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+% Adapted for use with thuthesis.
+% Original code is at https://github.com/goodfeli/dlbook_notation/blob/master/math_commands.tex
+
+%%%%% NEW MATH DEFINITIONS %%%%%
+
+\newcommand\ceil[1]{\lceil #1 \rceil}
+\newcommand\floor[1]{\lfloor #1 \rfloor}
+
+
+% Vectors
+\newcommand\Vector[1]{\symbf{#1}}
+
+\newcommand\0{{\Vector{0}}}
+\newcommand\vzero{{\Vector{0}}}
+\newcommand\1{{\Vector{1}}}
+\newcommand\vone{{\Vector{1}}}
+
+\newcommand\va{{\Vector{a}}}
+\newcommand\vb{{\Vector{b}}}
+\newcommand\vc{{\Vector{c}}}
+\newcommand\vd{{\Vector{d}}}
+\newcommand\ve{{\Vector{e}}}
+\newcommand\vf{{\Vector{f}}}
+\newcommand\vg{{\Vector{g}}}
+\newcommand\vh{{\Vector{h}}}
+\newcommand\vi{{\Vector{i}}}
+\newcommand\vj{{\Vector{j}}}
+\newcommand\vk{{\Vector{k}}}
+\newcommand\vl{{\Vector{l}}}
+\newcommand\vm{{\Vector{m}}}
+\newcommand\vn{{\Vector{n}}}
+\newcommand\vo{{\Vector{o}}}
+\newcommand\vp{{\Vector{p}}}
+\newcommand\vq{{\Vector{q}}}
+\newcommand\vr{{\Vector{r}}}
+\newcommand\vs{{\Vector{s}}}
+\newcommand\vt{{\Vector{t}}}
+\newcommand\vu{{\Vector{u}}}
+\newcommand\vv{{\Vector{v}}}
+\newcommand\vw{{\Vector{w}}}
+\newcommand\vx{{\Vector{x}}}
+\newcommand\vy{{\Vector{y}}}
+\newcommand\vz{{\Vector{z}}}
+
+\newcommand\valpha{{\Vector{\alpha}}}
+\newcommand\vbeta{{\Vector{\beta}}}
+\newcommand\vgamma{{\Vector{\gamma}}}
+\newcommand\vdelta{{\Vector{\delta}}}
+\newcommand\vepsilon{{\Vector{\epsilon}}}
+\newcommand\vtheta{{\Vector{\theta}}}
+\newcommand\viota{{\Vector{\iota}}}
+\newcommand\vkappa{{\Vector{\kappa}}}
+\newcommand\vlambda{{\Vector{\lambda}}}
+\newcommand\vmu{{\Vector{\mu}}}
+\newcommand\vnu{{\Vector{\nu}}}
+\newcommand\vxi{{\Vector{\xi}}}
+\newcommand\vpi{{\Vector{\pi}}}
+\newcommand\vrho{{\Vector{\rho}}}
+\newcommand\vsigma{{\Vector{\sigma}}}
+\newcommand\vtau{{\Vector{\tau}}}
+\newcommand\vupsilon{{\Vector{\upsilon}}}
+\newcommand\vphi{{\Vector{\phi}}}
+\newcommand\vchi{{\Vector{\chi}}}
+\newcommand\vpsi{{\Vector{\psi}}}
+\newcommand\vomega{{\Vector{\omega}}}
+
+
+% Matrix
+\newcommand\MATRIX[1]{\symbf{#1}}
+
+\newcommand\mA{{\MATRIX{A}}}
+\newcommand\mB{{\MATRIX{B}}}
+\newcommand\mC{{\MATRIX{C}}}
+\newcommand\mD{{\MATRIX{D}}}
+\newcommand\mE{{\MATRIX{E}}}
+\newcommand\mF{{\MATRIX{F}}}
+\newcommand\mG{{\MATRIX{G}}}
+\newcommand\mH{{\MATRIX{H}}}
+\newcommand\mI{{\MATRIX{I}}}
+\newcommand\mJ{{\MATRIX{J}}}
+\newcommand\mK{{\MATRIX{K}}}
+\newcommand\mL{{\MATRIX{L}}}
+\newcommand\mM{{\MATRIX{M}}}
+\newcommand\mN{{\MATRIX{N}}}
+\newcommand\mO{{\MATRIX{O}}}
+\newcommand\mP{{\MATRIX{P}}}
+\newcommand\mQ{{\MATRIX{Q}}}
+\newcommand\mR{{\MATRIX{R}}}
+\newcommand\mS{{\MATRIX{S}}}
+\newcommand\mT{{\MATRIX{T}}}
+\newcommand\mU{{\MATRIX{U}}}
+\newcommand\mV{{\MATRIX{V}}}
+\newcommand\mW{{\MATRIX{W}}}
+\newcommand\mX{{\MATRIX{X}}}
+\newcommand\mY{{\MATRIX{Y}}}
+\newcommand\mZ{{\MATRIX{Z}}}
+
+\newcommand\mGamma{{\MATRIX{\Gamma}}}
+\newcommand\mDelta{{\MATRIX{\Delta}}}
+\newcommand\mTheta{{\MATRIX{\Theta}}}
+\newcommand\mLambda{{\MATRIX{\Lambda}}}
+\newcommand\mXi{{\MATRIX{\Xi}}}
+\newcommand\mPi{{\MATRIX{\Pi}}}
+\newcommand\mSigma{{\MATRIX{\Sigma}}}
+\newcommand\mUpsilon{{\MATRIX{\Upsilon}}}
+\newcommand\mPhi{{\MATRIX{\Phi}}}
+\newcommand\mPsi{{\MATRIX{\Psi}}}
+\newcommand\mOmega{{\MATRIX{\Omega}}}
+
+
+% Tensor
+\newcommand\tens[1]{\symbfsf{#1}}
+\newcommand\tA{{\tens{A}}}
+\newcommand\tB{{\tens{B}}}
+\newcommand\tC{{\tens{C}}}
+\newcommand\tD{{\tens{D}}}
+\newcommand\tE{{\tens{E}}}
+\newcommand\tF{{\tens{F}}}
+\newcommand\tG{{\tens{G}}}
+\newcommand\tH{{\tens{H}}}
+\newcommand\tI{{\tens{I}}}
+\newcommand\tJ{{\tens{J}}}
+\newcommand\tK{{\tens{K}}}
+\newcommand\tL{{\tens{L}}}
+\newcommand\tM{{\tens{M}}}
+\newcommand\tN{{\tens{N}}}
+\newcommand\tO{{\tens{O}}}
+\newcommand\tP{{\tens{P}}}
+\newcommand\tQ{{\tens{Q}}}
+\newcommand\tR{{\tens{R}}}
+\newcommand\tS{{\tens{S}}}
+\newcommand\tT{{\tens{T}}}
+\newcommand\tU{{\tens{U}}}
+\newcommand\tV{{\tens{V}}}
+\newcommand\tW{{\tens{W}}}
+\newcommand\tX{{\tens{X}}}
+\newcommand\tY{{\tens{Y}}}
+\newcommand\tZ{{\tens{Z}}}
+
+
+% Graph
+\newcommand\gA{{\mathcal{A}}}
+\newcommand\gB{{\mathcal{B}}}
+\newcommand\gC{{\mathcal{C}}}
+\newcommand\gD{{\mathcal{D}}}
+\newcommand\gE{{\mathcal{E}}}
+\newcommand\gF{{\mathcal{F}}}
+\newcommand\gG{{\mathcal{G}}}
+\newcommand\gH{{\mathcal{H}}}
+\newcommand\gI{{\mathcal{I}}}
+\newcommand\gJ{{\mathcal{J}}}
+\newcommand\gK{{\mathcal{K}}}
+\newcommand\gL{{\mathcal{L}}}
+\newcommand\gM{{\mathcal{M}}}
+\newcommand\gN{{\mathcal{N}}}
+\newcommand\gO{{\mathcal{O}}}
+\newcommand\gP{{\mathcal{P}}}
+\newcommand\gQ{{\mathcal{Q}}}
+\newcommand\gR{{\mathcal{R}}}
+\newcommand\gS{{\mathcal{S}}}
+\newcommand\gT{{\mathcal{T}}}
+\newcommand\gU{{\mathcal{U}}}
+\newcommand\gV{{\mathcal{V}}}
+\newcommand\gW{{\mathcal{W}}}
+\newcommand\gX{{\mathcal{X}}}
+\newcommand\gY{{\mathcal{Y}}}
+\newcommand\gZ{{\mathcal{Z}}}
+
+
+% Sets
+\newcommand\sA{{\mathbb{A}}}
+\newcommand\sB{{\mathbb{B}}}
+\newcommand\sC{{\mathbb{C}}}
+\newcommand\sD{{\mathbb{D}}}
+% Don't use a set called E, because this would be the same as our symbol
+% for expectation.
+\newcommand\sF{{\mathbb{F}}}
+\newcommand\sG{{\mathbb{G}}}
+\newcommand\sH{{\mathbb{H}}}
+\newcommand\sI{{\mathbb{I}}}
+\newcommand\sJ{{\mathbb{J}}}
+\newcommand\sK{{\mathbb{K}}}
+\newcommand\sL{{\mathbb{L}}}
+\newcommand\sM{{\mathbb{M}}}
+\newcommand\sN{{\mathbb{N}}}
+\newcommand\sO{{\mathbb{O}}}
+\newcommand\sP{{\mathbb{P}}}
+\newcommand\sQ{{\mathbb{Q}}}
+\newcommand\sR{{\mathbb{R}}}
+\newcommand\sS{{\mathbb{S}}}
+\newcommand\sT{{\mathbb{T}}}
+\newcommand\sU{{\mathbb{U}}}
+\newcommand\sV{{\mathbb{V}}}
+\newcommand\sW{{\mathbb{W}}}
+\newcommand\sX{{\mathbb{X}}}
+\newcommand\sY{{\mathbb{Y}}}
+\newcommand\sZ{{\mathbb{Z}}}
+
+
+% Random variables
+\newcommand\RandomVariable[1]{\symit{#1}}
+
+\newcommand\rA{{\RandomVariable{A}}}
+\newcommand\rB{{\RandomVariable{B}}}
+\newcommand\rC{{\RandomVariable{C}}}
+\newcommand\rD{{\RandomVariable{D}}}
+\newcommand\rE{{\RandomVariable{E}}}
+\newcommand\rF{{\RandomVariable{F}}}
+\newcommand\rG{{\RandomVariable{G}}}
+\newcommand\rH{{\RandomVariable{H}}}
+\newcommand\rI{{\RandomVariable{I}}}
+\newcommand\rJ{{\RandomVariable{J}}}
+\newcommand\rK{{\RandomVariable{K}}}
+\newcommand\rL{{\RandomVariable{L}}}
+\newcommand\rM{{\RandomVariable{M}}}
+\newcommand\rN{{\RandomVariable{N}}}
+\newcommand\rO{{\RandomVariable{O}}}
+\newcommand\rP{{\RandomVariable{P}}}
+\newcommand\rQ{{\RandomVariable{Q}}}
+\newcommand\rR{{\RandomVariable{R}}}
+\newcommand\rS{{\RandomVariable{S}}}
+\newcommand\rT{{\RandomVariable{T}}}
+\newcommand\rU{{\RandomVariable{U}}}
+\newcommand\rV{{\RandomVariable{V}}}
+\newcommand\rW{{\RandomVariable{W}}}
+\newcommand\rX{{\RandomVariable{X}}}
+\newcommand\rY{{\RandomVariable{Y}}}
+\newcommand\rZ{{\RandomVariable{Z}}}
+
+% Random vectors
+\newcommand\RandomVector[1]{\symbf{#1}}
+
+\newcommand\rvA{{\RandomVector{A}}}
+\newcommand\rvB{{\RandomVector{B}}}
+\newcommand\rvC{{\RandomVector{C}}}
+\newcommand\rvD{{\RandomVector{D}}}
+\newcommand\rvE{{\RandomVector{E}}}
+\newcommand\rvF{{\RandomVector{F}}}
+\newcommand\rvG{{\RandomVector{G}}}
+\newcommand\rvH{{\RandomVector{H}}}
+\newcommand\rvI{{\RandomVector{I}}}
+\newcommand\rvJ{{\RandomVector{J}}}
+\newcommand\rvK{{\RandomVector{K}}}
+\newcommand\rvL{{\RandomVector{L}}}
+\newcommand\rvM{{\RandomVector{M}}}
+\newcommand\rvN{{\RandomVector{N}}}
+\newcommand\rvO{{\RandomVector{O}}}
+\newcommand\rvP{{\RandomVector{P}}}
+\newcommand\rvQ{{\RandomVector{Q}}}
+\newcommand\rvR{{\RandomVector{R}}}
+\newcommand\rvS{{\RandomVector{S}}}
+\newcommand\rvT{{\RandomVector{T}}}
+\newcommand\rvU{{\RandomVector{U}}}
+\newcommand\rvV{{\RandomVector{V}}}
+\newcommand\rvW{{\RandomVector{W}}}
+\newcommand\rvX{{\RandomVector{X}}}
+\newcommand\rvY{{\RandomVector{Y}}}
+\newcommand\rvZ{{\RandomVector{Z}}}
+
+\newcommand\laplace{\mathrm{Laplace}} % Laplace distribution
+
+\newcommand\E{\mathbb{E}}
+\newcommand\Ls{\mathcal{L}}
+\newcommand\R{\mathbb{R}}
+\newcommand\emp{\tilde{p}}
+\newcommand\lr{\alpha}
+\newcommand\reg{\lambda}
+\newcommand\rect{\mathrm{rectifier}}
+\newcommand\softmax{\mathrm{softmax}}
+\newcommand\sigmoid{\sigma}
+\newcommand\softplus{\zeta}
+\newcommand\KL{D_{\mathrm{KL}}}
+\newcommand\Var{\mathrm{Var}}
+\newcommand\standarderror{\mathrm{SE}}
+\newcommand\Cov{\mathrm{Cov}}
+% Wolfram Mathworld says $L^2$ is for function spaces and $\ell^2$ is for vectors
+% But then they seem to use $L^2$ for vectors throughout the site, and so does
+% wikipedia.
+\newcommand\normlzero{L^0}
+\newcommand\normlone{L^1}
+\newcommand\normltwo{L^2}
+\newcommand\normlp{L^p}
+\newcommand\normmax{L^\infty}
+
+\DeclareMathOperator*{\argmax}{arg\,max}
+\DeclareMathOperator*{\argmin}{arg\,min}
+
+\DeclareMathOperator{\sign}{sign}
+\DeclareMathOperator{\Tr}{Tr}
+\let\ab\allowbreak