神经网络的基本元素

1. 权重 (w₁, w₂, w₃, ...) ：每个输入都乘以相应的权重。这些权重是模型在训练过程中学习到的参数。
2. 偏置 (b) ：这是一个额外的参数，加到加权输入上以调整激活函数。它有助于模型做出更好的预测。
3. 求和和激活函数 ：输入的加权和加上偏置后，通过一个激活函数 (f)。这个函数决定了神经元的输出。
4. 输出 (hᵥ,ₓ(x)) ：这是神经元在应用激活函数后的最终输出。

数学表示如下：
<span class="katex"><span class="katex-mathml">hw,b(x)=f(WTx+b)<span class="katex-html"><span class="base"><span class="strut"><span class="mord"><span class="mord mathnormal">h<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="pstrut"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">w<span class="mpunct mtight">,<span class="mord mathnormal mtight">b<span class="vlist-s">​<span class="vlist-r"><span class="vlist"><span class="mopen">(<span class="mord mathnormal">x<span class="mclose">)<span class="mspace"><span class="mrel">=<span class="mspace"><span class="base"><span class="strut"><span class="mord mathnormal">f<span class="mopen">(<span class="mord"><span class="mord mathnormal">W<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="pstrut"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">T<span class="mord mathnormal">x<span class="mspace"><span class="mbin">+<span class="mspace"><span class="base"><span class="strut"><span class="mord mathnormal">b<span class="mclose">)

这个方程式表示，输出 <span class="katex"><span class="katex-mathml">hw,b(x)<span class="katex-html"><span class="base"><span class="strut"><span class="mord"><span class="mord mathnormal">h<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="pstrut"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">w<span class="mpunct mtight">,<span class="mord mathnormal mtight">b<span class="vlist-s">​<span class="vlist-r"><span class="vlist"><span class="mopen">(<span class="mord mathnormal">x<span class="mclose">) 是加权输入的和 <span class="math math-inline"><span class="katex"><span class="katex-mathml">WTx<span class="katex-html"><span class="base"><span class="strut"><span class="mord"><span class="mord mathnormal">W<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="pstrut"><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">T<span class="mord mathnormal">x 加上偏置 <span class="math math-inline"><span class="katex"><span class="katex-mathml">b<span class="katex-html"><span class="base"><span class="strut"><span class="mord mathnormal">b 后通过激活函数 <span class="math math-inline"><span class="katex"><span class="katex-mathml">f<span class="katex-html"><span class="base"><span class="strut"><span class="mord mathnormal">f 得到的结果。

图片底部的中文文字是对上述解释的翻译。

 

 激活函数是非线性的：防止多层神经网络坍缩成单层