INTERACTIVE FIGURE 8Extract an automaton yourself — L★ against a black-box oracle
oracle: “ring alive?” for move strings over {f = fill inner liberty, g = fill ring liberty}
oracle queries (incl. equivalence sampling): 0 distinct positions probed: 0 hypothesis states: —
The learner knows only the alphabet. Press Next hypothesis ▸.
Angluin's L★, live, against a black box implementing a simplified race rule with the same shape as KataGo's (counting rows plus an absorbing ALIVE state — here: inner group starts with 3 liberties, ring with 6; the ring is read alive while it stays comfortably ahead, and permanently alive once the inner group hits atari). The learner asks only yes/no membership questions, proposes a machine, gets a counterexample, refines. When it converges, the states are laid out by the (inner, ring) liberty count each one corresponds to — a post-hoc placement the learner never saw, revealing that it reconstructed the counting lattice from answers alone. The held-out check at the end mirrors the paper's: thousands of random strings, zero disagreements. The real extraction, against the actual network, produced 19 states from 28 forward passes.