Place the probe on the terrain or use the exact start. Predict before moving: gradient gives a local direction, not a safe jump size.
The saved lesson starts on loss x minus one squared plus twice y plus one half squared. At x three and y two, loss is sixteen point five and gradient is four, ten. Gradient descent subtracts learning rate times gradient. With rate point one, the next point is two point six, one, whose loss is seven point zero six. The drawn displacement uses sixty pixels for each coordinate unit; the downward gradient step changes x by minus point four and y by minus one. This is a deterministic two-variable teaching surface, not training a neural network. A locally downhill direction does not guarantee that a large finite step lowers loss. Keep the exact starting point and change rate to point six. Subtracting point six times gradient four, ten yields point six, minus four. Its loss is twenty-four point six six, which exceeds sixteen point five. These bars measure actual loss on a common scale of twenty pixels per loss unit. The source calls this overshoot and asks you to diagnose it using the measured trajectory. It does not invoke random noise or reverse the gradient sign. The transfer surface is x plus one point five squared plus one half times y minus one squared. From two, minus two, its gradient is seven, minus three. Subtracting rate point two moves x down to point six while raising y to minus one point four. Loss falls from sixteen point seven five to seven point two nine. These positions use eighty pixels per coordinate unit. The negative y-gradient must be subtracted, so y increases. The lesson exports the entire trajectory, optimizer velocity and mastery answers; its mastery badge records completed source conditions rather than proving general optimization skill.