标题： 在单细胞VAEs中强制潜在欧几里得几何用于流形插值 显示英文标题

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

摘要： 潜在空间插值是在应用环境中导航深度生成模型的强大工具。 一个例子是单细胞RNA测序，其中现有方法将细胞状态转换建模为具有变分自编码器的潜在空间插值，通常假设线性变化和欧几里得几何。 然而，除非明确强制，潜在空间中的线性插值可能不代表数据流形上的测地线路径，这限制了在数据表示中假设欧几里得几何的方法。 我们引入了FlatVI，一种新的训练框架，它将离散似然变分自编码器的潜在流形正则化为欧几里得几何，特别适用于建模单细胞计数数据。 通过鼓励潜在空间中的直线近似解码后的单细胞流形上的测地线插值，FlatVI提高了与假设欧几里得潜在几何的下游方法的兼容性。 在合成数据上的实验支持了我们方法的理论合理性，而应用于时间分辨的单细胞RNA测序数据则展示了改进的轨迹重建和流形插值。 显示英文摘要

摘要： 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.