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| %%%%% NEW MATH DEFINITIONS %%%%% | |
| \usepackage{amsmath,amsfonts,bm} | |
| % Mark sections of captions for referring to divisions of figures | |
| \newcommand{\figleft}{{\em (Left)}} | |
| \newcommand{\figcenter}{{\em (Center)}} | |
| \newcommand{\figright}{{\em (Right)}} | |
| \newcommand{\figtop}{{\em (Top)}} | |
| \newcommand{\figbottom}{{\em (Bottom)}} | |
| \newcommand{\captiona}{{\em (a)}} | |
| \newcommand{\captionb}{{\em (b)}} | |
| \newcommand{\captionc}{{\em (c)}} | |
| \newcommand{\captiond}{{\em (d)}} | |
| % Highlight a newly defined term | |
| \newcommand{\newterm}[1]{{\bf #1}} | |
| % Figure reference, lower-case. | |
| \def\figref#1{figure~\ref{#1}} | |
| % Figure reference, capital. For start of sentence | |
| \def\Figref#1{Figure~\ref{#1}} | |
| \def\twofigref#1#2{figures \ref{#1} and \ref{#2}} | |
| \def\quadfigref#1#2#3#4{figures \ref{#1}, \ref{#2}, \ref{#3} and \ref{#4}} | |
| % Section reference, lower-case. | |
| \def\secref#1{section~\ref{#1}} | |
| % Section reference, capital. | |
| \def\Secref#1{Section~\ref{#1}} | |
| % Reference to two sections. | |
| \def\twosecrefs#1#2{sections \ref{#1} and \ref{#2}} | |
| % Reference to three sections. | |
| \def\secrefs#1#2#3{sections \ref{#1}, \ref{#2} and \ref{#3}} | |
| % Reference to an equation, lower-case. | |
| \def\eqref#1{equation~\ref{#1}} | |
| % Reference to an equation, upper case | |
| \def\Eqref#1{Equation~\ref{#1}} | |
| % A raw reference to an equation---avoid using if possible | |
| \def\plaineqref#1{\ref{#1}} | |
| % Reference to a chapter, lower-case. | |
| \def\chapref#1{chapter~\ref{#1}} | |
| % Reference to an equation, upper case. | |
| \def\Chapref#1{Chapter~\ref{#1}} | |
| % Reference to a range of chapters | |
| \def\rangechapref#1#2{chapters\ref{#1}--\ref{#2}} | |
| % Reference to an algorithm, lower-case. | |
| \def\algref#1{algorithm~\ref{#1}} | |
| % Reference to an algorithm, upper case. | |
| \def\Algref#1{Algorithm~\ref{#1}} | |
| \def\twoalgref#1#2{algorithms \ref{#1} and \ref{#2}} | |
| \def\Twoalgref#1#2{Algorithms \ref{#1} and \ref{#2}} | |
| % Reference to a part, lower case | |
| \def\partref#1{part~\ref{#1}} | |
| % Reference to a part, upper case | |
| \def\Partref#1{Part~\ref{#1}} | |
| \def\twopartref#1#2{parts \ref{#1} and \ref{#2}} | |
| \def\ceil#1{\lceil #1 \rceil} | |
| \def\floor#1{\lfloor #1 \rfloor} | |
| \def\1{\bm{1}} | |
| \newcommand{\train}{\mathcal{D}} | |
| \newcommand{\valid}{\mathcal{D_{\mathrm{valid}}}} | |
| \newcommand{\test}{\mathcal{D_{\mathrm{test}}}} | |
| \def\eps{{\epsilon}} | |
| % Random variables | |
| \def\reta{{\textnormal{$\eta$}}} | |
| \def\ra{{\textnormal{a}}} | |
| \def\rb{{\textnormal{b}}} | |
| \def\rc{{\textnormal{c}}} | |
| \def\rd{{\textnormal{d}}} | |
| \def\re{{\textnormal{e}}} | |
| \def\rf{{\textnormal{f}}} | |
| \def\rg{{\textnormal{g}}} | |
| \def\rh{{\textnormal{h}}} | |
| \def\ri{{\textnormal{i}}} | |
| \def\rj{{\textnormal{j}}} | |
| \def\rk{{\textnormal{k}}} | |
| \def\rl{{\textnormal{l}}} | |
| % rm is already a command, just don't name any random variables m | |
| \def\rn{{\textnormal{n}}} | |
| \def\ro{{\textnormal{o}}} | |
| \def\rp{{\textnormal{p}}} | |
| \def\rq{{\textnormal{q}}} | |
| \def\rr{{\textnormal{r}}} | |
| \def\rs{{\textnormal{s}}} | |
| \def\rt{{\textnormal{t}}} | |
| \def\ru{{\textnormal{u}}} | |
| \def\rv{{\textnormal{v}}} | |
| \def\rw{{\textnormal{w}}} | |
| \def\rx{{\textnormal{x}}} | |
| \def\ry{{\textnormal{y}}} | |
| \def\rz{{\textnormal{z}}} | |
| % Random vectors | |
| \def\rvepsilon{{\mathbf{\epsilon}}} | |
| \def\rvtheta{{\mathbf{\theta}}} | |
| \def\rva{{\mathbf{a}}} | |
| \def\rvb{{\mathbf{b}}} | |
| \def\rvc{{\mathbf{c}}} | |
| \def\rvd{{\mathbf{d}}} | |
| \def\rve{{\mathbf{e}}} | |
| \def\rvf{{\mathbf{f}}} | |
| \def\rvg{{\mathbf{g}}} | |
| \def\rvh{{\mathbf{h}}} | |
| \def\rvu{{\mathbf{i}}} | |
| \def\rvj{{\mathbf{j}}} | |
| \def\rvk{{\mathbf{k}}} | |
| \def\rvl{{\mathbf{l}}} | |
| \def\rvm{{\mathbf{m}}} | |
| \def\rvn{{\mathbf{n}}} | |
| \def\rvo{{\mathbf{o}}} | |
| \def\rvp{{\mathbf{p}}} | |
| \def\rvq{{\mathbf{q}}} | |
| \def\rvr{{\mathbf{r}}} | |
| \def\rvs{{\mathbf{s}}} | |
| \def\rvt{{\mathbf{t}}} | |
| \def\rvu{{\mathbf{u}}} | |
| \def\rvv{{\mathbf{v}}} | |
| \def\rvw{{\mathbf{w}}} | |
| \def\rvx{{\mathbf{x}}} | |
| \def\rvy{{\mathbf{y}}} | |
| \def\rvz{{\mathbf{z}}} | |
| % Elements of random vectors | |
| \def\erva{{\textnormal{a}}} | |
| \def\ervb{{\textnormal{b}}} | |
| \def\ervc{{\textnormal{c}}} | |
| \def\ervd{{\textnormal{d}}} | |
| \def\erve{{\textnormal{e}}} | |
| \def\ervf{{\textnormal{f}}} | |
| \def\ervg{{\textnormal{g}}} | |
| \def\ervh{{\textnormal{h}}} | |
| \def\ervi{{\textnormal{i}}} | |
| \def\ervj{{\textnormal{j}}} | |
| \def\ervk{{\textnormal{k}}} | |
| \def\ervl{{\textnormal{l}}} | |
| \def\ervm{{\textnormal{m}}} | |
| \def\ervn{{\textnormal{n}}} | |
| \def\ervo{{\textnormal{o}}} | |
| \def\ervp{{\textnormal{p}}} | |
| \def\ervq{{\textnormal{q}}} | |
| \def\ervr{{\textnormal{r}}} | |
| \def\ervs{{\textnormal{s}}} | |
| \def\ervt{{\textnormal{t}}} | |
| \def\ervu{{\textnormal{u}}} | |
| \def\ervv{{\textnormal{v}}} | |
| \def\ervw{{\textnormal{w}}} | |
| \def\ervx{{\textnormal{x}}} | |
| \def\ervy{{\textnormal{y}}} | |
| \def\ervz{{\textnormal{z}}} | |
| % Random matrices | |
| \def\rmA{{\mathbf{A}}} | |
| \def\rmB{{\mathbf{B}}} | |
| \def\rmC{{\mathbf{C}}} | |
| \def\rmD{{\mathbf{D}}} | |
| \def\rmE{{\mathbf{E}}} | |
| \def\rmF{{\mathbf{F}}} | |
| \def\rmG{{\mathbf{G}}} | |
| \def\rmH{{\mathbf{H}}} | |
| \def\rmI{{\mathbf{I}}} | |
| \def\rmJ{{\mathbf{J}}} | |
| \def\rmK{{\mathbf{K}}} | |
| \def\rmL{{\mathbf{L}}} | |
| \def\rmM{{\mathbf{M}}} | |
| \def\rmN{{\mathbf{N}}} | |
| \def\rmO{{\mathbf{O}}} | |
| \def\rmP{{\mathbf{P}}} | |
| \def\rmQ{{\mathbf{Q}}} | |
| \def\rmR{{\mathbf{R}}} | |
| \def\rmS{{\mathbf{S}}} | |
| \def\rmT{{\mathbf{T}}} | |
| \def\rmU{{\mathbf{U}}} | |
| \def\rmV{{\mathbf{V}}} | |
| \def\rmW{{\mathbf{W}}} | |
| \def\rmX{{\mathbf{X}}} | |
| \def\rmY{{\mathbf{Y}}} | |
| \def\rmZ{{\mathbf{Z}}} | |
| % Elements of random matrices | |
| \def\ermA{{\textnormal{A}}} | |
| \def\ermB{{\textnormal{B}}} | |
| \def\ermC{{\textnormal{C}}} | |
| \def\ermD{{\textnormal{D}}} | |
| \def\ermE{{\textnormal{E}}} | |
| \def\ermF{{\textnormal{F}}} | |
| \def\ermG{{\textnormal{G}}} | |
| \def\ermH{{\textnormal{H}}} | |
| \def\ermI{{\textnormal{I}}} | |
| \def\ermJ{{\textnormal{J}}} | |
| \def\ermK{{\textnormal{K}}} | |
| \def\ermL{{\textnormal{L}}} | |
| \def\ermM{{\textnormal{M}}} | |
| \def\ermN{{\textnormal{N}}} | |
| \def\ermO{{\textnormal{O}}} | |
| \def\ermP{{\textnormal{P}}} | |
| \def\ermQ{{\textnormal{Q}}} | |
| \def\ermR{{\textnormal{R}}} | |
| \def\ermS{{\textnormal{S}}} | |
| \def\ermT{{\textnormal{T}}} | |
| \def\ermU{{\textnormal{U}}} | |
| \def\ermV{{\textnormal{V}}} | |
| \def\ermW{{\textnormal{W}}} | |
| \def\ermX{{\textnormal{X}}} | |
| \def\ermY{{\textnormal{Y}}} | |
| \def\ermZ{{\textnormal{Z}}} | |
| % Vectors | |
| \def\vzero{{\bm{0}}} | |
| \def\vone{{\bm{1}}} | |
| \def\vmu{{\bm{\mu}}} | |
| \def\vtheta{{\bm{\theta}}} | |
| \def\va{{\bm{a}}} | |
| \def\vb{{\bm{b}}} | |
| \def\vc{{\bm{c}}} | |
| \def\vd{{\bm{d}}} | |
| \def\ve{{\bm{e}}} | |
| \def\vf{{\bm{f}}} | |
| \def\vg{{\bm{g}}} | |
| \def\vh{{\bm{h}}} | |
| \def\vi{{\bm{i}}} | |
| \def\vj{{\bm{j}}} | |
| \def\vk{{\bm{k}}} | |
| \def\vl{{\bm{l}}} | |
| \def\vm{{\bm{m}}} | |
| \def\vn{{\bm{n}}} | |
| \def\vo{{\bm{o}}} | |
| \def\vp{{\bm{p}}} | |
| \def\vq{{\bm{q}}} | |
| \def\vr{{\bm{r}}} | |
| \def\vs{{\bm{s}}} | |
| \def\vt{{\bm{t}}} | |
| \def\vu{{\bm{u}}} | |
| \def\vv{{\bm{v}}} | |
| \def\vw{{\bm{w}}} | |
| \def\vx{{\bm{x}}} | |
| \def\vy{{\bm{y}}} | |
| \def\vz{{\bm{z}}} | |
| % Elements of vectors | |
| \def\evalpha{{\alpha}} | |
| \def\evbeta{{\beta}} | |
| \def\evepsilon{{\epsilon}} | |
| \def\evlambda{{\lambda}} | |
| \def\evomega{{\omega}} | |
| \def\evmu{{\mu}} | |
| \def\evpsi{{\psi}} | |
| \def\evsigma{{\sigma}} | |
| \def\evtheta{{\theta}} | |
| \def\eva{{a}} | |
| \def\evb{{b}} | |
| \def\evc{{c}} | |
| \def\evd{{d}} | |
| \def\eve{{e}} | |
| \def\evf{{f}} | |
| \def\evg{{g}} | |
| \def\evh{{h}} | |
| \def\evi{{i}} | |
| \def\evj{{j}} | |
| \def\evk{{k}} | |
| \def\evl{{l}} | |
| \def\evm{{m}} | |
| \def\evn{{n}} | |
| \def\evo{{o}} | |
| \def\evp{{p}} | |
| \def\evq{{q}} | |
| \def\evr{{r}} | |
| \def\evs{{s}} | |
| \def\evt{{t}} | |
| \def\evu{{u}} | |
| \def\evv{{v}} | |
| \def\evw{{w}} | |
| \def\evx{{x}} | |
| \def\evy{{y}} | |
| \def\evz{{z}} | |
| % Matrix | |
| \def\mA{{\bm{A}}} | |
| \def\mB{{\bm{B}}} | |
| \def\mC{{\bm{C}}} | |
| \def\mD{{\bm{D}}} | |
| \def\mE{{\bm{E}}} | |
| \def\mF{{\bm{F}}} | |
| \def\mG{{\bm{G}}} | |
| \def\mH{{\bm{H}}} | |
| \def\mI{{\bm{I}}} | |
| \def\mJ{{\bm{J}}} | |
| \def\mK{{\bm{K}}} | |
| \def\mL{{\bm{L}}} | |
| \def\mM{{\bm{M}}} | |
| \def\mN{{\bm{N}}} | |
| \def\mO{{\bm{O}}} | |
| \def\mP{{\bm{P}}} | |
| \def\mQ{{\bm{Q}}} | |
| \def\mR{{\bm{R}}} | |
| \def\mS{{\bm{S}}} | |
| \def\mT{{\bm{T}}} | |
| \def\mU{{\bm{U}}} | |
| \def\mV{{\bm{V}}} | |
| \def\mW{{\bm{W}}} | |
| \def\mX{{\bm{X}}} | |
| \def\mY{{\bm{Y}}} | |
| \def\mZ{{\bm{Z}}} | |
| \def\mBeta{{\bm{\beta}}} | |
| \def\mPhi{{\bm{\Phi}}} | |
| \def\mLambda{{\bm{\Lambda}}} | |
| \def\mSigma{{\bm{\Sigma}}} | |
| % Tensor | |
| \DeclareMathAlphabet{\mathsfit}{\encodingdefault}{\sfdefault}{m}{sl} | |
| \SetMathAlphabet{\mathsfit}{bold}{\encodingdefault}{\sfdefault}{bx}{n} | |
| \newcommand{\tens}[1]{\bm{\mathsfit{#1}}} | |
| \def\tA{{\tens{A}}} | |
| \def\tB{{\tens{B}}} | |
| \def\tC{{\tens{C}}} | |
| \def\tD{{\tens{D}}} | |
| \def\tE{{\tens{E}}} | |
| \def\tF{{\tens{F}}} | |
| \def\tG{{\tens{G}}} | |
| \def\tH{{\tens{H}}} | |
| \def\tI{{\tens{I}}} | |
| \def\tJ{{\tens{J}}} | |
| \def\tK{{\tens{K}}} | |
| \def\tL{{\tens{L}}} | |
| \def\tM{{\tens{M}}} | |
| \def\tN{{\tens{N}}} | |
| \def\tO{{\tens{O}}} | |
| \def\tP{{\tens{P}}} | |
| \def\tQ{{\tens{Q}}} | |
| \def\tR{{\tens{R}}} | |
| \def\tS{{\tens{S}}} | |
| \def\tT{{\tens{T}}} | |
| \def\tU{{\tens{U}}} | |
| \def\tV{{\tens{V}}} | |
| \def\tW{{\tens{W}}} | |
| \def\tX{{\tens{X}}} | |
| \def\tY{{\tens{Y}}} | |
| \def\tZ{{\tens{Z}}} | |
| % Graph | |
| \def\gA{{\mathcal{A}}} | |
| \def\gB{{\mathcal{B}}} | |
| \def\gC{{\mathcal{C}}} | |
| \def\gD{{\mathcal{D}}} | |
| \def\gE{{\mathcal{E}}} | |
| \def\gF{{\mathcal{F}}} | |
| \def\gG{{\mathcal{G}}} | |
| \def\gH{{\mathcal{H}}} | |
| \def\gI{{\mathcal{I}}} | |
| \def\gJ{{\mathcal{J}}} | |
| \def\gK{{\mathcal{K}}} | |
| \def\gL{{\mathcal{L}}} | |
| \def\gM{{\mathcal{M}}} | |
| \def\gN{{\mathcal{N}}} | |
| \def\gO{{\mathcal{O}}} | |
| \def\gP{{\mathcal{P}}} | |
| \def\gQ{{\mathcal{Q}}} | |
| \def\gR{{\mathcal{R}}} | |
| \def\gS{{\mathcal{S}}} | |
| \def\gT{{\mathcal{T}}} | |
| \def\gU{{\mathcal{U}}} | |
| \def\gV{{\mathcal{V}}} | |
| \def\gW{{\mathcal{W}}} | |
| \def\gX{{\mathcal{X}}} | |
| \def\gY{{\mathcal{Y}}} | |
| \def\gZ{{\mathcal{Z}}} | |
| % Sets | |
| \def\sA{{\mathbb{A}}} | |
| \def\sB{{\mathbb{B}}} | |
| \def\sC{{\mathbb{C}}} | |
| \def\sD{{\mathbb{D}}} | |
| % Don't use a set called E, because this would be the same as our symbol | |
| % for expectation. | |
| \def\sF{{\mathbb{F}}} | |
| \def\sG{{\mathbb{G}}} | |
| \def\sH{{\mathbb{H}}} | |
| \def\sI{{\mathbb{I}}} | |
| \def\sJ{{\mathbb{J}}} | |
| \def\sK{{\mathbb{K}}} | |
| \def\sL{{\mathbb{L}}} | |
| \def\sM{{\mathbb{M}}} | |
| \def\sN{{\mathbb{N}}} | |
| \def\sO{{\mathbb{O}}} | |
| \def\sP{{\mathbb{P}}} | |
| \def\sQ{{\mathbb{Q}}} | |
| \def\sR{{\mathbb{R}}} | |
| \def\sS{{\mathbb{S}}} | |
| \def\sT{{\mathbb{T}}} | |
| \def\sU{{\mathbb{U}}} | |
| \def\sV{{\mathbb{V}}} | |
| \def\sW{{\mathbb{W}}} | |
| \def\sX{{\mathbb{X}}} | |
| \def\sY{{\mathbb{Y}}} | |
| \def\sZ{{\mathbb{Z}}} | |
| % Entries of a matrix | |
| \def\emLambda{{\Lambda}} | |
| \def\emA{{A}} | |
| \def\emB{{B}} | |
| \def\emC{{C}} | |
| \def\emD{{D}} | |
| \def\emE{{E}} | |
| \def\emF{{F}} | |
| \def\emG{{G}} | |
| \def\emH{{H}} | |
| \def\emI{{I}} | |
| \def\emJ{{J}} | |
| \def\emK{{K}} | |
| \def\emL{{L}} | |
| \def\emM{{M}} | |
| \def\emN{{N}} | |
| \def\emO{{O}} | |
| \def\emP{{P}} | |
| \def\emQ{{Q}} | |
| \def\emR{{R}} | |
| \def\emS{{S}} | |
| \def\emT{{T}} | |
| \def\emU{{U}} | |
| \def\emV{{V}} | |
| \def\emW{{W}} | |
| \def\emX{{X}} | |
| \def\emY{{Y}} | |
| \def\emZ{{Z}} | |
| \def\emSigma{{\Sigma}} | |
| % entries of a tensor | |
| % Same font as tensor, without \bm wrapper | |
| \newcommand{\etens}[1]{\mathsfit{#1}} | |
| \def\etLambda{{\etens{\Lambda}}} | |
| \def\etA{{\etens{A}}} | |
| \def\etB{{\etens{B}}} | |
| \def\etC{{\etens{C}}} | |
| \def\etD{{\etens{D}}} | |
| \def\etE{{\etens{E}}} | |
| \def\etF{{\etens{F}}} | |
| \def\etG{{\etens{G}}} | |
| \def\etH{{\etens{H}}} | |
| \def\etI{{\etens{I}}} | |
| \def\etJ{{\etens{J}}} | |
| \def\etK{{\etens{K}}} | |
| \def\etL{{\etens{L}}} | |
| \def\etM{{\etens{M}}} | |
| \def\etN{{\etens{N}}} | |
| \def\etO{{\etens{O}}} | |
| \def\etP{{\etens{P}}} | |
| \def\etQ{{\etens{Q}}} | |
| \def\etR{{\etens{R}}} | |
| \def\etS{{\etens{S}}} | |
| \def\etT{{\etens{T}}} | |
| \def\etU{{\etens{U}}} | |
| \def\etV{{\etens{V}}} | |
| \def\etW{{\etens{W}}} | |
| \def\etX{{\etens{X}}} | |
| \def\etY{{\etens{Y}}} | |
| \def\etZ{{\etens{Z}}} | |
| % The true underlying data generating distribution | |
| \newcommand{\pdata}{p_{\rm{data}}} | |
| % The empirical distribution defined by the training set | |
| \newcommand{\ptrain}{\hat{p}_{\rm{data}}} | |
| \newcommand{\Ptrain}{\hat{P}_{\rm{data}}} | |
| % The model distribution | |
| \newcommand{\pmodel}{p_{\rm{model}}} | |
| \newcommand{\Pmodel}{P_{\rm{model}}} | |
| \newcommand{\ptildemodel}{\tilde{p}_{\rm{model}}} | |
| % Stochastic autoencoder distributions | |
| \newcommand{\pencode}{p_{\rm{encoder}}} | |
| \newcommand{\pdecode}{p_{\rm{decoder}}} | |
| \newcommand{\precons}{p_{\rm{reconstruct}}} | |
| \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} | |
| \newcommand{\parents}{Pa} % See usage in notation.tex. Chosen to match Daphne's book. | |
| \DeclareMathOperator*{\argmax}{arg\,max} | |
| \DeclareMathOperator*{\argmin}{arg\,min} | |
| \DeclareMathOperator{\sign}{sign} | |
| \DeclareMathOperator{\Tr}{Tr} | |
| \let\ab\allowbreak | |