Reparameterization through Coverings and Topological Weight Priors
We generalise the reparameterization trick (RT) applied in variational autoencoders (VAEs) letting these have latent spaces of non-trivial topology - i.e. that of base manifolds covered with other ones, on which some technique for RT is available. That is possible since covering maps are measurable - moreover, this allows to establish an inequality on KL-divergence between pushforward (PF) densities on the base latent manifold, bounding it with KL-divergence between pullbacks on the cover, in some cases making the KL-term of VAE's ELBO analytically tractable, despite the topological non-triviality of the supporting latent manifold. Our development follows a route close but somewhat altern...
| Authors | Maxim Beketov, Pavel Snopov |
|---|---|
| Primary category | cs.LG |
| Published | 26 April 2026 |
| Last updated at source | 1 September 2026 |
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