Deep Learning - Gradient and Directional Derivative

Derivative 導數

Derivative f’ 是 f 增長或減少之速度的函數或數值

Example

Gradient of

The gradient at the point(1, -1) is

unit vector

Let be a unit vector

The rate of change in the direction :

Directional Derivative

Example

Find the directional derivative of at the point in the direction of

The gradient of

Let be the unit vector in the direction of

The

The derivative of at in the direction of is:

Greatest

Greatest increase

The greatest value of is (if )

is the direction of

The direction of greatest increase of is the same direction as the gradient vector

Greatest decrease

The greatest negative value of is (if )

is the opposite direction of

The direction of greatest decrease of is the opposite direction to the gradient vector

Reference

• 黃貞瑛老師的深度學習課程 - Gradients and Directional Derivative

• 記筆記順便練習 語法

• 語法筆記