Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds

Xingzhi Sun, Danqi Liao, Kincaid MacDonald, Yanlei Zhang, Guillaume Huguet, Guy Wolf, Ian Adelstein, Tim G. J. Rudner, Smita Krishnaswamy
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1018-1026, 2025.

Abstract

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over SOTA in single-cell population-level trajectory inference.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-sun25c, title = {Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds}, author = {Sun, Xingzhi and Liao, Danqi and MacDonald, Kincaid and Zhang, Yanlei and Huguet, Guillaume and Wolf, Guy and Adelstein, Ian and Rudner, Tim G. J. and Krishnaswamy, Smita}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1018--1026}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/sun25c/sun25c.pdf}, url = {https://proceedings.mlr.press/v258/sun25c.html}, abstract = {Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over SOTA in single-cell population-level trajectory inference.} }
Endnote
%0 Conference Paper %T Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds %A Xingzhi Sun %A Danqi Liao %A Kincaid MacDonald %A Yanlei Zhang %A Guillaume Huguet %A Guy Wolf %A Ian Adelstein %A Tim G. J. Rudner %A Smita Krishnaswamy %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-sun25c %I PMLR %P 1018--1026 %U https://proceedings.mlr.press/v258/sun25c.html %V 258 %X Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over SOTA in single-cell population-level trajectory inference.
APA
Sun, X., Liao, D., MacDonald, K., Zhang, Y., Huguet, G., Wolf, G., Adelstein, I., Rudner, T.G.J. & Krishnaswamy, S.. (2025). Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1018-1026 Available from https://proceedings.mlr.press/v258/sun25c.html.

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