topological similarity.tex (913B)
1 \begin{frame}{How to Exploit the Graph for Relation Extraction} 2 \begin{block}{Redefining similarity} 3 We keep the \alert{linguistic} similarity from MTB:\\ 4 \hspace{2cm}\(\operatorname{sim}_\text{ling}(x, x') = \operatorname{sigmoid}\left(\bertcoder(x)\transpose \bertcoder(x')\right)\) 5 6 \bigskip 7 8 But also define a \alert{topological} similarity: 9 10 Either using GCN:\\ 11 \hspace{2cm}\(\operatorname{sim}^\text{GCN}_\text{topo}(x, x') = \operatorname{sigmoid}\left(\operatorname{GCN}(G)_x\transpose \operatorname{GCN}(G)_{x'}\right)\) 12 13 Or 1-Wasserstein:\\ 14 \hspace{2cm}\(\operatorname{sim}^{W_1}_\text{topo}(x, x') = -W_1(\symfrak{S}(x, 1), \symfrak{S}(x', 1))\) 15 16 \bigskip 17 18 Define the \alert{topolinguistic} similarity as:\\ 19 \hspace{2cm}\(\operatorname{sim}_\text{topoling}(x, x') = \operatorname{sim}_\text{ling}(x, x') + \lambda \operatorname{sim}_\text{topo}(x, x')\) 20 \end{block} 21 \end{frame}