Villages in the string landscape
String theory needs the Ricci-flat metric on a Calabi–Yau manifold, and there is no closed form for it. Neural networks can approximate one metric for one shape — but the landscape holds a vast number of shapes. This note asks whether a network trained on a neighbourhood of similar shapes (a "village") transfers to shapes it has never seen.
- Inside a village, one epoch of fine-tuning from the village specialist matches what training from scratch reaches after roughly 185 epochs — and at convergence the warm-started network is still 1.4× more accurate. Scratch does not catch up.
- The village edge is a slope, not a cliff: accuracy degrades smoothly with distance, and warm-start beats an equal-budget scratch run at every radius tested.
- One network for the whole space does not work at this scale. A router plus a set of specialists is the working generalist — so covering the landscape is a tiling problem, not a modelling problem.
Replicate on a second family (a quintic or a CICY), locate the village boundary, then push downstream to Yukawa couplings on a three-generation quotient — where the metric’s accuracy actually cashes out.