# 深度学习: BP (反向传播) 计算 & 链式法则

## BP

Arg:

• ωω\omega：欧米茄；
• ηη\eta：艾塔。

Note

• BP中的 ∂L∂ωn∂L∂ωn\frac{\partial L}{\partial \omega^{n}} 和 ∂L∂xn∂L∂xn\frac{\partial L}{\partial x^{n}} 的计算结果 来源于 对 前馈计算时 的 L=f(wnxn)L=f(wnxn)L = f(w^{n}x^{n}) 的求导

## 链式法则

∂L∂ωn=∂L∂xn+1∂xn+1∂ωn=(∂L∂xn+1)∂xn+1∂ωn=(∂L∂xn+2∂xn+2∂xn+1)∂xn+1∂ωn=(∂L∂xn+3∂xn+3∂xn+2∂xn+2∂xn+1)∂xn+1∂ωn∂L∂ωn=∂L∂xn+1∂xn+1∂ωn=(∂L∂xn+1)∂xn+1∂ωn=(∂L∂xn+2∂xn+2∂xn+1)∂xn+1∂ωn=(∂L∂xn+3∂xn+3∂xn+2∂xn+2∂xn+1)∂xn+1∂ωn\frac{\partial L}{\partial \omega^{n}} = \frac{\partial L}{\partial x^{n+1}} \frac{\partial x^{n+1}}{\partial \omega^{n}} = (\frac{\partial L}{\partial x^{n+1}}) \frac{\partial x^{n+1}}{\partial \omega^{n}} = (\frac{\partial L}{\partial x^{n+2}} \frac{\partial x^{n+2}}{\partial x^{n+1}}) \frac{\partial x^{n+1}}{\partial \omega^{n}} = (\frac{\partial L}{\partial x^{n+3}} \frac{\partial x^{n+3}}{\partial x^{n+2}} \frac{\partial x^{n+2}}{\partial x^{n+1}}) \frac{\partial x^{n+1}}{\partial \omega^{n}}

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