General Covariant Action Modeling: Constructing Generalized Manifolds via Spatio-Temporal Decoupling
For embodied intelligence systems, this work addresses the fundamental issue of poor generalization from limited demonstrations by enforcing physical invariances, though the empirical gains over baselines are not quantified with specific numbers.
The paper introduces the Generalized Action Manifold (GAM) framework to achieve robust generalization from limited data in embodied intelligence by enforcing general covariance through spatio-temporal decoupling. Empirical results show GAM outperforms geometry-agnostic baselines in transfer and robustness.
Achieving robust generalization from limited data is a central challenge in embodied intelligence. Prevailing methods fail by regressing absolute coordinates, which violates the principle of general covariance. Fundamentally, this conflates the intrinsic task geometry with rigid execution patterns, binding policies to specific motion styles and fixed speeds. To resolve this, we propose the Generalized Action Manifold (GAM) framework that enforces general covariance through structural disentanglement. Specifically, GAM realizes the manifold by enforcing invariance across two orthogonal dimensions: (1) Temporal Invariance, utilizing an Arc-Length Parameterizer to orthogonalize the spatial path geometry from temporal dynamics, ensuring robustness to velocity variations; (2) Geometric Invariance, where a Schema-Affine-Factorization mechanism maps trajectories to canonical ``world lines'' in a pose-normalized coordinate frame. This distinguishes invariant geometric schemas from affine modulations, ensuring spatial generalizability. By integrating GAM within a structured Vision-Language-Action (VLA) architecture, we enable sparse demonstrations to densely populate a continuous, valid action manifold. Empirical results demonstrate that GAM enables superior transfer and robustness capabilities, outperforming geometry-agnostic baselines.