Riemannian generative decoder

• URL: http://arxiv.org/abs/2506.19133v1
• Date: Mon, 23 Jun 2025 21:06:13 GMT
• Title: Riemannian generative decoder
• Authors: Andreas Bjerregaard, Søren Hauberg, Anders Krogh,
• Abstract summary: We present a new method for learning representations based on manifold-valued latents.<n>Our method is compatible with existing architectures and yields interpretable latent spaces aligned with data geometry.<n>We validate our approach on three case studies -- a synthetic branching diffusion process, human migrations inferred from mitochondrial DNA, and cells undergoing a cell division cycle.
• Score: 11.074080383657453
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Riemannian representation learning typically relies on approximating densities on chosen manifolds. This involves optimizing difficult objectives, potentially harming models. To completely circumvent this issue, we introduce the Riemannian generative decoder which finds manifold-valued maximum likelihood latents with a Riemannian optimizer while training a decoder network. By discarding the encoder, we vastly simplify the manifold constraint compared to current approaches which often only handle few specific manifolds. We validate our approach on three case studies -- a synthetic branching diffusion process, human migrations inferred from mitochondrial DNA, and cells undergoing a cell division cycle -- each showing that learned representations respect the prescribed geometry and capture intrinsic non-Euclidean structure. Our method requires only a decoder, is compatible with existing architectures, and yields interpretable latent spaces aligned with data geometry.

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