Review for NeurIPS paper: Disentangling by Subspace Diffusion

Strengths: This paper provides new insights into the problem of disentangling independent latent factors, viewed here through the lens of factorizing groups of transformations on a data manifold. The authors base their construction on the de Rham decomposition, which itself is based on the holonomy group that considers parallel transport over loops on a manifold. Essentially, the authors seek to extract multiple representations of input data, such as each of them encodes a submanifold with holonomy group independent from all other submanifolds. This provides an important formalism to an important problem that is often ill defined, with mostly heuristic qualitative goals that depend on specific applications rather than studied with rigor. The construction itself here is based on extending the work of Singer and Wu on vector diffusion maps, which enriches more traditional manifold learning by encoding information about tangent spaces and the operation of the connection Laplacian on tangent vector fields.