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fix: 修复underline
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YJJ-228 committed Mar 9, 2025
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14 changes: 7 additions & 7 deletions 神经网络与深度学习/2.机器学习概述.md
Original file line number Diff line number Diff line change
Expand Up @@ -165,11 +165,11 @@ $$

$$
\begin{aligned}
\frac{\partial \mathbf{z}^{(l)}}{\partial w_{ij}^{(l)}} &= \left[ \frac{\partial z_1^{(l)}}{\partial w_{ij}^{(l)}}, \dots, \frac{\partial z_i^{(l)}}{\partial w_{ij}^{(l)}}, \dots, \frac{\partial z_{m^{(l)}}^{(l)}}{\partial w_{ij}^{(l)}} \right] \\
&= \left[ 0, \dots, \frac{\partial (\mathbf{w}_{i:}^{(l)} \mathbf{a}^{(l-1)} + b_i^{(l)})}{\partial w_{ij}^{(l)}}, \dots, 0 \right] \\
&= \left[ 0, \dots, a_j^{(l-1)}, \dots, 0 \right] \\
&\triangleq \mathbb{I}_i (a_j^{(l-1)}) \in \mathbb{R}^{m^{(l)}}, \\\\
\frac{\partial \mathbf{z}^{(l)}}{\partial \mathbf{b}^{(l)}} &= \mathbf{I}_{m^{(l)}} \in \mathbb{R}^{m^{(l)} \times m^{(l)}}
\frac{\partial \mathbf{z}^{(l)}}{\partial w_ {ij}^{(l)}} &= \left[ \frac{\partial z_ 1^{(l)}}{\partial w_ {ij}^{(l)}}, \dots, \frac{\partial z_ i^{(l)}}{\partial w_ {ij}^{(l)}}, \dots, \frac{\partial z_ {m^{(l)}}^{(l)}}{\partial w_ {ij}^{(l)}} \right] \\
&= \left[ 0, \dots, \frac{\partial (\mathbf{w}_ {i:}^{(l)} \mathbf{a}^{(l-1)} + b_ i^{(l)})}{\partial w_ {ij}^{(l)}}, \dots, 0 \right] \\
&= \left[ 0, \dots, a_ j^{(l-1)}, \dots, 0 \right] \\
&\triangleq \mathbb{I}_ i (a_ j^{(l-1)}) \in \mathbb{R}^{m^{(l)}}, \\\\
\frac{\partial \mathbf{z}^{(l)}}{\partial \mathbf{b}^{(l)}} &= \mathbf{I}_ {m^{(l)}} \in \mathbb{R}^{m^{(l)} \times m^{(l)}}
\end{aligned}
$$

Expand Down Expand Up @@ -276,8 +276,8 @@ $f(\cdot)$ 为激活函数
作用: 降低特征维数,避免过拟合

常用的汇聚函数
- 最大汇聚(Maximun Pooling): 取一个区域内所有神经元的最大值
- 平均汇聚(Mean Pooling): 一般是取区域内所有神经元的平均值
- 最大汇聚 (Maximun Pooling): 取一个区域内所有神经元的最大值
- 平均汇聚 (Mean Pooling): 一般是取区域内所有神经元的平均值

## 反向传播算法

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