Relaxation times of non-reversible Markov processes

What the math gives to ML

The paper’s transferable asset is an operator-theoretic way to analyze mixing of non-reversible stochastic dynamics through singular values rather than eigenvalues. This suggests a practical diagnostic and control rule for stochastic optimizers: estimate contraction of the optimizer’s transition operator on centered observables, then tune noise, momentum, or step size to improve the singular-value gap and reduce long-lived oscillatory modes. The same construction can be used as a training regularizer by penalizing slow two-step correlations of parameter or representation trajectories. The approach is most promising for momentum SGD, Adam-like methods, and Langevin training, where non-reversibility makes ordinary spectral-gap or autocorrelation diagnostics misleading.