Global Convergence of Third-Order Langevin Dynamics for Non-Convex Optimization via Simulated Annealing

arXiv:2609.28611 · math.NA, cs.NA, math.OC, math.PR, stat.ML · Submitted 2026-09-23 · Read on arXiv

math.NA, cs.NA, math.OC, math.PR, stat.ML

Submitted: 2026-09-23

Updated: 2026-10-01

Code: https://github.com/gagawjbytw/simulated-annealing-third-order-langevin

Terminology

• Langevin Dynamics — 26× in this paper · explained in 2 episodes
• Fisher Information — 14× in this paper · explained in 3 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Convergence Guarantees — 4× in this paper · explained in 3 episodes
• Diffusion Processes — 4× in this paper · explained in 2 episodes
• Metastability — 4× in this paper · explained in 3 episodes
• Regularization — 4× in this paper · explained in 3 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Kullback-Leibler (KL) Divergence — 1× in this paper · explained in 3 episodes
• Lyapunov function — 1× in this paper · explained in 2 episodes
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Stochastic Dynamics — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• High-Order Langevin Monte Carlo Algorithms
• Weak Equilibrium Measures and Capacity--Hitting Identities for the Hypoelliptic Third-Order Langevin Diffusion
• Eyring-Kramers Law for the Underdamped Langevin Process
• Fast and Efficient Parallel Sampling Using Higher Order Langevin Dynamics
• An Eyring--Kramers Law for the Hypoelliptic Third-Order Langevin Diffusion

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