Reproduce “Heavy-Tailed Flow Matching via Random Clocks” on OpenResearch

About this paper

Zhouhao Yang, Yezhen Wang, Kenji Kawaguchi, Vladimir Braverman, Haoyang Cao

Researchers at Johns Hopkins University and the National University of Singapore developed Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that reinterprets heavy-tailed generative processes through a path-valued random clock. This method allows flow matching models to learn various heavy-tailed data distributions, achieving superior mode coverage and tail-statistic recovery while preserving the computational efficiency of flow matching over existing heavy-tailed baselines.

Key insights

• Heavy-tailed source distributions can be realized by marginalizing over a randomly sampled clock, allowing the application of standard conditional Gaussian flow matching techniques.
• Specific choices of random clock laws (e.g., alpha-stable subordinator, inverse-gamma) enable the unified generation of various heavy-tailed data families within the same framework.
• Encoding the clock path via logsignature features is crucial for the neural network to adapt its velocity field to the specific conditional Gaussian space defined by the clock, improving generation accuracy.

Summary by alphaXiv.