marcheggiani.tex (1326B)
1 \begin{frame}[t]{Related Work: Marcheggiani (discriminative, 2016)}% 2 \begin{columns}[T]% 3 \begin{column}{6.5cm}% 4 A conditional \(\beta\)-VAE: 5 \begin{center}% 6 \input{mainmatter/relation extraction/marcheggiani plate.tex} 7 8 \tikz{\draw[arrow, dashed] (0, 0) -- (1cm, 0);} Encoder 9 10 \tikz{\draw[arrow] (0, 0) -- (1cm, 0);} Decoder 11 \end{center} 12 Autoencode the entities \(\rndmvctr{e}\) given the sentence features \(\rndmvctr{f}\). 13 \end{column}% 14 \begin{column}{7.5cm}% 15 \(\loss{vae}(\vctr{\theta}, \vctr{\phi}) = \symcal{L}_\text{reconstruction}(\vctr{\theta}, \vctr{\phi}) + \loss{vae reg}(\vctr{\phi})\) 16 17 \medskip 18 19 \(\loss{vae reg}(\vctr{\phi}) = \kl(Q(\rndm{r}\mid \rndmvctr{e}; \vctr{\phi}) \mathrel{\|} \uniformDistribution(\relationSet))\) 20 21 \vspace{1cm} 22 23 Assume \hypothesis{uniform}: All relations occur with equal frequency.\\ 24 \(\displaystyle \forall r\in\relationSet\colon P(r) = \frac{1}{|\relationSet|}\) 25 26 \medskip 27 28 Assume \hypothesis{\(1\to1\)}: All relations are bijective.\\ 29 \( \forall r\in\relationSet\colon r\relationComposition \breve{r} \relationOr \relationIdentity = \breve{r}\relationComposition r \relationOr \relationIdentity = \relationIdentity \) 30 \end{column}% 31 \end{columns} 32 33 \bigskip 34 35 \problemBox{Still uses hand designed features.} 36 \end{frame}