From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data

Geometric analysis fundamentally distinguishes between \textit{extrinsic} and \textit{intrinsic} perspectives. The dominant paradigm in current 3D representation learning relies on either extrinsic spatial structures or high-level semantics, struggling to capture the essence of shape identity and underlying manifold topology. To bridge this gap, we introduce a novel 3D representation learning paradigm, namely \textbf{PRISM}, for \textbf{P}re-training, which learns isometric embeddings by \textbf{R}ecovering the \textbf{I}ntrinsic \textbf{S}urface geodesic \textbf{M}etric. PRISM incorporates a topology-enforcing objective that explicitly constrains the structure of latent space, alongside a specialized two-stage training recipe mitigating sample imbalance inherent in the distribution of geodesic distances. Experiments demonstrate that our approach shows satisfactory accuracy, robustness, and high efficiency in geodesic distance prediction and achieves superior performance across diverse downstream tasks, including shape recognition, surface parameterization, and non-rigid correspondence. The code will be publicly available at https://github.com/AidenZhao/PRISM.

Semi-Supervised Learning for In-Game Expert-Level Music-to-Dance Translation

Music-to-dance translation is a brand-new and powerful feature in recent role-playing games. Players can now let their characters dance along with specified music clips and even generate fan-made dance videos. Previous works of this topic consider music-to-dance as a supervised motion generation problem based on time-series data. However, these methods suffer from limited training data pairs and the degradation of movements. This paper provides a new perspective for this task where we re-formulate the translation problem as a piece-wise dance phrase retrieval problem based on the choreography theory. With such a design, players are allowed to further edit the dance movements on top of our generation while other regression based methods ignore such user interactivity. Considering that the dance motion capture is an expensive and time-consuming procedure which requires the assistance of professional dancers, we train our method under a semi-supervised learning framework with a large unlabeled dataset (20x than labeled data) collected. A co-ascent mechanism is introduced to improve the robustness of our network. Using this unlabeled dataset, we also introduce self-supervised pre-training so that the translator can understand the melody, rhythm, and other components of music phrases. We show that the pre-training significantly improves the translation accuracy than that of training from scratch. Experimental results suggest that our method not only generalizes well over various styles of music but also succeeds in expert-level choreography for game players.