Latest / Embodied AI 101 / PoLAR: Factorizing Extent and Mode in Latent Actions for Robot Policy Learning
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- PoLAR: Factorizing Extent and Mode in Latent Actions for Robot Policy Learning. Teaching robots to act from vision and language often relies on large datasets or expert teleoperation, which can be expensive or impractical. Recent trends have explored latent action learning – that is, learning an internal “action” space from videos or unlabeled demos – so that robot policies can be trained without explicit action labels. Work like CLAM and LAPA has shown this can dramatically improve data efficiency. For example, the CLAM approach infers continuous latent actions from video frames and then grounds them to real robot controls; it reported up to 2–3× gains in task success over previous latent-action methods. Similarly, LAPA learns a VQ-VAE of discrete latent “verbs” from internet videos, and uses those to pretrain vision-language-action (VLA) models for manipulation. These methods confirm that latent actions – representing visual transitions without requiring true action labels – are a powerful tool for policy learning on novel robot tasks. However, most prior latent-action models treat each transition as an unconstrained vector, with no built-in structure. Jeong et al. (2026) argue that this “unstructured” approach overlooks a natural geometric factorization of actions into how far something moves (the extent) and what kind of change occurs (the mode). For instance, pushing a block one centimeter or ten centimeters are intuitively the same type of action (push) but with different magnitudes. If a latent representation treats them as unrelated points, the policy has to learn this relationship from scratch. Instead, PoLAR imposes a polar-like geometry on the latent space so that one coordinate encodes the extent (radial distance) and the other coordinates encode the mode (direction). In other words, radius = “how much”, while angle = “which behavior”. This radial–direction factorization is at the heart of PoLAR. Concretely, the authors introduce Polar Latent Actions with a Radial structure in latent space. The intuition is that two transitions involving the same mode but different extents should lie in a similar direction but at different radii. Jeong et al. put it succinctly: existing latent models “entangle transition extent and transition mode,” whereas PoLAR structures them so that the latent radius encodes the extent and the latent direction encodes the mode. Geometrically, imagine actions arranged in a kind of polar coordinate system: all “push” actions might lie along one ray, with longer pushes placed farther from the origin, whereas “rotate” actions lie along a different ray, etc. This geometry allows the model to exploit the insight that a mode can reoccur at multiple extents and that actions with similar modes should cluster in direction. But how can a model learn which transitions are “larger” and should map to a longer radius? PoLAR leverages a simple cue: time gaps. When training on video or robot data, a pair of observations separated by more frames (or a longer temporal offset) usually means more has happened. For example, the difference between frame 1 and frame 6 in a running video is typically larger than between frame 1 and frame 2. PoLAR uses this idea as a weak supervision signal: it encourages the latent actions from frame-pairs with greater temporal separation to have larger radii. As the paper states, “PoLAR uses temporal offset between two observations as a weak proxy for transition extent, encouraging latent actions from pairs separated by larger temporal gaps to occupy larger radii”. In practice this is enforced via an ordering loss (forcing larger-gap pairs to map to a point farther out than smaller-gap pairs) and a radial progression loss (encouraging the latent radius to grow proportionally with the time offset). The result is that during pretraining, the model automatically discovers that time gap correlates with how “big” the action is, without any hand-labeled distances. Another key design choice is the use of hyperbolic geometry for the latent space. A standard Euclidean space could in principle also represent actions in polar coordinates, but hyperbolic space has a valuable property: exponentially increasing volume with radius. In plain terms, points at large radii have much more “room” around them in hyperbolic space compared to Euclidean. This matches the intuition that big, long-horizon actions come in many varieties. As the authors explain, “hyperbolic space’s expanding volume with radius offers a natural fit for more diverse transition modes at larger extents”. In other words, if a robot can take a tiny step or a huge leap, the space of possible kinds of huge leaps is vast (it could do any of many motions for a long time), and hyperbolic space can allocate that capacity. By contrast, in Euclidean space a long-radii region would be linearly growing, potentially crowding different long-horizon behaviors too close together. Behind these ideas lies PoLAR’s latent action model. It starts with a standard two-part architecture: an inverse dynamics encoder and a forward prediction decoder (or diffusion model) works together on image pairs. The inverse model takes two observations (e.g. before and after an unlabeled demonstration) and computes a latent action that would transform the first image to the second. The forward model then tries to roll out or reconstruct the change given the first image and the latent action. This is much like CLAM and others: the model learns a latent action space by predicting frames. On top of this, PoLAR introduces the geometric constraints. During training, for each pair of images the latent action is first mapped into hyperbolic space and converted to a (radius, direction) representation. The radius is pushed to grow with the temporal gap between the images, while the direction is left to capture whatever change type is needed. The authors call these the Ordering loss (enforce rank order by gap) and Radial Progression loss (encourage smooth, proportional radius increase). Together they lead to latent actions that align in cones: actions of similar type cluster by angle, while their distance from the origin reflects how big the change is. For many recent robot policies, particularly VLA (Vision-Language-Action) models, the latent actions are actually discrete tokens rather than continuous vectors. PoLAR extends its design to this setting by factorizing the codebook. Instead of a single flat codebook of “action” tokens, PoLAR uses one small magnitude codebook and one larger mode codebook. One token encodes the extent (a “radius token”) drawn from an ordered set, and another token (or token sequence) encodes the type (direction) of behavior. This way a generated action in the sequence might consist of a “radius token” plus a “direction token,” explicitly decoupling how far to act from what to do. Although the paper focuses on the continuous latent model in most experiments, this discrete factorization makes the same point for token-based models: even the “fast action language model” scenario can benefit from separating scale and type. This structured latent space pays off in practice. Jeong et al. pretrain PoLAR on a large robotics video corpus (BridgeData V2, an internet-scale collection of diverse robot demonstrations), and then fine-tune policies for various tasks. They test on several benchmarks: RoboMimic (a simulated suite of pick-and-place and manipulation tasks), MimicGen (NVIDIA’s scalable demo generation tasks), and SimplerEnv-WidowX (a simplified robotic cabinet manipulation scenario). Across all these simulated tasks, policies that use PoLAR’s latent actions outperform ones using standard (unstructured) latents. For instance, in diffusion-based visuomotor policies on RoboMimic and MimicGen, PoLAR-consistent latents gave higher success rates. Even more strikingly, on the SimplerEnv-WidowX benchmark, the PoLAR-pretrained model (trained only on BridgeData V2) beat strong baselines including “SmolVLA” (a compact VLA model) that had seen much broader pretraining. This suggests that PoLAR’s geometry bias provides extra data efficiency. The gains hold up in the real world as well. The authors deployed PoLAR-augmented VLA policies on an actual tabletop robot performing three multi-step manipulation tasks: picking and placing a banana, stacking cups, and opening a pot to grab a banana. In every case, the PoLAR-based policy succeeded far more often than baseline VLAs. Qualitatively, the project videos show that when using PoLAR, the robot reliably achieves its goals (green checkmark), whereas alternate models either fail to fully complete the task or simply do nothing useful (red X). Summarizing the quantitative results, the paper reports that “Across in-task and large-scale pretraining settings, PoLAR improves downstream policy performance in simulation and real-world experiments, outperforming latent-action baselines and strong pretrained VLAs.”. In other words, structuring the latent space by extent and mode consistently helped the policies learn these tasks faster and more robustly than before, even in real-world trials. Why does this geometry matter? The authors emphasize that the choice of latent space geometry is a design decision that can make a real difference. By carving the latent space into polar form, PoLAR imposes a useful inductive bias: continuity in one coordinate (extent) and clusterability in the others (mode). Intuitively, this means a policy can be simpler: to increase the reach of an action, it only needs to push the latent point farther out along the same ray, without jumping to a different latent region. The hyperbolic expansion further means that as actions become more extreme, the model has exponentially more capacity to encode many different ways such extreme actions could play out – something Euclidean spaces struggle with. This insight is somewhat reminiscent of how latent spaces in other domains (like word embeddings or trees) have used hyperbolic space for hierarchical or continuum-like data; here the “hierarchy” is extent. In summary, PoLAR demonstrates that factoring out the magnitude of change from its type can help robot learning. It adds only modest extra loss terms and a change of geometry during pretraining, yet delivers systematic gains. For practitioners, the take-home is that one should be mindful of what the latent action space represents. If you’re training a latent-action model from visual data, consider whether the dataset itself provides cues about magnitude (like time gaps) or structure, and whether imposing a coordinate system (e.g. polar) would encode a meaningful bias. The PoLAR code (available on GitHub) even includes checkpoints of the trained tokenizer and VLA, so others can experiment with the polar latent space on new tasks. Looking forward, this work suggests several avenues. One can probe how different geometric spaces affect learning – for instance, would elliptical or spherical constraints serve other tasks? Also, combining PoLAR’s structure with other advances (like stronger forward-world modeling or hierarchical latent plans) could yield further improvements. And while PoLAR used only time as a proxy for extent, future work might incorporate other signals too (like explicit object distance changes). Regardless, PoLAR highlights that not all action embeddings are created equal – building in the right geometry can give policies a powerful shortcut to understanding transitions. Citations: The PoLAR method is introduced by Jeong et al. in their recent preprint, as summarized in their paper. Related work includes CLAM (Continuous Latent Action Models) which also learns latent actions from video, and LAPA which learns discrete latent actions with VQ-VAE for VLA pretraining.