用微分几何融合谱系信息，更准推断生物演化路径。
Learning Lineage-guided Geodesics with Finsler Geometry
- 引入芬斯勒度量融合空间几何与谱系分类先验
- 在合成与真实数据上提升插值精度
- 适合发育生物学等有明确演化方向的任务
轨迹推断旨在通过动态系统的时序观测点（如时间解析的种群分布）推断未观测时刻的路径，以更好地理解系统演化。以往方法依赖连续几何先验，利用数据相关的空间特征定义黎曼度量。但在许多场景中，存在离散的、有向的可接受转移先验（如发育生物学中的谱系树）。本文提出一种结合几何与分类的芬斯勒度量，同时整合两类先验，在合成数据和真实数据上的插值任务中均取得性能提升。
原文摘要 · Abstract (English)
Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better understanding system dynamics. Previous work has focused on continuous geometric priors, utilizing data-dependent spatial features to define a Riemannian metric. In many applications, there exists discrete, directed prior knowledge over admissible transitions (e.g. lineage trees in developmental biology). We introduce a Finsler metric that combines geometry with classification and incorporate both types of priors in trajectory inference, yielding improved performance on interpolation tasks in synthetic and real-world data.
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