problems.tex (3118B)
1 \begin{frame}{Source of Low Scores}% 2 \begin{block}{Degenerate distributions} 3 \begin{columns}% 4 \begin{column}{6.5cm}% 5 \centering% 6 \begin{tikzpicture} 7 \drawDistribution{activation}{\(P(\rndm{r}\mid s_1) = \)}{4.5}{0/0.32, 1/0.35, 2/0.31, 3/0.37, 4/0.38, 5/0.36, 6/0.34, 7/0.36, 8/0.36, 9/0.31} 8 \drawDistribution{activation}{\(P(\rndm{r}\mid s_2) = \)}{4}{0/0.31, 1/0.37, 2/0.38, 3/0.35, 4/0.32, 5/0.33, 6/0.37, 7/0.36, 8/0.32, 9/0.35} 9 \drawDistribution{activation}{\(P(\rndm{r}\mid s_3) = \)}{3.5}{0/0.32, 1/0.35, 2/0.31, 3/0.38, 4/0.32, 5/0.33, 6/0.37, 7/0.33, 8/0.32, 9/0.33} 10 \drawDistribution{activation}{\(P(\rndm{r}\mid s_4) = \)}{3}{0/0.33, 1/0.31, 2/0.34, 3/0.36, 4/0.34, 5/0.33, 6/0.37, 7/0.35, 8/0.36, 9/0.32} 11 \node at (0.75, 2.665) {\(\vdots\)}; 12 \end{tikzpicture}% 13 \end{column} 14 \begin{column}{6.5cm}% 15 \centering% 16 \begin{tikzpicture} 17 \drawDistribution{activation}{\(P(\rndm{r}\mid s_1) = \)}{5.5}{0/0.02, 1/0.05, 2/0.01, 3/0.87, 4/0.08, 5/0.06, 6/0.04, 7/0.06, 8/0.06, 9/0.01} 18 \drawDistribution{activation}{\(P(\rndm{r}\mid s_2) = \)}{5}{0/0.01, 1/0.07, 2/0.08, 3/0.85, 4/0.02, 5/0.03, 6/0.07, 7/0.06, 8/0.02, 9/0.05} 19 \drawDistribution{activation}{\(P(\rndm{r}\mid s_3) = \)}{4.5}{0/0.02, 1/0.05, 2/0.01, 3/0.88, 4/0.02, 5/0.03, 6/0.07, 7/0.03, 8/0.02, 9/0.03} 20 \drawDistribution{activation}{\(P(\rndm{r}\mid s_4) = \)}{4}{0/0.03, 1/0.01, 2/0.04, 3/0.86, 4/0.04, 5/0.03, 6/0.07, 7/0.05, 8/0.06, 9/0.02} 21 \node at (0.75, 3.665) {\(\vdots\)}; 22 \end{tikzpicture}% 23 \end{column} 24 \end{columns} 25 \end{block} 26 \begin{columns} 27 \begin{column}{6cm}% 28 \begin{block}{Desired distribution}% 29 \centering% 30 \begin{tikzpicture} 31 \drawDistribution{activation}{\(P(\rndm{r}\mid s_1) = \)}{1.5}{0/0.02, 1/0.05, 2/0.01, 3/0.07, 4/0.88, 5/0.06, 6/0.04, 7/0.06, 8/0.06, 9/0.01} 32 \drawDistribution{activation}{\(P(\rndm{r}\mid s_2) = \)}{1}{0/0.01, 1/0.07, 2/0.88, 3/0.05, 4/0.02, 5/0.03, 6/0.07, 7/0.06, 8/0.02, 9/0.05} 33 \drawDistribution{activation}{\(P(\rndm{r}\mid s_3) = \)}{0.5}{0/0.02, 1/0.05, 2/0.01, 3/0.88, 4/0.02, 5/0.03, 6/0.07, 7/0.03, 8/0.02, 9/0.03} 34 \drawDistribution{activation}{\(P(\rndm{r}\mid s_4) = \)}{0}{0/0.03, 1/0.01, 2/0.04, 3/0.06, 4/0.04, 5/0.03, 6/0.87, 7/0.05, 8/0.06, 9/0.02} 35 \node at (0.75, -0.335) {\(\vdots\)}; 36 \end{tikzpicture}% 37 \end{block} 38 \end{column}% 39 \begin{column}{7cm}% 40 \begin{block}{VAE Model Reminder (Marcheggiani)} 41 \vspace*{3mm}% 42 \(\displaystyle\overbrace{P(e_{-i} \mid s, e_i)}^{\text{fill-in-the-blank}} = \sum_{r\in\relationSet} \overbrace{P(r\mid s)}^{\text{classifier}} \overbrace{P(e_{-i} \mid r, e_i)}^{\text{entity predictor}}\) 43 44 \bigskip 45 46 \(\loss{vae reg}(\vctr{\phi}) = \kl(Q(\rndm{r}\mid \rndmvctr{e}; \vctr{\phi}) \mathrel{\|} \uniformDistribution(\relationSet))\) 47 \end{block} 48 \end{column}% 49 \end{columns}% 50 \pause 51 \begin{tikzpicture}[overlay, remember picture] 52 \node[inner sep=0, draw=black] at (current page.center) {\problemBoxContent{Marcheggiani's model cannot handle deep encoder.}}; 53 \end{tikzpicture} 54 \end{frame}