Indexing the archive…
Your Universe of Digital Possibilities
Train a model to predict who repays a loan, publish its rule, and people move to the right side of it. Retrain on the new data and the rule moves too. Whether the two settle down depends on one ratio, and the place they settle is not the best one.
Deploy θₜ, collect the data D(θₜ) the deployment produces, refit on it, deploy again. With a γ-strongly convex, β-smooth loss and a distribution map that moves ε per unit of θ, each step contracts by εβ/γ.
A model that is optimal for the data it itself induces — calibrated against the future it causes. Retraining reaches it when ε < γ/β. It is not in general the performative optimum, which minimises the loss counting the data’s reaction.
A published rule invites a best response: change your features to improve your verdict, at a cost. With a reward linear in the rule and a quadratic cost the response is a shift of εθ — the location family in which the stable point and the optimum have closed forms.
The ninth prophecy is a model in production. The Proxy’s metric drifted because people aimed at it; here the model notices the drift, retrains, and is aimed at again. Whether the chase ends is a contraction condition, the same arithmetic as The Cobweb’s farmers: a response map with slope below one settles. Where it ends is a fixed point of the model and the world together — calibrated against the future it causes, not the past it saw. Next, The Prophecy lays every instrument’s response map side by side.