ML: Sampling

Machine-learning ideas tagged Sampling in the ML taxonomy of the Math2NN corpus.

2 ideas found

ML: Sampling Math: Spectral theory Clear all

✗ Failed on benchmark 2026

Cubic-Rate Third-Order Langevin Optimizer

Replace the usual parameter-plus-momentum Langevin state with a three-level chain consisting of parameters, velocity, and acceleration, while injecting Gaussian noise only into the highest auxiliary state. At a saddle, the escaping direction has a positive rate given by a cubic characteristic equation; use this rate to choose damping or adapt the temperature so that basin escape is accelerated without making the dynamics unstable.

Useful7/10

Difficulty5/10

Novelty6/10

Dynamics Speedup Stability Sample efficiency

Paper: An Eyring--Kramers Law for the Hypoelliptic Third-Order Langevin Diffusion arXiv:2607.20882

Unverified 2026

Dual-Gibbs Gaussian latent layer

Replace slow primal-coordinate Gibbs sampling of a graph-structured Gaussian latent feature field with Gibbs sampling in the Fourier-dual factor graph. Use the primal convergence formula to determine when dual sampling is worthwhile, and map dual samples back to neural features through the graph incidence operator.

Useful6/10

Difficulty7/10

Novelty7/10

Sampling Speedup Stability Sample efficiency

Paper: Accelerated Random-Sweep Gibbs Sampling for Gaussian Graphical Models via Dual Normal Factor Graphs arXiv:2607.28706