\appendix

\chapter{补充推导}

\section{梯度下降的推导}
\label{app:gd}

对均方误差损失
\begin{equation}
  J(\theta) = \frac{1}{2m}\sum_{i=1}^{m}\left(h(x^{(i)}) - y^{(i)}\right)^2
  \label{eq:appendix-mse}
\end{equation}
求关于第 $j$ 个参数的偏导，可得
\begin{equation}
  \frac{\partial J(\theta)}{\partial \theta_j}
  = \frac{1}{m} \sum_{i=1}^{m}
    \left( h(x^{(i)}) - y^{(i)} \right) x_j^{(i)}
  \label{eq:appendix-grad}
\end{equation}
式~\ref{eq:appendix-grad} 即梯度项的逐分量形式。

\section{反向传播的链式法则}

略。

\subsection{三级子标题（条目）}

略

\chapter{补充数据}

\section{实验参数}

模型训练使用的主要参数见表~\ref{tab:appendix-params}。

\begin{table}[htbp]
  \centering
  \caption{训练参数设置}
  \label{tab:appendix-params}
  \begin{tabular}{ccc}
    \hline
    编号 & 参数 & 数值 \\
    \hline
    1 & 学习率   & 0.01 \\
    2 & 批大小   & 64   \\
    3 & 迭代次数 & 1000 \\
    \hline
  \end{tabular}
\end{table}

\section{补充结果}

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.225\linewidth,page=3]{abc}
  \caption{附图}
  \label{fig:futu}
\end{figure}

\chapter{代码示例}

\section{代码块}

\begin{lstlisting}[language=Python]
for (int i = 0; i < n; i++) {
  sum += a[i] * w[i];   # 累加加权和
}
\end{lstlisting}

\begin{lstlisting}[language=Python,numbers=none]
for (int i = 0; i < n; i++) {
  sum += a[i] * w[i];   # 累加加权和
}
\end{lstlisting}

\section{等宽字体及代码配色}

\begin{lstlisting}[language=Python, style=codeMono]
for (int i = 0; i < n; i++) {
  sum += a[i] * w[i];   # 累加加权和
}
\end{lstlisting}

\hautocodestyle[vscode]

\begin{lstlisting}[language=JavaScript, style=codeMono]
const sig = x => 1 / (1 + Math.exp(-x));            // sigmoid 激活函数
const pred = (X, w) => X.map(r => sig(r.reduce((s, v, i) => s + v * w[i], 0)));
const loss = (X, y, w) => -y.reduce((s, v, i) => s + v * Math.log(pred(X, w)[i]), 0) / y.length;
const X = [[1,0],[0,1],[1,1]], y = [1,0,1];
let w = [0,0];
for (let t = 0; t < 100; t++) {
  w = w.map((v, j) => v - 0.1 * X.reduce((s, r, i) => s + (pred(X, w)[i] - y[i]) * r[j], 0) / y.length);
}
console.log("权重:", w);                             // 输出结果
console.log("损失:", loss(X, y, w));
\end{lstlisting}

\section{引入代码文件}

\hautocodestyle[print]

\codeinputhl[language=python, numbers=none]{code/test.py}

\hautocodestyle[classic]

\codeinputhl[language=python, style=codeMono]{code/test.py}