Constructing VAE Latent Spaces with Prescribed Topology
Variational autoencoders (VAEs) learn low-dimensional latent representations of high-dimensional data. When the data lies on a manifold with non-Euclidean topology, the standard Gaussian prior introduces a topological mismatch that degrades reconstruction quality and prevents faithful representation. We present a constructive mathematical framework that resolves this mismatch for all manifolds that admit a product covering space. These are manifolds expressible as products of elementary factors (circles, intervals, or lines) or as quotients of such products by a finite symmetry group. The class includes cylinders, tori, Möbius strips, Klein bottles, and real projective spaces. Factorized ...
| Authors | Jilles S. van Hulst, Jakub M. Tomczak, W. P. M. H. Heemels et al. |
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| Primary category | cs.LG |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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