Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling

What the math gives to ML

The paper provides a constructive multiscale sampling mechanism for frustrated systems: transform configurations into wavelet coefficients, learn conditional distributions of fine-scale coefficients given coarser coefficients, and sample recursively from coarse to fine. Its key transferable asset is a factorization of a difficult high-dimensional distribution into scale-conditioned sampling problems whose conditional dynamics remain decorrelated in O(1) sweeps per scale, giving O(log L) total scale complexity. For neural networks, the most direct use is a learned wavelet-coordinate sampler for spatial energy-based models or diffusion-like inference, replacing pixel-space local MCMC with hierarchical conditional generation. The falsifiable tradeoff is that mixing should become nearly scale-independent while distributional error decreases as the conditional model becomes more expressive.