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diff --git a/paper/paper.tex b/paper/paper.tex
index b677e6c..86ef9d8 100644
--- a/paper/paper.tex
+++ b/paper/paper.tex
@@ -46,6 +46,17 @@
% Therefore, a short form for the running title is supplied here:
\icmltitlerunning{Cracking Cascades: Sparse Recovery for Graph Inference}
+\usepackage{amsmath, amsfonts, amssymb}
+\newcommand{\reals}{\mathbb{R}}
+\newcommand{\ints}{\mathbb{N}}
+\DeclareMathOperator{\E}{\mathbb{E}}
+\let\P\relax
+\DeclareMathOperator{\P}{\mathbb{P}}
+\newcommand{\ex}[1]{\E\left[#1\right]}
+\newcommand{\prob}[1]{\P\left[#1\right]}
+\newcommand{\inprod}[2]{#1 \cdot #2}
+\newcommand{\defeq}{\equiv}
+
\begin{document}
\twocolumn[