用能量引导的几何流匹配，让时间序列更贴合数据本体结构。
Energy Guided Geometric Flow Matching
- 通过得分匹配和退火能量蒸馏学习数据几何度量张量
- 在合成流形上实现接近解析解的测地线插值
- 适合需要精准轨迹建模的生物细胞等时序数据
对时序数据而言，轨迹应贴近数据流形是一种有益的归纳偏置。传统流匹配依赖直线条件路径，而学习测地线的方法多采用径向基函数核或近邻图，面临维度灾难问题。本文提出利用得分匹配与退火能量蒸馏来学习能忠实捕捉底层数据几何的度量张量，从而指导更精确的流形生成。我们在具有解析测地线的合成流形上验证了该方法的有效性，并展示了其在细胞数据插值中的应用效果。
原文摘要 · Abstract (English)
A useful inductive bias for temporal data is that trajectories should stay close to the data manifold. Traditional flow matching relies on straight conditional paths, and flow matching methods which learn geodesics rely on RBF kernels or nearest neighbor graphs that suffer from the curse of dimensionality. We propose to use score matching and annealed energy distillation to learn a metric tensor that faithfully captures the underlying data geometry and informs more accurate flows. We demonstrate the efficacy of this strategy on synthetic manifolds with analytic geodesics, and interpolation of cell
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。