% !TeX root = ./thuthesis-example.tex % 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