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MHYCWasTaken committed Apr 15, 2023
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47 changes: 45 additions & 2 deletions EP05 梯度下降/EP05.md
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---

欢迎回来
现有一函数

$$
f(x)=x^2
$$

图像如下

![fx](images/fx.png)

现在函数图像上有一点 $Q$,如何找到 $Q'$ 使得 $Q'$ 点的 $y$ 值最小?

如果你是人类,应该可以一眼看出当 $x$ 取 $0$ 时, $y$ 值最小

但是很可惜,神经网络不会想你一样思考,那么神经网络如何找到最低点?

换句话说,当你作为一个点落在函数图像上时,怎么找到最低点?




先回到EP02中的简易单层网络,回顾一下之前的参数是如何自动调整的

```mermaid
graph LR
a(X1); b(X2); c(y); d(Y); e(W+=ΔW); f(END)
a --W1--> c
b --W2--> c
c --> d
d -- correct --> f
d -- wrong --> e
e --> f
```

那么 $\Delta W$ 如何计算?

$$
(Y-y)X_i
$$

由于 $Y$ 和 $y$ 只有 $0$ 和 $1$

- 当判断错误,结果为蛇时,期望值Y为1F,现值y为0F,Y-y为1,即W+=ΔW
- 当判断错误,结果为鳄鱼时,期望值Y为0F,现值y为1F,Y-y为-1,即W-=ΔW


上一节我们的神经网络可以在人工调节下分隔线性不可分的数据了,这次我们的目标是让机器自动调整参数,完成分类

首先,再仔细看一看这个神经网络

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