# Revisiting the Continuity of Rotation Representations in Neural Networks

arXiv: https://arxiv.org/abs/2006.06234 · HTML: https://mlsanity.com/paper/2006.06234/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 9 of 9)

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- [Pose Representations for Deep Skeletal Animation](https://mlsanity.com/paper/2111.13907/) (2021)
- [Exploring the Adjugate Matrix Approach to Quaternion Pose Extraction](https://mlsanity.com/paper/2205.09116/) (2022)
- [Human Motion Synthesis_ A Diffusion Approach for Motion Stitching and In-Betweening](https://mlsanity.com/paper/2409.06791/) (2024)
- [Predicting build orientation for SLM dental parts: a comparison of rotation representations and direct vector regression](https://mlsanity.com/paper/2609.15710/) (2026)
- [PART: Learning 3D Part Assembly and Retrieval with Transformers](https://mlsanity.com/paper/2609.19872/) (2026)

## Abstract (arXiv)

In this paper, we provide some careful analysis of certain pathological behavior of Euler angles and unit quaternions encountered in previous works related to rotation representation in neural networks. In particular, we show that for certain problems, these two representations will provably produce completely wrong results for some inputs, and that this behavior is inherent in the topological property of the problem itself and is not caused by unsuitable network architectures or training procedures. We further show that previously proposed embeddings of SO(3) into higher dimensional Euclidean spaces aimed at fixing this behavior are not universally effective, due to possible symmetry in the input causing changes to the topology of the input space. We propose an ensemble trick as an alternative solution.