Speaker
Description
An autoregressive neural sampler writes a lattice configuration site by site, each site conditioned on the sites already written, and it returns independent samples with an exact likelihood. Each conditional sees only a context window of fixed reach, and nothing in the architecture says how far that reach has to extend.
Set the reach one unit short of what the target needs and the interior bonds come out if anything too ordered, while the susceptibility can be statistically indistinguishable from the truth. But the susceptibility only integrates the correlation function, and its shape is wrong by an order of magnitude more.
The requirement is combinatorial. In a local model the sites already written act on the rest only through the frontier between them, and the generation order never pushes that frontier further back than its own bandwidth. We prove that a contiguous window represents the exact conditionals of every such target precisely when its reach is at least that bandwidth, the largest gap the order leaves between two coupled sites. Across more than a hundred temperature-conditioned samplers, spanning lattice sizes, boundary conditions, orders, depths and targets beyond Ising, the verdict follows the bandwidth. One unit of bandwidth is enough to flip it, and in a separate pair orders that tie on cut width still split.
The required context can therefore be computed from the interaction graph of any local target before a single training run, and on the torus a well-chosen order drops it from the number of sites to its square root. The thermodynamic observables can pass either way, so a check without ground truth has to read the shape of the correlation function.