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Your Universe of Digital Possibilities
How does a machine find the best answer when the landscape is full of traps? Gradient descent — The Descent — just rolls downhill and stops in the first valley it meets. Annealing borrows a trick from metal and glass: heat the search until it jitters freely, then cool it slowly. While hot it accepts the occasional worse move (with probability e−ΔE/T) and so climbs out of shallow traps; as it cools it settles, and if you cool slowly enough it freezes in the global minimum. The deepest answers are found not by always improving — but by sometimes accepting worse.
Always take a downhill move; take an uphill move of cost ΔE only with probability e−ΔE/T. High T accepts almost anything; as T → 0 only improvements pass. This one rule lets a search climb out of a trap.
In thermal equilibrium a state of energy E is occupied with weight e−E/kT. Temperature sets how readily the system pays energy to leave a comfortable valley — the physics annealing borrows and aims.
Temperature falls a little each sweep. Cool slowly (α → 1, anneal) and the search settles in the global minimum; cool fast (quench) and it freezes wherever it happens to be — a defect.
Annealing’s opposite number — pure downhill, never uphill, so it halts in the first valley it meets (The Descent, INST·27). The Anneal adds temperature to climb back out, then removes it to settle.
This is the rack’s optimization instrument — the decide verb of the engine cast as search. It runs the exact Metropolis–Boltzmann rule of The Threshold (INST·04) and the temperature/entropy of The Arrow (INST·18), but turns physics into an algorithm: melt the problem, then cool it. It is the global-search twin of The Descent (INST·27), which only flows downhill and traps in the nearest valley — and it moves by The Walk’s (INST·19) random proposals, kept or rejected by a single exponential.