Reproduce “Revisiting the Continuity of Rotation Representations in Neural Networks” on OpenResearch

About this paper

Sitao Xiang, Hao Li

A topological analysis reveals that neural networks inherently produce 180-degree rotation errors when converting SO(3) to quaternions or Euler angles, and that input symmetries compromise standard continuous representations. The "self-selected ensemble" method, employing four or more continuous functions, effectively overcomes these topological limitations, reducing maximum errors for 3D rotations to approximately 0.1 degrees.

Key insights

• Any continuous neural network function converting 3D rotation matrices to quaternions or Euler angles is topologically guaranteed to produce a 180-degree error for at least one input rotation.
• Input data with rotational symmetries can cause even topologically continuous higher-dimensional embeddings (e.g., R^5, R^6) to incur large errors, often matching derived theoretical lower bounds (e.g., 120 degrees for D2 symmetry).
• An ensemble of four specifically designed continuous functions is theoretically sufficient to accurately represent all 3D rotations without encountering 180-degree errors or gimbal lock.

Summary by alphaXiv.