# Taxonomy-aware Dynamic Motion Generation on Hyperbolic Manifolds

arXiv: https://arxiv.org/abs/2509.21281 · HTML: https://mlsanity.com/paper/2509.21281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Metrics for Probabilistic Geometries](https://mlsanity.com/paper/1411.7432/) (2014)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds](https://mlsanity.com/paper/2210.01672/) (2022)
- [A Motion Taxonomy for Manipulation Embedding](https://mlsanity.com/paper/2007.06695/) (2020)
- [Riemann2: Learning Riemannian Submanifolds from Riemannian Data](https://mlsanity.com/paper/2503.05540/) (2025)
- [On Probabilistic Pullback Metrics for Latent Hyperbolic Manifolds](https://mlsanity.com/paper/2410.20850/) (2024)

## Abstract (arXiv)

Human-like motion generation for robots often draws inspiration from biomechanical studies, which often categorize complex human motions into hierarchical taxonomies. While these taxonomies provide rich structural information about how movements relate to one another, this information is frequently overlooked in motion generation models, leading to a disconnect between the generated motions and their underlying hierarchical structure. This paper introduces the acgphdm, a novel approach that learns latent representations preserving both the hierarchical structure of motions and their temporal dynamics to ensure physical consistency. Our model achieves this by extending the dynamics prior of the Gaussian Process Dynamical Model (GPDM) to the hyperbolic manifold and integrating it with taxonomy-aware inductive biases. Building on this geometry- and taxonomy-aware frameworks, we propose three novel mechanisms for generating motions that are both taxonomically-structured and physically-consistent: two probabilistic recursive approaches and a method based on pullback-metric geodesics. Experiments on generating realistic motion sequences on the hand grasping taxonomy show that the proposed GPHDM faithfully encodes the underlying taxonomy and temporal dynamics, and it generates novel physically-consistent trajectories.