6D vs Euler rotation regression

Shows the continuous 6D rotation representation is far easier for a network to regress than Euler angles.

Trained from scratch in Ropedia Academy — an interactive, bilingual course on embodied & spatial AI. Educational model: small and quick to train; the value is the method and a reproducible pipeline, not a leaderboard score. Try it live in the Ropedia demos Space.

At a glance

Dataset

• Name: Random SO(3) rotations
• Type: synthetic — procedural
• Size / stats: uniform rotations via random quaternions; input = rotation applied to 8 fixed 3D points (24-D); 256/batch
• Split: generative (infinite)
• Source: procedural

Training config

Adam (lr 1e-3), 3000 steps; geodesic rotation loss; two heads (6D vs Euler) compared.

Evaluation results

Inference example

import torch
state = torch.load("rot6d.pt", map_location="cpu")   # this repo's checkpoint
# Rebuild the exact module from the lab notebook (see "Reproduce"), then:
# model.load_state_dict(state); model.eval()

Limitations

Educational scale. Trained quickly on CPU on small or synthetic data, so absolute numbers are not competitive with production systems — the value is the method and a reproducible pipeline. No large-scale data, no hyperparameter sweep, and no multi-seed variance is reported. Not for production use.

Failure cases

The Euler baseline fails near gimbal lock / the ±180° wrap (a representation discontinuity) — exactly what 6D fixes.

Reproduce / train your own

One click: open the notebook in Colab → Runtime → GPU → Run all, then run its Publish to the Hugging Face Hub cell.

From a shell:

git clone https://github.com/ChaoYue0307/ropedia-academy.git && cd ropedia-academy
pip install torch numpy matplotlib scikit-learn scikit-image gymnasium
jupyter nbconvert --to notebook --execute notebooks/training/A_rotation_6d.ipynb --output run.ipynb
# optional: override training length, e.g.  STEPS=2000  (or EPISODES=600)  before running

Files

• figure.png
• metrics.json
• rot6d.pt

License

Code & weights: MIT (this repository) — educational use encouraged.
Data: generated procedurally in the notebook — no external dataset.

Citation

If you use this model or the course materials, please cite:

@misc{ropedia_academy,
  title  = {Ropedia Academy: an interactive course on embodied & spatial AI},
  author = {Ropedia Academy},
  year   = {2026},
  howpublished = {\url{https://chaoyue0307.github.io/ropedia-academy/}}
}

Method / original work: Zhou et al., On the Continuity of Rotation Representations in Neural Networks, CVPR 2019.

Related assets

• 🚀 Live demos: https://huggingface.co/spaces/cy0307/ropedia-demos
• 🤗 All trained models + collection: https://huggingface.co/cy0307
• 📚 Course & all labs: https://chaoyue0307.github.io/ropedia-academy/ · Labs tab
• 💻 Source / notebooks: github.com/ChaoYue0307/ropedia-academy

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Part of the Ropedia Academy trained-model collection. Contributions & issues welcome on GitHub.