Hierarchical structures of motion exist across research fields, including computer vision, graphics, and robotics, where complex dynamics typically arise from coordinated interactions among simpler motion components. Existing methods to model such dynamics typically rely on manually-defined or heuristic hierarchies with fixed motion primitives, limiting their generalizability across different tasks. In this work, we propose a general hierarchical motion modeling method that learns structured, interpretable motion relationships directly from data. Our method represents observed motions using graph-based hierarchies, explicitly decomposing global absolute motions into parent-inherited patterns and local motion residuals. We formulate hierarchy inference as a differentiable graph learning problem, where vertices represent elemental motions and directed edges capture learned parent-child dependencies through graph neural networks. We evaluate our hierarchical reconstruction approach on three examples: 1D translational motion, 2D rotational motion, and dynamic 3D scene deformation via Gaussian splatting. Experimental results show that our method reconstructs the intrinsic motion hierarchy in 1D and 2D cases, and produces more realistic and interpretable deformations compared to the baseline on dynamic 3D Gaussian splatting scenes. By providing an adaptable, data-driven hierarchical modeling paradigm, our method offers a formulation applicable to a broad range of motion-centric tasks. Project Page: https://light.princeton.edu/HEIR/

Evolving consumer demands and market trends have led to businesses increasingly embracing a production approach that prioritizes flexibility and customization. Consequently, factory workers must engage in tasks that are more complex than before. Thus, productivity depends on each worker's skills in assembling products. Therefore, analyzing the behavior of a worker is crucial for work improvement. However, manual analysis is time consuming and does not provide quick and accurate feedback. Machine learning have been attempted to automate the analyses; however, most of these methods need several labels for training. To this end, we extend the Gaussian process hidden semi-Markov model (GP-HSMM), to enable the rapid and automated analysis of worker behavior without pre-training. The model does not require labeled data and can automatically and accurately segment continuous motions into motion classes. The proposed model is a probabilistic model that hierarchically connects GP-HSMM and HSMM, enabling the extraction of behavioral patterns with different granularities. Furthermore, it mutually infers the parameters between the GP-HSMM and HSMM, resulting in accurate motion pattern extraction. We applied the proposed method to motion data in which workers assembled products at an actual production site. The accuracy of behavior pattern extraction was evaluated using normalized Levenshtein distance (NLD). The smaller the value of NLD, the more accurate is the pattern extraction. The NLD of motion patterns captured by GP-HSMM and HSMM layers in our proposed method was 0.50 and 0.33, respectively, which are the smallest compared to that of the baseline methods.