New Algorithm Learns AC^0 Circuits Under Correlated Distributions

A significant advancement in computational learning theory has been made with the development of a quasipolynomial-time learner for constant-depth circuits, known as AC^0. Previously, such learning guarantees were primarily established for uniform distributions or specific Gibbs distributions with strong spatial mixing and polynomial growth. This new research extends these capabilities to a broader class of correlated distributions. The key innovation lies in its ability to learn AC^0 under graphical models that support efficient local samplers, effectively removing the restrictive polynomial-growth requirement found in earlier work. This is achieved through a novel low-degree approximation for Gibbs distributions, which is derived by simulating and appropriately truncating the classical Glauber dynamics. This framework has practical applications, enabling the learning of two-spin systems, including the hard-core model and Ising model, on any bounded-degree graphs. Crucially, it operates in regimes that approach their respective sampling thresholds, pushing the boundaries of what is learnable under complex, correlated data distributions.