Commit caac3b7a by xiaotong

tensor of neural networks

parent 1037ae94
\frametitle{线性变换(续)}
\begin{itemize}
\item 线性变换也适用于更加复杂的情况,这也给神经网络提供了拟合不同数据分布的能力
\begin{itemize}
\item 比如,我们可以把三维图形投影到二维平面上
\item 再比如,我们也可以把二维平面上的图形映射到三维平面上
\end{itemize}
\end{itemize}
\vspace{1em}
\newcommand{\plane}[1]{
(-1.95, #1, 1.35) --
++(3.6, 0.6, 0.0) --
++(0.3, -1.8, -2.7) --
++(-3.6, -0.6, -0.0) --
cycle}
\newcommand{\nullspacepicture}{
% bottom part of the row space line
\draw (0,0,0) -- (0.3,-1.8,1.233);
% five planes
\draw[fill=gray!20]\plane{-0.2};
\draw[fill=gray!20]\plane{0.2};
\draw[fill=blue!70!gray]\plane{0.6};
\draw[fill=gray!20]\plane{1};
\draw[fill=gray!20]\plane{1.4};
% top part of the row space line
\draw (-.094,.562,-.385) -- (-0.3,1.8,-1.233);
}
\newcommand{\rangepicture}[1]{
% axes
\draw[help lines,->] (-2,0) -- (2,0);
\draw[help lines,->] (0,-2) -- (0,2);
% the line and circles
\draw (1,-2) -- (-1,2);
\draw[fill=#1] (0,0) circle (2.5pt);
\draw[fill=gray!50] (0.2,-0.4) circle (2.5pt);
\draw[fill=gray!50] (0.4,-0.8) circle (2.5pt);
\draw[fill=gray!50] (-0.2,0.4) circle (2.5pt);
\draw[fill=gray!50] (-0.4,0.8) circle (2.5pt);
}
\begin{tikzpicture}[scale=0.95]
\centering
\nullspacepicture
% the label
\node at (-2,1.8) {$\mathbb{R}^3$};
% arrow between diagrams
\path[->] (3,0) edge[bend left] node[above] {线性变换} (4.5,0);
\begin{scope}[xshift=7cm]
\rangepicture{blue!70!gray}
\node at (1.8,1.8) {$\mathbb{R}^2$};
\end{scope}
\end{tikzpicture}
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