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

Researchers introduce PoLAR, a novel latent action representation framework that uses radial-direction structure in hyperbolic space to separately encode transition extent and mode for robot policy learning. The method improves downstream performance across simulation and real-world experiments by leveraging temporal gaps as a proxy for transition magnitude, outperforming existing latent action baselines and vision-language models.

PoLAR addresses a fundamental limitation in current latent action pretraining methods: the entanglement of transition extent and transition mode within unstructured representations. By factorizing these dimensions through a radial-direction architecture, the framework enables more interpretable and transferable visual representations for robotic control. This approach uses temporal offset between observations as a weak supervisory signal, with larger time gaps encouraging latent actions to occupy larger radii in hyperbolic space.

The choice of hyperbolic geometry is particularly significant. Hyperbolic space's exponentially expanding volume with increasing radius naturally accommodates greater diversity of transition modes at larger extents, providing a geometric inductive bias aligned with the problem structure. This differs fundamentally from Euclidean approaches that struggle to scale diversity with magnitude.

The results demonstrate meaningful improvements in both controlled simulation environments and real robot deployments, with PoLAR outperforming strong baselines including pretrained vision-language action models. This suggests that geometric considerations in representation learning are underexplored in robot policy transfer. For the broader AI community, this work indicates that pretraining objectives should explicitly consider the mathematical space in which representations live, not just the training signals provided.

The research validates that thoughtful architectural choices about latent space geometry can yield tangible improvements in downstream task performance. This opens avenues for exploring how other geometric structures might benefit different representation learning problems in robotics and beyond.

• →PoLAR factorizes latent action representations into extent (radius) and mode (direction) using radial-direction structure in hyperbolic space
• →Temporal offset between observations serves as a weak proxy for transition extent, guiding learning without explicit magnitude annotations
• →Hyperbolic geometry naturally accommodates increasing diversity of transition modes at larger extents, providing geometric alignment with the learning problem
• →PoLAR achieves superior performance compared to existing latent action baselines and vision-language action models in simulation and real-world robot experiments
• →Geometric design of latent action spaces emerges as a critical but underexplored factor for effective transfer learning in robotic control