arXiv:2606.13769v1 Announce Type: cross 
Abstract: World models that capture how actions induce physical change enable scalable robot learning without reliance on embodiment-specific action labels. Pixel-space video models provide broad visual priors but expend model capacity on dense appearance reconstruction, while direct action models require embodiment-specific labels that hinder scalability. We present $\mu_0$, a scalable world model based on 3D traces. Rather than predicting dense pixels or directly modeling actions, $\mu_0$ forecasts smooth 3D trajectories for salient interaction points such as objects, tools, hands, and contact regions, yielding a compact, embodiment-agnostic motion interface. To enable training from diverse video sources, our TraceExtract system automatically extracts 3D supervision by selecting keypoints, constructing globally aligned traces, and associating motion segments with hierarchical language captions. This TraceExtract supervision pretrains $\mu_0$ by combining a pretrained vision-language backbone with a modular trace expert, which represents each query via B-spline control points and predicts future traces. Experiments show that $\mu_0$ outperforms baselines in both 2D and 3D trace prediction, including trace prediction models and tokenized VLM methods. Because $\mu_0$ is frozen and reusable, it can be paired with action experts for downstream robot embodiments. Despite action-free pretraining, the resulting trace-conditioned policies achieve performance competitive with VLA models pretrained with action supervision, such as $\pi_0$. These results establish 3D traces as a scalable and transferable representation for cross-embodiment manipulation.

تقديم نموذج $bc_0$، وهو نموذج عالم تفاعلي ثلاثي الأبعاد قابل للتوسع، يمثل تقدمًا كبيرًا في تعلم الروبوتات من خلال تمكين التنبؤ بمسارات ثلاثية الأبعاد سلسة لنقاط التفاعل دون الاعتماد على تسميات الإجراءات المحددة للجسد. يستخدم هذا النموذج نظام TraceExtract الجديد لاستخراج الإشراف ثلاثي الأبعاد تلقائيًا من مصادر الفيديو المتنوعة، مما يعزز عملية التدريب.

La introducción de $bc_0$, un modelo de mundo de interacción 3D escalable, marca un avance significativo en el aprendizaje de robots al permitir la predicción de trayectorias 3D suaves para puntos de interacción sin depender de etiquetas de acción específicas de la encarnación. Este modelo utiliza un nuevo sistema TraceExtract para extraer automáticamente supervisión 3D de diversas fuentes de video, mejorando así el proceso de entrenamiento.

L'introduction de $bc_0$, un modèle de monde d'interaction en 3D évolutif, représente une avancée significative dans l'apprentissage des robots en permettant la prédiction de trajectoires 3D fluides pour les points d'interaction sans dépendre d'étiquettes d'action spécifiques à l'incarnation. Ce modèle utilise un nouveau système TraceExtract pour extraire automatiquement une supervision 3D à partir de diverses sources vidéo, améliorant ainsi le processus d'entraînement.

The introduction of $bc_0$, a scalable 3D interaction-trace world model, marks a significant advancement in robot learning by enabling the prediction of smooth 3D trajectories for interaction points without relying on embodiment-specific action labels. This model utilizes a novel TraceExtract system to automatically extract 3D supervision from diverse video sources, enhancing the training process.