深度学习应用到的数学知识

2019-03-05  本文已影响0人  kokana

导数

f'(a) = \lim_{h\to0}\frac {f(a + h) - f(a)}{h}

导数的基本求导法则传送门

梯度和Hessian矩阵

f'(x); \Delta f(x) = \frac {\delta f(x)}{\delta x} = \begin{bmatrix} \frac {\delta f(x)}{\delta x_1} \\\vdots\\ \frac {\delta f(x)}{\delta x_n}\end{bmatrix} \quad

f''(x); H(x) = \Delta ^ 2 f(x) = \begin{bmatrix} \frac {\delta ^2 f(x)}{\delta x^2_1}&\frac {\delta ^2 f(x)}{\delta x_1\delta x_2}&\dots & \frac {\delta ^2 f(x)}{\delta x_1\delta x_n} & \dots \\ \frac {\delta ^2 f(x)}{\delta x_2\delta x_1}& \frac {\delta ^2 f(x)}{\delta x^2_2} \\ &&\ddots \\\frac {\delta ^2 f(x)}{\delta x_n\delta x_1}&\frac {\delta ^2 f(x)}{\delta x_n\delta x_2}&& \frac {\delta ^2 f(x)}{\delta x^2_n}\end{bmatrix}

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