Proper implementation of the no‑U‑turn mechanism for RMHMC

Develop and validate a proper implementation of the no‑U‑turn (NUTS) mechanism for Riemannian‑manifold Hamiltonian Monte Carlo that reliably avoids random‑walk behavior, analogous to its established use in Euclidean HMC.

Background

No‑U‑turn mechanisms have been influential in improving Euclidean HMC by mitigating random‑walk behavior and adaptively choosing path lengths.

Although a no‑U‑turn mechanism has been proposed for RMHMC, the authors explicitly note that it has not yet been properly implemented, leaving a practical algorithmic gap that could significantly impact RMHMC performance.

References

For example, avoiding random-walk behavior with a no-U-turn mechanism was proposed for Euclidean HMC [Hoffman2014] and RMHMC [Betancourt2013b], but it has not yet been properly implemented for the latter.

— Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models  (2511.06407 - Hayakawa et al., 9 Nov 2025) in Section 4 (Discussion)