THE FOLD / GRIND / GRADIENT DESCENT / THE BOWL
THE BOWL
roll downhill until the floor stops falling
loss f(x,y)=x²+y² : —
position : — · step 0
η learning rate 0.30
fate: —
LIT Genuine gradient descent. The gradient of f(x,y)=x²+y² is (2x,2y); each step is x←x−η·2x. For this quadratic the update multiplies the coordinate by (1−2η), so it provably converges iff |1−2η|<1 (0<η<1), lands exactly on 0 at η=0.5, and diverges for η≥1. The path, the loss, and the fate readout are all computed live — no scripted animation.
FIG The 'ball rolling into a bowl' and the arcade dressing are the metaphor; the bowl is a top-down contour plot, not a real 3D render. The math underneath is the honest part.
FIG The 'ball rolling into a bowl' and the arcade dressing are the metaphor; the bowl is a top-down contour plot, not a real 3D render. The math underneath is the honest part.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GRADIENT DESCENT · David Lee Wise (ROOT0), with AVAN