|
|
|
|
|
\newcommand{\expect}[2]{\mathds{E}_{{#1}} \left[ {#2} \right]} |
|
|
\newcommand{\myvec}[1]{\boldsymbol{#1}} |
|
|
\newcommand{\myvecsym}[1]{\boldsymbol{#1}} |
|
|
\newcommand{\vx}{\myvec{x}} |
|
|
\newcommand{\vy}{\myvec{y}} |
|
|
\newcommand{\vz}{\myvec{z}} |
|
|
\newcommand{\vtheta}{\myvecsym{\theta}} |
|
|
|
|
|
\section{Introduction} |
|
|
|
|
|
\kant[1] |
|
|
\kant[2] |
|
|
\kant[3] |
|
|
|
|
|
\section{Using Figures} |
|
|
|
|
|
We can add figures in the usual way. Figure \ref{fig:image1}. |
|
|
\begin{figure}[t] |
|
|
\centering |
|
|
\includegraphics[width=\columnwidth]{kurt-cotoaga-1210012-unsplash} |
|
|
\caption{Image. This image comes from unsplash.com, which is a great website to get |
|
|
free to use high quality images.} |
|
|
\label{fig:image1} |
|
|
\end{figure} |
|
|
|
|
|
\section{Latex Environments} |
|
|
Using paragraph environment. |
|
|
\paragraph{Opening Paragraph.} Paragraph is a way to have a bolded heading, and that can also |
|
|
enter into the pdf bookmark structure. |
|
|
|
|
|
\section{Equations} |
|
|
|
|
|
We can write equations this way: |
|
|
\begin{align} |
|
|
\log p(\vx) & = \log \int p_\theta(\vx,\vz) p(\vz) d\vz \nonumber \\ |
|
|
& = \log \expect{p(\vz)}{p_\theta(\vx,\vz)} |
|
|
\label{eq:marginalisation1} |
|
|
\end{align} |
|
|
We refer to the previous equation \eqref{eq:marginalisation1}. |
|
|
Later let's compute the gradient $\nabla_\theta \log p(\vx)$. The commands |
|
|
\verb|\vz|, \verb|\vx|, \verb|\expect| are locally-defined macros. |
|
|
The file \texttt{defns.tex} provides a larger set of short macros for |
|
|
common constructions, but some of them clash with existing packages. |
|
|
\begin{align} |
|
|
\log p(\vx) & = \nabla_{\vtheta} \sum_{i=1}^N \log p(y | x(\vtheta)) + \mathcal{R}(x) \nonumber \\ |
|
|
& + \|\nabla_{\vtheta}\vx(\vtheta)\|^2_2 \\ |
|
|
& y \in \mathbb{R}; \vx \in \mathbb{R}^D \qquad \text{using \texttt{\textbackslash mathbb}} \\ |
|
|
& y \in \mathds{R}; \vx \in \mathds{R}^D \qquad \text{using \texttt{\textbackslash mathds}} |
|
|
\label{eq:marginalisation2} |
|
|
\end{align} |
|
|
|
|
|
\subsection{Tables} |
|
|
Use \href{https://www.tablesgenerator.com/latex_tables}{\texttt{www.tablesgenerator.com/latex\_tables}} to help make tables. |
|
|
|
|
|
\begin{table}[tb] |
|
|
\centering |
|
|
\caption{Sizes of datasets. Testing with a much longer caption to see how it looks over |
|
|
multiple lines. } |
|
|
\begin{tabular}{lll} |
|
|
\hline |
|
|
Dataset & N & D \\ |
|
|
\hline \hline |
|
|
MNIST & 60,000 & $32\times32$ \\ |
|
|
ImageNet & 1m & $64\times64$\\ |
|
|
\hline |
|
|
\end{tabular} |
|
|
\end{table} |
|
|
|
|
|
\subsubsection{Using lists} |
|
|
|
|
|
Itemize lists |
|
|
\begin{itemize} |
|
|
\item Item 1 |
|
|
\item Item 2 |
|
|
\item Item 3 |
|
|
\end{itemize} |
|
|
|
|
|
\noindent Enumerate lists |
|
|
\begin{enumerate} |
|
|
\item Item 1 |
|
|
\item Item 2 |
|
|
\item Item 3 |
|
|
\end{enumerate} |
|
|
|
|
|
\section{DeepMind Brand Colours} |
|
|
The brand standard specifies a colour palette that is available using the package \texttt{dm-colors}, which is already included in this template. Colours include: \textcolor{dmblue400}{This} \textcolor{dmyellow500}{text} \textcolor{dmteal400}{is} \textcolor{dmpurple400}{rendered} \textcolor{dmred400}{using} \textcolor{dmorange400}{dmcolors}. |
|
|
|
|
|
\section{Including References and Bibliography} |
|
|
\begin{figure*}[t] |
|
|
\centering |
|
|
\includegraphics[width=\columnwidth]{kurt-cotoaga-1210012-unsplash} |
|
|
\includegraphics[width=\columnwidth]{kurt-cotoaga-1210012-unsplash} |
|
|
\caption{Image. This image comes from unsplash.com, which is a great website to get |
|
|
free to use high quality images.} |
|
|
\label{fig:image2} |
|
|
\end{figure*} |
|
|
References can be formatted in two styles with the \texttt{citep} |
|
|
command \citep{silver2016mastering} and with the \texttt{citet} |
|
|
command \citet{silver2016mastering}. |
|
|
|
