Generative Reach in Active Learning under Non-Stationarity

Active learning is commonly formulated as a problem of selecting the next observation that is maximally informative for the current predictive model. Uncertainty sampling, information gain, and representative subset selection all instantiate variants of this idea. This paper investigates a different hypothesis- a useful query may be valuable not because it most reduces present uncertainty, but because its incorporation changes the organization of what the learner can subsequently construct, infer, or learn. We call this quantity generative reach. We report a sequence of progressively harder computational experiments designed both to test and to falsify this proposal. We test it on a hard construction in which local structural importance, immediate utility, and long-horizon generativity are deliberately separated. Deep modules have low immediate branching but support delayed compositional reuse; decoy modules have high local branching but terminate. Generative reach yields a mean final reach of 42.71 versus 33.45 for uncertainty sampling, 38.35 for immediate reach, and 32.01 for a local structural heuristic. Crucially, these gains occur with nearly the same number of primitive products discovered, indicating that the advantage lies in the organization and reuse potential of acquired knowledge rather than in raw acquisition volume. Adding uncertainty as an independent objective does not reliably improve over pure expected future reach. Active learning under generative, compositional, and non-stationary conditions should optimize expected future learnability, not merely present uncertainty.