Covering-Space Normalizing Flows: Approximating Pushforwards on Lens Spaces
This work addresses a domain-specific problem in geometric machine learning for approximating distributions on non-Euclidean spaces, which is incremental as it builds on existing normalizing flow techniques.
The paper tackles the problem of approximating pushforward distributions on lens spaces using normalizing flows, and demonstrates the method by approximating pushforward densities from von Mises-Fisher and symmetric Boltzmann distributions on S^3, with specific applications like modeling benzene.
We construct pushforward distributions via the universal covering map rho: S^3 -> L(p;q) with the goal of approximating these distributions using flows on L(p;q). We highlight that our method deletes redundancies in the case of a symmetric S^3 distribution. Using our model, we approximate the pushforwards of von Mises-Fisher-induced target densities as well as that of a Z_12-symmetric Boltzmann distribution on S^3 constructed to model benzene.