$$ \newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} \newcommand{\ceil}[1]{\left\lceil #1 \right\rceil} \newcommand{\N}{\mathbb{N}} \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} \renewcommand{\L}{\mathcal{L}} \newcommand{\x}{\times} \newcommand{\contra}{\scalebox{1.5}{$\lightning$}} \newcommand{\inner}[2]{\left\langle #1 , #2 \right\rangle} \newcommand{\st}{\text{ such that }} \newcommand{\for}{\text{ for }} \newcommand{\Setcond}[2]{ \left\{\, #1 \mid #2 \, \right\}} \newcommand{\setcond}[2]{\Setcond{#1}{#2}} \newcommand{\seq}[1]{ \left\langle #1 \right\rangle} \newcommand{\Set}[1]{ \left\{ #1 \right\}} \newcommand{\set}[1]{ \set{#1} } \newcommand{\sgn}{\text{sign}} \newcommand{\halfline}{\vspace{0.5em}} \newcommand{\diag}{\text{diag}} \newcommand{\legn}[2]{\left(\frac{#1}{#2}\right)} \newcommand{\ord}{\text{ord}} \newcommand{\di}{\mathrel{|}} \newcommand{\gen}[1] \newcommand{\irr}{\mathrm{irr }} \renewcommand{\deg}{\mathrm{deg }} \newcommand{\nsgeq}{\trianglelefteq} \newcommand{\nsg}{\triangleleft} \newcommand{\argmin}{\mathrm{argmin}} \newcommand{\argmax}{\mathrm{argmax}} \newcommand{\minimize}{\mathrm{minimize}} \newcommand{\maximize}{\mathrm{maximize}} \newcommand{\subto}{\mathrm{subject\ to}} \newcommand{\DKL}[2]{D_{\mathrm{KL}}\left(#1 \di\di #2\right)} \newcommand{\ReLU}{\mathrm{ReLU}} \newcommand{\E}{\mathsf{E}} \newcommand{\V}{\mathsf{Var}} \newcommand{\Corr}{\mathsf{Corr}} \newcommand{\Cov}{\mathsf{Cov}} \newcommand{\covariance}[1]{\Cov\left(#1\right)} \newcommand{\variance}[1]{\V\left[#1\right]} \newcommand{\variancewith}[1]{\V\left[#1\right]} \newcommand{\expect}[1]{\E\left[#1\right]} \newcommand{\expectwith}[2]{\E_{#1}\left[#2\right]} \renewcommand{\P}{\mathsf{P}} \newcommand{\uniform}[2]{\mathrm{Uniform}\left(#1 \dots #2\right)} \newcommand{\gdist}[2]{\mathcal{N}\left(#1, #2\right)} \DeclarePairedDelimiter{\norm}{\lVert}{\rVert} $$ \everymath{\displaystyle}

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