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Bringing Motion Taxonomies to Continuous Domains via GPLVM on Hyperbolic manifolds

ICML 2024 · Probabilistic and scientific modeling › Molecules and proteins · approach: Sparse graphical and tensor models · 0 citations (OpenAlex)

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Proposes a Gaussian process hyperbolic latent variable model (GPHLVM) that embeds human motion taxonomy data on the Lorentz hyperboloid, using graph-distance stress priors and graph-based back-constraints.

Problem

Human motion taxonomies are discrete hierarchical structures that are hard to combine with high-dimensional taxonomy-associated data for motion analysis and generation; existing latent models do not embed the hierarchy continuously.

Approach

Extends the GPLVM to hyperbolic latent spaces (Lorentz model) with hyperbolic wrapped Gaussian priors and heat-kernel-based hyperbolic GP kernels (including a positive-definite Monte Carlo approximation for H^2), and injects taxonomy structure via a graph-distance stress prior and graph-kernel back-constraints, optimized with Riemannian Adam.

Key results

• On the support pose taxonomy with 2D latent spaces, regularized GPHLVM outperforms Euclidean GPLVM in stress (e.g., 0.51±0.82 vs 0.58±0.94 for stress prior).
• On hand grasps 2D, GPHLVM with stress prior reduces stress to 0.14±0.16 vs 0.39±0.41 for the Euclidean GPLVM.
• Hyperbolic 3D models match or beat Euclidean 3D on bimanual and grasp taxonomies, but Euclidean 3D is slightly better on the cyclic support pose taxonomy.

Measured effects reported in the paper

Surprising findings

• Hyperbolic 2D GPHLVM outperforms Euclidean 3D GPLVM on the cyclic support pose taxonomy, despite the graph not being tree-like.
• Unregularized models encode no meaningful distance structure; the stress prior is needed to match taxonomy graph distances.

Limitations

• The 2D hyperbolic kernel is computationally expensive due to Monte Carlo sampling; training is much slower than the Euclidean GPLVM.
• Relies on the taxonomy being accurate; the stress scale must be tuned to allow discovery of additional structure.
• Geodesic motion generation does not enforce physical feasibility or contact constraints.

Experimental setup

Datasets: bimanual manipulation taxonomy poses (60, 86-dim joint angles) hand grasp taxonomy recordings (94 grasps, 24-dim) whole-body support pose taxonomy data (100 poses, 44-dim)

Benchmarks: bimanual manipulation taxonomy hand grasp taxonomy whole-body support pose taxonomy

Metrics: stress between embedding geodesic and graph distances runtime (training and decoding) reconstruction error

Baselines: GPLVM (Euclidean R^2 and R^3) VAE (vanilla and hyperbolic) VPoser linear interpolation in GPLVM latent space

Builds on: GPLVM back-constrained GPLVM hyperbolic wrapped normal distribution Riemannian Adam sparse variational GP (Bayesian GPLVM)

Closest papers by meaning

• Homogeneous Dynamics Space for Heterogeneous Humans (CVPR 2025 · similarity 0.88)
• Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry (ICML 2018 · similarity 0.86)
• SAMoR: Motion Modelling for Articulated Objects of Any Skeleton and Topology (NeurIPS 2026 · similarity 0.86)
• Scaling Large Motion Models with Million-Level Human Motions (ICML 2025 · similarity 0.86)
• Universal Humanoid Motion Representations for Physics-Based Control (ICLR 2024 · similarity 0.85)
• H-MoRe: Learning Human-centric Motion Representation for Action Analysis (CVPR 2025 · similarity 0.85)