# PoLAR: Factorizing Extent and Mode in Latent Actions for Robot Policy Learning

arXiv: https://arxiv.org/abs/2606.21139 · HTML: https://mlsanity.com/paper/2606.21139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 46 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [R3M: A Universal Visual Representation for Robot Manipulation](https://mlsanity.com/paper/2203.12601/) (2022)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [BridgeData V2: A Dataset for Robot Learning at Scale](https://mlsanity.com/paper/2308.12952/) (2023)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [Evaluating Real-World Robot Manipulation Policies in Simulation](https://mlsanity.com/paper/2405.05941/) (2024)
- [Time-Contrastive Networks: Self-Supervised Learning from Video](https://mlsanity.com/paper/1704.06888/) (2017)
- [UniVLA: Learning to Act Anywhere with Task-centric Latent Actions](https://mlsanity.com/paper/2505.06111/) (2025)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Prismatic VLMs: Investigating the Design Space of Visually-Conditioned Language Models](https://mlsanity.com/paper/2402.07865/) (2024)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [Latent Action Pretraining from Videos](https://mlsanity.com/paper/2410.11758/) (2024)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Temporal Cycle-Consistency Learning](https://mlsanity.com/paper/1904.07846/) (2019)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Learning to Act without Actions](https://mlsanity.com/paper/2312.10812/) (2023)
- [AdaWorld: Learning Adaptable World Models with Latent Actions](https://mlsanity.com/paper/2503.18938/) (2025)
- [villa-X: Enhancing Latent Action Modeling in Vision-Language-Action Models](https://mlsanity.com/paper/2507.23682/) (2025)

## Abstract (arXiv)

Robot actions vary in both extent and mode: how much change they produce and what kind of change they produce. A latent action space that reflects this structure may make it easier for downstream policies to map latent actions to robot actions. However, existing latent action methods typically rely on visual reconstruction from observation pairs without explicitly encouraging such structure. We introduce Polar Latent Actions with Radial structure (PoLAR), which imposes a radial-direction structure on latent actions, encouraging radius to encode transition extent and direction to retain transition mode. PoLAR uses temporal offsets between observations as a weak proxy for transition extent, encouraging transitions with larger offsets to occupy larger radii. We instantiate this structure in hyperbolic space, whose expanding volume with radius offers a natural fit for more diverse transition modes at larger extents. Across in-task and large-scale pretraining settings, PoLAR improves downstream policy performance in simulation and real-world robot experiments, outperforming latent action baselines and strong pretrained VLAs. These results suggest that structuring latent actions by extent and mode helps transfer visual pretraining to robot policy learning.