Anisotropic error sensitivity in high-precision robotic control

Establish whether, in high-precision robotic manipulation tasks, sensitivity to action errors is non-homogeneous across directions in action space, and formalize the proposed on-manifold inductive bias as aligning with minimizing error along the most consequential directions while tolerating error along directions of lesser consequence.

Background

The authors introduce "manifold adherence" as an inductive bias explaining why generative control policies and the proposed MIP outperform regression despite similar validation losses. They show these methods yield lower off-manifold error on out-of-distribution states, which correlates better with closed-loop performance.

To interpret this effect, they explicitly conjecture that error sensitivity is direction-dependent in action space for high-precision tasks and hypothesize that an on-manifold bias prioritizes minimizing error along impactful directions. This conjecture motivates a formal characterization of anisotropic error sensitivity and the role of manifold adherence.