Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference

Key points

• Population dynamics are often observed only as unpaired snapshots, which leave the evolution between measurements underdetermined.1
• 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.1
• 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.1
• Learned potentials (NWSP-N) sharpen acceleration estimates.1

Sources (1)

• [1]Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 09:32 AM

  We therefore introduce Neural Wasserstein Splines (NWSP), a sample-based method that learns a continuous population curve under a Wasserstein smoothness prior.

  Population dynamics are often observed only as unpaired snapshots, which leave the evolution between measurements underdetermined.

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