The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space
arXiv:2606.01847v1 Announce Type: cross Abstract: Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost. We introduce $\textbf{Lie Diffuser Actor (LDA)}$, a diffusion framework operating intrinsically on SE(3). Our
The continuous advancements in diffusion models necessitate more geometrically sound approaches to improve the robustness and efficiency of AI in physical world applications.
This development addresses fundamental limitations in current AI models for robotic manipulation, offering a path to more reliable, efficient, and safer autonomous systems.
Vision-language-action policies can now operate intrinsically on the mathematical manifold of robotic poses, leading to more accurate control and reduced kinematic errors.
- · Robotics companies
- · AI research institutions
- · Automation sector
- · Developers relying on Euclidean approximations for robotic control
Improved performance and reliability of diffusion-based robotic manipulation systems.
Faster development and deployment of complex robotic tasks in manufacturing, logistics, and exploration.
Accelerated commercialization of general-purpose humanoid robots due to enhanced perception-action capabilities.
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Read at arXiv cs.LG