Marginal assistance and the cost of development [ftip-00ND]
✍️source

    A marginal comparison begins with a specified pretrained lineage and an already-developed contributor. It charges the closed campaign's new search and learning, and the assisted campaign's contribution production, failed help, communication, interpretation, checking and learning. Both face the same final evaluation and resource accounting. Their prior histories are disclosed endowments. A gap here means that assistance makes new acquisition affordable from those starting states; it does not mean that producing the contributor was cheaper than producing the model.

    For an additive scalar work measure, let \(D_M\) be the model lineage's prior development, \(D_C\) the contributor's prior development not already included in \(D_M\), and \(W_0(m)\), \(W_1(m)\) the closed and assisted marginal work for a specified portfolio of \(m\) tasks. With any shared preparation charged once, the corresponding lifetime totals are

    \[ \begin {aligned} T_0(m)&=D_M+W_0(m),\\ T_1(m)&=D_M+D_C+W_1(m). \end {aligned} \]

    Thus \(W_1(m)<W_0(m)\) need not imply \(T_1(m)<T_0(m)\). Shared expertise may be amortized across a declared portfolio; one cannot divide its cost by an arbitrary number of hypothetical future beneficiaries. Human-created training data, cultural resources, teachers and infrastructure follow the same inclusion convention on both sides. Unmeasured historical costs remain unmeasured.

    The full resource comparison is a vector as in Definition [ftip-00MK]. Human time and accelerator work need an explicit conversion before a scalar inequality compares them. Wall time, peak hardware and memory follow the actual schedule, including causal dependencies. A model may copy states and run many experiments in parallel; an environment may impose an interaction rate. Whether simulation or accumulated experience can remove that delay is part of the setting, not an assumed advantage for either side.

    A first proof target is marginal assistance, with bounded prior development specified separately. A lifetime comparison is a stronger additional question. Even with identical architectures, environmental access and prior duration can differ; equalizing architecture alone does not equalize all costs. State whether a claimed prohibitive expense is work, money, memory or elapsed time, and give the corresponding operational cap.