Diffeomorphic Markov Chain Monte Carlo: fast mixing for heavy-tailed distributions

What the math gives to ML

The paper's transferable asset is a radial diffeomorphism that converts an unbounded heavy-tailed distribution into a distribution on a bounded Euclidean ball while explicitly accounting for volume distortion through the Jacobian. This can make Bayesian neural-network posterior sampling more stable when weight posteriors have polynomial tails and posterior gradients vanish at large norms. The direct implementation is a transformed-space MCMC sampler: maintain parameters in a unit ball, map them to unconstrained network weights through radial expansion, and include the Jacobian determinant in the transformed target density. The construction is particularly suitable as a robustness baseline against unconstrained random-walk Metropolis or HMC on heavy-tailed Bayesian neural networks.