Randomized quasi-Monte Carlo integration

What the math gives to ML

The paper provides a principled way to replace independent Monte Carlo samples with randomized, space-filling samples that remain individually unbiased. The transferable asset is the combination of low discrepancy, randomization, and independent replications: smooth expectations can achieve lower integration error than the usual O(n^{-1/2}) Monte Carlo rate while retaining variance estimation. This is directly applicable to neural objectives containing inner expectations, including VAE latent-variable objectives and diffusion noise expectations. The best first experiment is to use randomized low-discrepancy base-noise points for a fixed-compute gradient estimate and measure gradient variance and loss descent against IID sampling.