A Network That Conserves Energy
A pendulum never forgets its energy, and a trained network has no such number to forget. This post builds a residual network whose hidden state carries a conservation law by construction: the block is a symplectic step of a learned energy, so the quantity is held by the architecture, not encouraged by a loss. The learned pendulum keeps its energy to 0.6% where a plain field model leaks 36%, the classifier lands in the pack on accuracy, and the law pays where composition fails: trained at depth 16 and run at four times that, the plain net gives up 31 points on spirals while the leapfrog net holds.