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diff --git a/.agents/skills/ml-paper-writing/templates/colm2025/math_commands.tex b/.agents/skills/ml-paper-writing/templates/colm2025/math_commands.tex new file mode 100644 index 0000000..0668f93 --- /dev/null +++ b/.agents/skills/ml-paper-writing/templates/colm2025/math_commands.tex @@ -0,0 +1,508 @@ +%%%%% 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 |