Conformal Coordinate Frames for Disentanglement

Edmond Cunningham

Track: tiny paper (up to 4 pages)

Keywords: disentanglement, independent component analysis, independent mechanisms, coordinate frame

TL;DR: We propose learning a conformal frame as a scalable alternative to global conformal ICA for disentangled representation learning.

Abstract:

Disentangled representations are central to interpretable machine learning, yet learning them without supervision is unidentifiable.
Conformal ICA, a special case of independent mechanism analysis (IMA), provides identifiability guarantees but is too restrictive to be practically useful. We propose to locally approximate conformal ICA by learning a conformal frame field that fits data, is integrable, and has implicit independent components. We enforce integrability and statistical independence through stochastic losses in a scalable way that require only Jacobian-vector products. On Neal's funnel distribution in dimensions 4 through 64, our approach consistently recovers the ground truth structure, demonstrating that local conformal frame fields offer a scalable foundation for geometrically grounded disentanglement.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Submission Number: 126