Fresh transfer and the discovery-cost argument [ftip-00NJ]
Fresh transfer and the discovery-cost argument [ftip-00NJ]
Fix a final success threshold and a resource vector before comparing methods. The assisted upper-bound problem is constructive: specify bounded development, a prospective source-selection procedure, contribution production and recipient learning, and establish their joint probability of reaching the threshold. Charge failed development and teaching runs where selection uses them. The marginal comparison discloses earlier contributor development separately; a lifetime claim includes that work under § [ftip-00ND]. Communication length, token count, accelerator work and elapsed time are distinct quantities unless an explicit conversion relates them.
Several controlled comparisons can locate the benefit. Giving the recipient a completed grounded representation measures acquisition after discovery. Replaying a successful curriculum measures learning after its selection. Replacing adaptive teaching with fixed examples tests the value of recipient feedback; varying the final expression size and composition tests reuse. A closed campaign that builds its own curricula, revises representations and updates its models tests affordable reconstruction. The supplied-representation and replay experiments are positive controls, not estimates of unaided discovery cost.
The mechanism predicts that a useful developmental curriculum reduces recipient work on unseen compositions, and that failures caused by lost abstract distinctions decrease after grounded refinement. If gains vanish when the source is removed, depend on near-duplicate evaluation instances, or disappear under a cheap alternative solver, the proposed explanation must change. Measuring these outcomes can reject a candidate construction. An observed advantage over the implemented comparison agents still leaves the all-campaign claim open.
For that claim, start with an arbitrary successful closed campaign in Definition [ftip-00MJ]. Its code search, implicit representations, retrieval, synthetic tasks, self-play, active interventions, training updates, heterogeneous models and resource-allocation choices are all admissible when allowed by the declared endowment and caps. The lower-bound argument must connect its checked fresh-task success to work that every such route incurs. It cannot require the campaign to discover the contributor's particular invariant or follow its curriculum. Direct solving is an alternative to conceptual reconstruction.
A family-specific reduction could show that any successful closed campaign solves an independently hard computational problem, while the bounded developmental process and assistance yield an affordable upper bound under the disclosed prior endowments. A restricted representation language or response interface may admit a first, narrower theorem. Neither case permits assuming that every useful curriculum or representation is negligibly likely under arbitrary adaptive search: that would assume the desired discovery barrier. The absence of the contributor's experience in § [ftip-00N8] supplies the starting condition; the prohibitive cost of every equivalent capability is still to be derived.