梯度為零，為何不是谷底？Zero gradient does not imply a minimum

IDL115 · CH03 · KP03 · 7/44
鞍點沿一個方向上升，沿另一方向下降。 / A saddle rises in one direction and falls in another.

鞍點範例Saddle example

在原點梯度為零，但仍有下降方向。 / The origin is stationary but not minimal.

f(x,y)=x2−y2,∇f(0,0)=0f(x,y)=x^2-y^2,\quad\nabla f(0,0)=0

看曲率Inspect curvature

Hessian 的負特徵值對應局部下降曲率。 / Negative curvature reveals a descent direction.

H=(200−2)H=\begin{pmatrix}2&0\\0&-2\end{pmatrix}

停止判斷Stopping decision

小梯度搭配損失趨勢與驗證集表現判讀。 / Inspect loss trends and validation performance.

教材 / Source KP3 · 目錄 / Index