Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation

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Hauptverfasser: Palma, Alessandro, Rybakov, Sergei, Hetzel, Leon, Günnemann, Stephan, Theis, Fabian J.
Format: Preprint
Veröffentlicht: 2025
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author Palma, Alessandro
Rybakov, Sergei
Hetzel, Leon
Günnemann, Stephan
Theis, Fabian J.
author_facet Palma, Alessandro
Rybakov, Sergei
Hetzel, Leon
Günnemann, Stephan
Theis, Fabian J.
contents Latent space interpolations are a powerful tool for navigating deep generative models in applied settings. An example is single-cell RNA sequencing, where existing methods model cellular state transitions as latent space interpolations with variational autoencoders, often assuming linear shifts and Euclidean geometry. However, unless explicitly enforced, linear interpolations in the latent space may not correspond to geodesic paths on the data manifold, limiting methods that assume Euclidean geometry in the data representations. We introduce FlatVI, a novel training framework that regularises the latent manifold of discrete-likelihood variational autoencoders towards Euclidean geometry, specifically tailored for modelling single-cell count data. By encouraging straight lines in the latent space to approximate geodesic interpolations on the decoded single-cell manifold, FlatVI enhances compatibility with downstream approaches that assume Euclidean latent geometry. Experiments on synthetic data support the theoretical soundness of our approach, while applications to time-resolved single-cell RNA sequencing data demonstrate improved trajectory reconstruction and manifold interpolation.
format Preprint
id arxiv_https___arxiv_org_abs_2507_11789
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation
Palma, Alessandro
Rybakov, Sergei
Hetzel, Leon
Günnemann, Stephan
Theis, Fabian J.
Machine Learning
Quantitative Methods
Latent space interpolations are a powerful tool for navigating deep generative models in applied settings. An example is single-cell RNA sequencing, where existing methods model cellular state transitions as latent space interpolations with variational autoencoders, often assuming linear shifts and Euclidean geometry. However, unless explicitly enforced, linear interpolations in the latent space may not correspond to geodesic paths on the data manifold, limiting methods that assume Euclidean geometry in the data representations. We introduce FlatVI, a novel training framework that regularises the latent manifold of discrete-likelihood variational autoencoders towards Euclidean geometry, specifically tailored for modelling single-cell count data. By encouraging straight lines in the latent space to approximate geodesic interpolations on the decoded single-cell manifold, FlatVI enhances compatibility with downstream approaches that assume Euclidean latent geometry. Experiments on synthetic data support the theoretical soundness of our approach, while applications to time-resolved single-cell RNA sequencing data demonstrate improved trajectory reconstruction and manifold interpolation.
title Enforcing Latent Euclidean Geometry in Single-Cell VAEs for Manifold Interpolation
topic Machine Learning
Quantitative Methods
url https://arxiv.org/abs/2507.11789