gcn.tex (1238B)
1 \begin{frame}{Capturing Neighborhoods}% 2 \begin{block}{Modeling Hypothesis} 3 \hypothesis{1-neighborhood}: Two samples with the same neighborhood in the relation extraction graph convey the same relation.\\ 4 \( \forall a, a'\in\arcSet\colon \gfeneighbors(a) = \gfeneighbors(a') \implies \gfrelation(a)=\gfrelation(a') \) 5 \end{block}% 6 \begin{columns}% 7 \begin{column}{6.5cm}% 8 \begin{block}{Graph Convolutional Network} 9 \centering% 10 \input{mainmatter/graph/graph convolution parallel.tex}% 11 12 \begin{tikzpicture} 13 \node[inner sep=1mm, draw] (v) at (0, 0) {\(v\)}; 14 \node[inner sep=1mm, draw] (n1) at (1, 1) {\(n_1\)}; 15 \node[inner sep=1mm, draw] (n2) at (-1.5, 0.75) {\(n_2\)}; 16 \node[inner sep=1mm, draw] (n3) at (1.75, -0.25) {\(n_3\)}; 17 18 \draw[arrow] (n1) -- (v) node[midway, above left, yshift=-1mm, xshift=1mm] {\(\mtrx{W}\)}; 19 \draw[arrow] (n2) -- (v) node[midway, above] {\(\mtrx{W}\)}; 20 \draw[arrow] (n3) -- (v) node[midway, below] {\(\mtrx{W}\)}; 21 \end{tikzpicture}% 22 \end{block}% 23 \end{column}% 24 \begin{column}{6.5cm}% 25 \begin{block}{Graph Isomorphism}% 26 \centering% 27 \input{mainmatter/graph/isomorphism.tex}% 28 \end{block}% 29 \end{column}% 30 \end{columns}% 31 \end{frame}