Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows
This provides a novel computational tool for researchers in statistical physics and computer science to analyze many-body systems, though it is incremental as it applies existing methods to a new domain.
The paper tackled modeling complex spin-glass systems using deep generative models with normalizing flows, demonstrating that key physical properties like multi-modal distributions and topological structures can be learned, with the learning process itself exhibiting a spin-glass phase transition.
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning. Computing the underlying structure and dynamics of such complex systems is extremely difficult due to the combinatorial explosion of their state space. Here, we develop deep generative continuous spin-glass distributions with normalizing flows to model correlations in generic discrete problems. We use a self-supervised learning paradigm by automatically generating the data from the spin-glass itself. We demonstrate that key physical and computational properties of the spin-glass phase can be successfully learned, including multi-modal steady-state distributions and topological structures among metastable states. Remarkably, we observe that the learning itself corresponds to a spin-glass phase transition within the layers of the trained normalizing flows. The inverse normalizing flows learns to perform reversible multi-scale coarse-graining operations which are very different from the typical irreversible renormalization group techniques.