Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentials
The paper proposes a momentum-preconditioned Langevin sampler for matrix-valued Gibbs distributions with rougher, nonconvex potentials.
Makras and Sabanis define non-quadratic kinetic energies whose gradients tame momentum spectrally in a new underdamped Langevin system. They prove the dynamics preserves the target Gibbs measure and converges exponentially in weighted total variation distance. The paper also shows the Euler-Maruyama discretization has time-uniform moment bounds without altering the potential gradient, supporting stability of the sampling algorithm. ArXiv · AI/CL/LG's note
Makras and Sabanis define non-quadratic kinetic energies whose gradients tame momentum spectrally in a new underdamped Langevin system. They prove the dynamics preserves the target Gibbs measure and converges exponentially in weighted total variation distance. The paper also shows the Euler-Maruyama discretization has time-uniform moment bounds without altering the potential gradient, supporting stability of the sampling algorithm. ArXiv · AI/CL/LG's note
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