Research map / Point clouds / Point cloud classification
On the Continuity of Rotation Representations in Neural Networks
Check your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a continuous 6D rotation representation instead of discontinuous representations | Rotation autoencoder · SO(3) rotation autoencoder | mean geodesic error: discontinuous representations can have up to 6 to 14 times higher mean errors | Helped |
| Use continuous 5D or 6D representations instead of quaternion, axis-angle, or Euler-angle representations | Rotation autoencoder · SO(3) rotation autoencoder | maximum geodesic error: up to 180$^\circ$ -> not higher than 2$^\circ$ | Helped |
| Use the continuous 6D representation instead of the tested rotation alternatives | Point-cloud rotation estimator · ShapeNet airplane point-cloud rotation estimation | mean geodesic error | Helped |
| Use the continuous 6D representation instead of Euler angles | Point-cloud rotation estimator · ShapeNet airplane point-cloud rotation estimation | errors below 5$^\circ$: around 95\% of errors lower than 5$^\circ$ | Helped |
| Use the continuous 6D representation instead of Euler angles | Point-cloud rotation estimator · ShapeNet airplane point-cloud rotation estimation | errors above 25$^\circ$: around 10\% of errors higher than 25$^\circ$ | Helped |
| Reduce the representation from 6D to 5D using normalized stereographic projection (ablation) | Point-cloud rotation estimator · ShapeNet airplane point-cloud rotation estimation | mean geodesic error | Hurt |
| Use the 5D representation instead of 3D or 4D representations | Point-cloud rotation estimator · ShapeNet airplane point-cloud rotation estimation | mean geodesic error | Helped |
| Use the continuous 6D representation instead of 3D or 4D representations | Human-pose inverse-kinematics network · CMU Motion Capture Database test set | pose reconstruction error | Helped |
| Reduce the representation from 6D to 5D using normalized stereographic projection (ablation) | Human-pose inverse-kinematics network · CMU Motion Capture Database test set | pose reconstruction error | No clear effect |
| Use a 3×3 matrix output with orthogonalization only at test time instead of the 6D representation | Human-pose inverse-kinematics network · CMU Motion Capture Database test set | pose reconstruction error | Hurt |
| Use the 5D stereographic-projection representation instead of the 6D Gram-Schmidt representation (ablation) | SO(3) rotation autoencoder · Rotation autoencoder | mean geodesic error | No clear effect |
| Use continuous rotation representations instead of discontinuous ones | Rotation autoencoder · SO(3) rotation autoencoder | convergence speed | Helped |
Closest papers by meaning
- Learning with 3D rotations, a hitchhiker's guide to SO(3) (ICML 2024 · similarity 0.90)
- Grounding Continuous Representations in Geometry: Equivariant Neural Fields (ICLR 2025 · similarity 0.86)
- Neural Isometries: Taming Transformations for Equivariant ML (NeurIPS 2024 · similarity 0.85)
- Platonic Representations in the Human Brain: Unsupervised Recovery of Universal Geometry (NeurIPS 2026 · similarity 0.85)
- Continuity-Preserving Convolutional Autoencoders for Learning Continuous Latent Dynamical Models from Images (ICLR 2025 · similarity 0.85)
- Asymptotically Stable Quaternion-valued Hopfield-structured Neural Network with Periodic Projection-based Supervised Learning Rules (NeurIPS 2025 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.