GNN-based active inference for Battleship

Active inference models connect beliefs, preferred outcomes, and information-seeking actions, but an implementation can obscure the assumptions behind its displayed quantities. We present a browser-based Battleship dashboard whose executable contract begins with a Generalized Notation Notation (GNN) specification. The assistant performs exact categorical Bayesian inference conditional on a reproducibly sampled finite catalog of legal fleets, and evaluates a one- step preference-and-information objective. An interactive decision explorer exposes occupancy, observation forecasts, information gain, preference cost, action probabilities, hypothetical posteriors, and parameter sensitivity for either actor. The selected fleet remains outside the assistant’s information boundary. We derive the implemented quantities, distinguish expected from realized information, and connect the model to active learning, active search, partially observable planning, and prior Battleship research. A two-fleet example isolates the preference–information trade- off. A retained descriptive demonstration motivates a prospectively specified 1,280-search follow-up across 256 fresh paired catalog/truth units and five strategies. Completion shots, five-shot hits, and normalized label entropy receive 24 planned Holm-adjusted paired sign tests, alongside descriptive paired mean-effect intervals. Standard greedy EFE and pragmatic completion counts tie in every pair. Pure epistemic selection has less favorable completion sign balance in both size strata. At 4096 labels, information weighting has favorable five-shot label-uncertainty sign balance; its completion comparison is not rejected. These findings concern the declared generator and objectives, not a generally superior strategy. Seeded traces, source hashes, tests, and a three-edition manuscript build support inspection and reuse. The contribution is an explicit, composable implementation and its interpretable evidence, rather than a new inference principle, an unrestricted Battleship solver, or a validated educational intervention. A typed core package and headless replay-analysis commands support reuse outside the browser. The Active Inference Institute publishes version 0.4.0 with source and reproducibility materials at ActInfInsti- tute/active_inference_battleship and the manuscript archived on Zenodo, DOI 10.5281/zenodo.23670188. The tagged GitHub release distributes the manuscript, interactive reader, dashboard, and reusable core package.