arXiv：cs.LG· Amartya Banerjee, Harlin Lee, Caroline Moosm\"uller·· 4 小时前
Neural Wasserstein Splines：面向轨迹推断的表示不变二阶先验
Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference
AI 导读
研究者提出 Neural Wasserstein Splines（NWSP），一种在 Wasserstein 平滑先验下学习连续种群曲线的采样方法，用神经网络将隐变量映射到三次样条控制点，无需数值积分即可在任意时刻采样。该方法在 16 项合成与单细胞基准中 11 项排名前二，其惩罚项在 16 项设置中 13 项优于无正则样条，并具备可证明的表示不变性。
正文
Abstract:Population dynamics are often observed only as unpaired snapshots, which leave the evolution between measurements underdetermined. Second-order regularization can constrain it, but a penalty on the accelerations of sampled particles is a prior on joint particle paths, and different particle representations of the same marginal curve can have different acceleration costs. We therefore introduce Neural Wasserstein Splines (NWSP), a sample-based method that learns a continuous population curve under a Wasserstein smoothness prior. A neural network maps latent variables to the control points of a cubic spline in time, so samples at any time come from the spline basis without numerical integration. We project the generator's velocity onto gradients of a finite dictionary of scalar potentials and differentiate this measure-dependent projection in time, obtaining a finite-dimensional surrogate for the intrinsic Wasserstein acceleration, trained jointly with distributional fit losses. For a fixed dictionary and ridge parameter, we prove that the population penalty depends only on the marginal curve and bound its sensitivity to moment-estimation errors. Learned potentials (NWSP-N) sharpen acceleration estimates. On various synthetic and single-cell benchmarks, NWSP is highly competitive with transport and flow-based methods, ranking in the top two in 11 of 16 settings. The penalty improves on an unregularized spline in 13 of 16 settings and, while competitive with a particle-acceleration penalty, adds provable representation invariance.
| Comments: | Code: this https URL |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.19878 [cs.LG] |
| (or arXiv:2610.19878v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19878 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Amartya Banerjee [view email]
[v1]
Wed, 14 Oct 2026 09:32:34 UTC (2,875 KB)
来源：arXiv：cs.LG · arxiv.org