) (2025)
- [tt MORALS: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space](https://mlsanity.com/paper/2310.03246/) (2023)
- [Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots](https://mlsanity.com/paper/2201.08538/) (2022)
- [Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers](https://mlsanity.com/paper/2202.08383/) (2022)
- [Augment-Connect-Explore: a Paradigm for Visual Action Planning with Data Scarcity](https://mlsanity.com/paper/2203.13034/) (2022)
- [Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees](https://mlsanity.com/paper/2210.01292/) (2022)
- [Ensemble Latent Space Roadmap for Improved Robustness in Visual Action Planning](https://mlsanity.com/paper/2303.15115/) (2023)

## Abstract (arXiv)

Reachability analysis has become increasingly important in robotics to distinguish safe from unsafe states. Unfortunately, existing reachability and safety analysis methods often fall short, as they typically require known system dynamics or large datasets to estimate accurate system models, are computationally expensive, and assume full state information. A recent method, called MORALS, aims to address these shortcomings by using topological tools to estimate Regions of Attraction (ROA) in a low-dimensional latent space. However, MORALS still relies on full state knowledge and has not been studied when only sensor measurements are available. This paper presents Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space (V-MORALS). V-MORALS takes in a dataset of image-based trajectories of a system under a given controller, and learns a latent space for reachability analysis. Using this learned latent space, our method is able to generate well-defined Morse Graphs, from which we can compute ROAs for various systems and controllers. V-MORALS provides capabilities similar to the original MORALS architecture without relying on state knowledge, and using only high-level sensor data. Our project website is at: https://v-morals.onrender.com.