Statistical Structure as an Interface to Frozen Computation

When a frozen model's parameters cannot be changed and no dedicated control input can be added, statistical structure in its ordinary context can still serve as an interface to its computation. Using Prior-Data Fitted Networks (PFNs) as a controlled testbed, we construct training distributions in which a latent control state is expressed only through a statistical property of the context, making that property a carrier of the state. After training, rewriting this carrier alone causally selects which computation the frozen model performs, with graded, multi-state control. How readily such an interface is learned is not fixed by the information it provides: across 48 carriers calibrated so that a Bayes-optimal decoder recovers the state from a 128-row context with the same accuracy, the number of training steps a PFN needs to read the carrier varies twelve-fold with its statistical structure. Interventions on prior mass, evidence strength, and training support show that a carrier's meaning is assigned by the training distribution: within the studied PFN families, predictions closely track the posterior it implies, multiple carriers combine according to learned likelihoods, and state combinations absent from training are increasingly suppressed with continued optimization. In pretrained language models, statistical properties of demonstrations already provide graded, multi-state behavioral control without any deliberate interface training. A property that shifts behavior, however, cannot in general be assigned an arbitrary new meaning by in-context demonstrations, and whether it can depends strongly on how the property is concretely instantiated in the prompt. Together, these results establish statistical structure as a writable input-side interface to frozen computation and characterize the principles governing its acquisition, meaning, and limits.