LaDy: Lagrangian-Dynamic Informed Network for Skeleton-based Action Segmentation via Spatial-Temporal Modulation

Skeleton-based Temporal Action Segmentation (STAS) aims to densely parse untrimmed skeletal sequences into frame-level action categories. However, existing methods, while proficient at capturing spatio-temporal kinematics, neglect the underlying physical dynamics that govern human motion. This oversight limits inter-class discriminability between actions with similar kinematics but distinct dynamic intents, and hinders precise boundary localization where dynamic force profiles shift. To address these, we propose the Lagrangian-Dynamic Informed Network (LaDy), a framework integrating principles of Lagrangian dynamics into the segmentation process. Specifically, LaDy first computes generalized coordinates from joint positions and then estimates Lagrangian terms under physical constraints to explicitly synthesize the generalized forces. To further ensure physical coherence, our Energy Consistency Loss enforces the work-energy theorem, aligning kinetic energy change with the work done by the net force. The learned dynamics then drive a Spatio-Temporal Modulation module: Spatially, generalized forces are fused with spatial representations to provide more discriminative semantics. Temporally, salient dynamic signals are constructed for temporal gating, thereby significantly enhancing boundary awareness. Experiments on challenging datasets show that LaDy achieves state-of-the-art performance, validating the integration of physical dynamics for action segmentation. Code is available at https://github.com/HaoyuJi/LaDy.