Store a pattern as the bottom of an energy valley, then show the network a corrupted version. It doesn’t search — it just rolls downhill, and the bottom of the valley IS the stored memory. Slide recall (or tap) and watch the noise fall away as the energy drops.
A Hopfield associative memory. A 5×5 pattern ξ is stored in the weights W = ξξᵀ (zero diagonal); a corrupted cue is dropped in and the units update by the sign rule sᵢ ← sign(Σ Wᵢⱼsⱼ), which can only DECREASE the energy E = −½ Σ Wᵢⱼsᵢsⱼ. The trajectory is precomputed once; the slider scrubs it. The recall is not a search — the stored pattern is a fixed point / energy minimum the corrupted state falls into. A fail-loud self-check throws unless the energy is monotonically non-increasing along the trajectory and the final state equals ξ exactly.
One stored pattern in 25 units (real Hopfield nets store ~0.14N patterns before crosstalk); async sign updates in a fixed order. The weight matrix, the sign dynamics and the energy are computed exactly.