%!PS-Adobe-2.0 %%Creator: dvips(k) 5.996 Copyright 2016 Radical Eye Software %%Title: arXiv:2002.07252v1 [cs.LG] 17 Feb 2020 %%CreationDate: Thu Aug 13 08:34:55 2020 %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: NimbusRomNo9L-Medi NimbusRomNo9L-Regu %%+ NimbusRomNo9L-ReguItal NimbusRomNo9L-MediItal %%DocumentPaperSizes: Letter %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R2 -P pk -z CCC_REG_7.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2020.08.13:0834 %%BeginProcSet: texc.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat {BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc 0 0 % File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 % % @@psencodingfile@{ % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, % W. Schmidt, P. Lehman", % version = "2.0", % date = "27nov06", % filename = "8r.enc", % email = "tex-fonts@@tug.org", % docstring = "This is the encoding vector for Type1 and TrueType % fonts to be used with TeX. This file is part of the % PSNFSS bundle, version 9" % @} % % The idea is to have all the characters normally included in Type 1 fonts % available for typesetting. This is effectively the characters in Adobe % Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, % MacRoman, and some extra characters from Lucida. % % Character code assignments were made as follows: % % (1) the Windows ANSI characters are almost all in their Windows ANSI % positions, because some Windows users cannot easily reencode the % fonts, and it makes no difference on other systems. The only Windows % ANSI characters not available are those that make no sense for % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen % (173). quotesingle and grave are moved just because it's such an % irritation not having them in TeX positions. % % (2) Remaining characters are assigned arbitrarily to the lower part % of the range, avoiding 0, 10 and 13 in case we meet dumb software. % % (3) Y&Y Lucida Bright includes some extra text characters; in the % hopes that other PostScript fonts, perhaps created for public % consumption, will include them, they are included starting at 0x12. % These are /dotlessj /ff /ffi /ffl. % % (4) hyphen appears twice for compatibility with both ASCII and Windows. % % (5) /Euro was assigned to 128, as in Windows ANSI % % (6) Missing characters from MacRoman encoding incorporated as follows: % % PostScript MacRoman TeXBase1 % -------------- -------------- -------------- % /notequal 173 0x16 % /infinity 176 0x17 % /lessequal 178 0x18 % /greaterequal 179 0x19 % /partialdiff 182 0x1A % /summation 183 0x1B % /product 184 0x1C % /pi 185 0x1D % /integral 186 0x81 % /Omega 189 0x8D % /radical 195 0x8E % /approxequal 197 0x8F % /Delta 198 0x9D % /lozenge 215 0x9E % /TeXBase1Encoding [ % 0x00 /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef /Zcaron /zcaron % 0x10 /caron /dotlessi /dotlessj /ff /ffi /ffl /notequal /infinity /lessequal /greaterequal /partialdiff /summation /product /pi /grave /quotesingle % 0x20 /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash % 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question % 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O % 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore % 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o % 0x70 /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef % 0x80 /Euro /integral /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /Omega /radical /approxequal % 0x90 /.notdef /.notdef /.notdef /quotedblleft /quotedblright /bullet /endash /emdash /tilde /trademark /scaron /guilsinglright /oe /Delta /lozenge /Ydieresis % 0xA0 /.notdef /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron % 0xB0 /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown % 0xC0 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis % 0xD0 /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls % 0xE0 /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis % 0xF0 /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: texps.pro 0 0 %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[ exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def end %%EndProcSet %%BeginProcSet: special.pro 0 0 %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup} ifelse scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N /erasepage{}N/setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{ count ocount sub{pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginProcSet: hps.pro 0 0 %! /HPSdict 20 dict dup begin/braindeaddistill 50 def/rfch{dup length 1 sub 1 exch getinterval}bind def/splituri{dup(#)search{exch pop}{()exch} ifelse dup(file:)anchorsearch{pop exch pop 3 -1 roll pop false}{pop 3 -1 roll exch pop true}ifelse}bind def/lookuptarget{exch rfch dup /TargetAnchors where{pop TargetAnchors dup 3 -1 roll known{exch get true }{pop(target unknown:)print == false}ifelse}{pop pop (target dictionary unknown\012)print false}ifelse}bind def/savecount 0 def/stackstopped{count counttomark sub/savecount exch store stopped count savecount sub 1 sub dup 0 gt{{exch pop}repeat}{pop}ifelse}bind def /tempstring 128 string def/targetvalidate{1 index dup length 127 gt exch tempstring cvs dup(/)search{pop pop pop exch pop true exch}{pop}ifelse token{pop length 0 ne}{true}ifelse or not}bind def/targetdump-hook where {pop}{/targetdump-hook{dup mark exch gsave initmat setmatrix{{mark/Dest 4 2 roll targetvalidate{aload pop exch pop/Page 3 1 roll/View exch[exch /FitH exch]/DEST pdfmark}{cleartomark}ifelse}forall}stackstopped pop grestore}bind def}ifelse/baseurl{mark exch 1 dict dup 3 -1 roll/Base exch put/URI exch/DOCVIEW{pdfmark}stackstopped pop}bind def /externalhack systemdict/PDF known def/oldstyle true def/initmat matrix currentmatrix def/actiondict 2 dict dup/Subtype/URI put def /weblinkhandler{dup 3 1 roll mark 4 1 roll/Title 4 1 roll splituri 3 -1 roll dup length 0 gt{cvn/Dest exch 4 2 roll}{pop}ifelse{externalhack{ /HTTPFile exch}{actiondict dup 3 -1 roll/URI exch put/Action exch} ifelse}{externalhack{/HTTPFile exch}{/File exch/Action/GoToR}ifelse} ifelse counttomark 2 sub -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll /Color exch oldstyle{/LNK}{/Subtype/Link/ANN}ifelse gsave initmat setmatrix{pdfmark}stackstopped grestore}bind def/externalhandler where{ pop}{/externalhandler{2 copy{weblinkhandler}exec{/externalhack externalhack not store 2 copy{weblinkhandler}exec{/externalhack externalhack not store/oldstyle false store 2 copy{weblinkhandler}exec{ (WARNING: external refs disabled\012)print/externalhandler{pop pop}bind store externalhandler}{pop pop}ifelse}{pop pop/externalhack externalhack not store}ifelse}{pop pop/externalhandler{weblinkhandler pop}bind store} ifelse}bind def}ifelse/pdfmnew{dup type/stringtype eq{externalhandler}{ exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll/Color exch/LNK gsave initmat setmatrix pdfmark grestore}{pop pop}ifelse}ifelse}bind def/pdfmold{dup type/stringtype eq{externalhandler}{exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop pop 0 3 getinterval /Rect 3 1 roll/Border exch/LNK gsave initmat setmatrix pdfmark grestore} {pop pop}ifelse}ifelse}bind def/pdfm where{pop}{/pdfm /currentdistillerparams where{pop currentdistillerparams dup /CoreDistVersion known{/CoreDistVersion get}{0}ifelse dup braindeaddistill le{(WARNING: switching to old pdfm because version =) print ==/pdfmold}{pop/pdfmnew}ifelse load}{/pdfmark where{pop{dup type /stringtype eq{externalhandler}{2 copy mark 3 1 roll{pdfmnew} stackstopped{2 copy mark 3 1 roll{pdfmold}stackstopped{ (WARNING: pdfm disabled\012)print/pdfm{pop pop}store}{ (WARNING: new pdfm failed, switching to old pdfm\012)print/pdfm/pdfmold load store}ifelse}{/pdfm/pdfmnew load store}ifelse pop pop}ifelse}}{{ pop pop}}ifelse}ifelse bind def}ifelse end def %%EndProcSet TeXDict begin @defspecial systemdict /pdfmark known{userdict /?pdfmark systemdict /exec get put}{userdict /?pdfmark systemdict /pop get put userdict /pdfmark systemdict /cleartomark get put}ifelse /DvipsToPDF{72.27 mul Resolution div} def/PDFToDvips{72.27 div Resolution mul} def/BPToDvips{72 div Resolution mul}def/BorderArrayPatch{[exch{dup dup type/integertype eq exch type/realtype eq or{BPToDvips}if}forall]}def/HyperBorder {1 PDFToDvips} def/H.V {pdf@hoff pdf@voff null} def/H.B {/Rect[pdf@llx pdf@lly pdf@urx pdf@ury]} def/H.S {currentpoint HyperBorder add /pdf@lly exch def dup DvipsToPDF 72 add /pdf@hoff exch def HyperBorder sub /pdf@llx exch def} def/H.L {2 sub dup/HyperBasePt exch def PDFToDvips /HyperBaseDvips exch def currentpoint HyperBaseDvips sub /pdf@ury exch def/pdf@urx exch def} def/H.A {H.L currentpoint exch pop vsize 72 sub exch DvipsToPDF HyperBasePt sub sub /pdf@voff exch def} def/H.R {currentpoint HyperBorder sub /pdf@ury exch def HyperBorder add /pdf@urx exch def currentpoint exch pop vsize 72 sub exch DvipsToPDF sub /pdf@voff exch def} def @fedspecial end %%BeginFont: NimbusRomNo9L-ReguItal %!PS-AdobeFont-1.0: NimbusRomNo9L-ReguItal 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Regular Italic) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Regular) readonly def /ItalicAngle -15.5 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-ReguItal def /PaintType 0 def /WMode 0 def /FontBBox {-169 -270 1010 924} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: NimbusRomNo9L-Medi %!PS-AdobeFont-1.0: NimbusRomNo9L-Medi 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Medium) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Bold) readonly def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-Medi def /PaintType 0 def /WMode 0 def /FontBBox {-168 -341 1000 960} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 6FBF7F9888E039AB60FCAF852EB4CE3AFEB979D5EA70FDE44A2AE5C8C0166C27 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93B516896E64BD03985CD18B996E6B129C3B835C82931D4134AD8042C9B65537 F26F179F15A310B46D905701D4C38744AE10C47709E1CE72EA4F49E4A0A7FCD6 584EE292C46FCBCC3737521664EA67DDFA0FC09E3550B5B69F82C651A86486F0 1AB1FE662189AE270BCE923406 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: NimbusRomNo9L-Regu %!PS-AdobeFont-1.0: NimbusRomNo9L-Regu 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Regular) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Regular) readonly def /ItalicAngle 0.0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-Regu def /PaintType 0 def /WMode 0 def /FontBBox {-168 -281 1000 924} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 6FBF7F9888E039AB60FCAF852EB4CE3AFEB979D5EA70FDE44A2AE5C8C0166C27 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cleartomark %%EndFont %%BeginFont: NimbusRomNo9L-MediItal %!PS-AdobeFont-1.0: NimbusRomNo9L-MediItal 1.05 %%CreationDate: Wed Dec 22 1999 % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % (URW)++,Copyright 1999 by (URW)++ Design & Development % See the file COPYING (GNU General Public License) for license conditions. % As a special exception, permission is granted to include this font % program in a Postscript or PDF file that consists of a document that % contains text to be displayed or printed using this font, regardless % of the conditions or license applying to the document itself. 12 dict begin /FontInfo 10 dict dup begin /version (1.05) readonly def /Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def /Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def /FullName (Nimbus Roman No9 L Medium Italic) readonly def /FamilyName (Nimbus Roman No9 L) readonly def /Weight (Bold) readonly def /ItalicAngle -15.3 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /NimbusRomNo9L-MediItal def /PaintType 0 def /WMode 0 def /FontBBox {-200 -324 996 964} readonly def /FontType 1 def /FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def /Encoding StandardEncoding def currentdict end currentfile eexec D9D66F633B846A989B9974B0179FC6CC445BC2C03103C68570A7B354A4A280AE 6FBF7F9888E039AB60FCAF852EB4CE3AFEB979D5EA70FDE44A2AE5C8C0166C27 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(cite.chen2018) cvn H.B /ANN pdfmark end 2474 1913 a FF(])f(and)f(W)-7 b(alklets)34 b([)3038 1913 y SDict begin H.S end 3038 1913 a FF(22)3121 1856 y SDict begin H.R end 3121 1856 a 3121 1913 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.perozzi2017) cvn H.B /ANN pdfmark end 3121 1913 a FF(])f(address)g(capturing)e(higher)n(-)2025 2012 y(order)18 b(proximity)f(by)i(adapting)f(the)h(random)e(w)o(alk)i (strate)o(gy)-5 b(.)18 b(While)2025 2112 y(HARP)44 b(coarsens)e(the)h (graph)f(and)h(learns)f(representations)g(via)2025 2212 y(hierarchically)c(collapsed)h(graphs,)f(W)-7 b(alklets)41 b(skips)f(o)o(v)o(er)f(steps)2025 2311 y(in)24 b(the)g(random)f(w)o (alks.)h(Compared)e(to)j(DeepW)-7 b(alk)24 b(or)f(Node2V)-9 b(ec,)2025 2411 y(both)31 b(HARP)j(and)d(W)-7 b(alklets)33 b(e)o(xhibit)f(additional)e(comple)o(xity)-5 b(,)30 b(as)2025 2511 y(the)22 b(node)g(representations)e(are)j(learned)e(on)h(multiple) g(le)n(v)o(els)g(-)h(The)2025 2610 y(collapsing)k(le)n(v)o(el)h(in)h (HARP)h(and)e(the)g(skip)h(le)n(v)o(el)f(in)g(W)-7 b(alklets.)2108 2750 y(Besides)24 b(most)g(of)f(these)h(approaches)d(utilizing)i (shallo)n(w)h(neural)2025 2849 y(netw)o(ork)39 b(architectures)g(to)h (learn)f(the)i(feature)e(representations,)2025 2949 y(deep)51 b(architectures)f(ha)n(v)o(e)h(been)g(proposed)f(as)i(well,)g(aiming) 2025 3049 y(at)42 b(capturing)e(non-linearity)g(in)i(the)g(graphs.)e (SDNE)i([)3777 3050 y SDict begin H.S end 3777 3050 a -1 x FF(23)3860 2992 y SDict begin H.R end 3860 2992 a 3860 3049 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.wang2016) cvn H.B /ANN pdfmark end 3860 3049 a FF(])g(and)2025 3148 y(DNGR)32 b([)2320 3148 y SDict begin H.S end 2320 3148 a FF(24)2402 3092 y SDict begin H.R end 2402 3092 a 2402 3148 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.cao2016) cvn H.B /ANN pdfmark end 2402 3148 a FF(])g(utilize)f (autoencoders,)d(GCN)k([)3426 3149 y SDict begin H.S end 3426 3149 a -1 x FF(25)3508 3092 y SDict begin H.R end 3508 3092 a 3508 3148 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.kipf2017) cvn H.B /ANN pdfmark end 3508 3148 a FF(])f(de\002nes)g(a)g(con-)2025 3248 y(v)n(olution)25 b(operator)f(on)i(the)h(graph.)d(Further)m(,)h(methods)g(that)h(incor)n (-)2025 3347 y(porate)c(additional)g(information,)e(such)i(as)i (particular)e(graph)f(prop-)2025 3447 y(erties,)35 b(e.g.)f (communities)f([)2908 3448 y SDict begin H.S end 2908 3448 a -1 x FF(26)2991 3390 y SDict begin H.R end 2991 3390 a 2991 3447 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Wang2017) cvn H.B /ANN pdfmark end 2991 3447 a FF(],)h([)3102 3448 y SDict begin H.S end 3102 3448 a -1 x FF(27)3185 3390 y SDict begin H.R end 3185 3390 a 3185 3447 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Keikha2018) cvn H.B /ANN pdfmark end 3185 3447 a FF(])h(or)f(node)f(attrib)n(utes)i([)3919 3447 y SDict begin H.S end 3919 3447 a FF(14)4002 3390 y SDict begin H.R end 4002 3390 a 4002 3447 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Yang2015) cvn H.B /ANN pdfmark end 4002 3447 a FF(],)2025 3547 y([)2053 3548 y SDict begin H.S end 2053 3548 a -1 x FF(28)2136 3490 y SDict begin H.R end 2136 3490 a 2136 3547 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Huang2017) cvn H.B /ANN pdfmark end 2136 3547 a FF(])20 b(ha)n(v)o(e)f(been)g(proposed.)f(While)i(random)e (w)o(alk)i(based)g(methods)2025 3646 y(in)37 b(principle)f(can)h (incorporate)d(the)j(direction)f(of)h(edges)f(during)2025 3746 y(the)43 b(random)f(w)o(alk,)h(this)h(asymmetry)e(is)i(not)f (encoded)f(in)i(the)2025 3846 y(\002nal)31 b(embeddings.)e(Khosla)i(et) h(al.)f([)3157 3848 y SDict begin H.S end 3157 3848 a -2 x FF(29)3240 3789 y SDict begin H.R end 3240 3789 a 3240 3846 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.khosla2018) cvn H.B /ANN pdfmark end 3240 3846 a FF(])g(proposed)f(an)h(approach) 2025 3945 y(to)38 b(maintain)f(the)h(dif)n(ferent)e(roles)i(of)g (nodes,)f(according)e(to)k(the)2025 4045 y(direction)27 b(of)h(edges.)2108 4184 y(The)f(focus)g(of)g(this)g(paper)g(is)h(on)f (methods)f(applied)g(to)i(the)f(ra)o(w)2025 4284 y(graph)h(and)g(the)h (most)g(closely)g(related)f(approaches)f(are)i(centered)2025 4384 y(around)19 b(random)g(w)o(alks,)i(i.e.)f(DeepW)-7 b(alk,)21 b(Node2V)-9 b(ec,)18 b(HARP)k(and)2025 4483 y(W)-7 b(alklets.)35 b(Experimental)e(results)h(reported)f(in)i(dif)n (ferent)d(papers)2025 4583 y(are)45 b(often)f(hard)h(to)g(compare,)e (due)i(to)g(v)n(arying)f(e)o(xperimental)2025 4682 y(setups,)d(e)n(v)n (aluation)e(metrics)j(or)e(datasets.)i(Ne)n(v)o(ertheless,)e(from)2025 4782 y(our)35 b(e)o(xperience,)e(the)j(random)e(w)o(alk)h(methods)g (deli)n(v)o(er)f(state)j(of)2025 4882 y(the)27 b(art)h(performance)c (in)j(tasks)h(such)f(as)h(node)e(classi\002cation)h(and)2025 4981 y(can)k(compete)e(with)i(e)n(v)o(en)f(f)o(ar)h(more)f(comple)o(x)f (models.)h(W)-7 b(e)32 b(will)2025 5081 y(pro)o(vide)j(more)i(details)h (on)f(the)g(aforementioned)d(random)h(w)o(alk)2025 5181 y(based)20 b(methods)f(in)h(the)g(upcoming)d(section)3352 5181 y SDict begin H.S end 3352 5181 a FF(III)3435 5125 y SDict begin H.R end 3435 5125 a 3435 5181 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.3) cvn H.B /ANN pdfmark end 3435 5181 a 21 w FF(when)i(we)h(describe)2025 5280 y(our)26 b(approach)e(and)j(also)g(compare)e(our)h(method)f (against)h(them)g(in)2025 5380 y(section)2289 5381 y SDict begin H.S end 2289 5381 a -1 x FF(IV)2377 5324 y SDict begin H.R end 2377 5324 a 2377 5380 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.4) cvn H.B /ANN pdfmark end 2377 5380 a FF(.)p eop end end %%Page: 3 3 TeXDict begin HPSdict begin 3 2 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -158 -258 a SDict begin H.S end -158 -258 a -158 -258 a SDict begin H.R end -158 -258 a -158 -258 a SDict begin [/View [/XYZ H.V]/Dest (page.3) cvn /DEST pdfmark end -158 -258 a -150 0 a SDict begin H.S end -150 0 a -150 0 a SDict begin 12 H.A end -150 0 a -150 0 a SDict begin [/View [/XYZ H.V]/Dest (section.3) cvn /DEST pdfmark end -150 0 a 588 100 a FF(I)t(I)t(I)t(.)45 b(A)t FA(P)t(P)t(R)q(O)r(A)q (C)t(H)-150 140 y SDict begin H.S end -150 140 a -150 140 a SDict begin 12 H.A end -150 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(\(opposed)g(to)i(embed-)-150 3322 y(ding\).)27 b(T)-6 b(echnically)h(,)27 b(this)j(is)f(implemented)e(by)i(a)g(shallo)n(w)g (neural)-150 3421 y(netw)o(ork,)g(with)h(a)g(linear)g(hidden)e(layer)m (,)h(where)h(the)g(embeddings)-150 3521 y(are)44 b(the)g(weights)g (between)f(the)h(input)g(layer)f(and)h(the)g(hidden)-150 3621 y(layer)22 b(and)f(the)h(projections)f(are)h(the)g(weights)g (between)f(the)h(hidden)-150 3720 y(layer)f(and)g(the)g(output)g(layer) -5 b(.)21 b(Ho)n(we)n(v)o(er)m(,)e(the)j(normalization)d(in)j(the)-150 3820 y(denominator)j(is)j(costly)g(to)f(compute)f(and)h(therefore,)e (we)j(replace)-150 3920 y Fv(P)12 b Fu(\()p Fv(v)-10 3889 y Fq(+)45 3920 y FD(j)p Fv(\036)p Fu(\()p Fv(u)p Fu(\)\))28 b FF(by)e(ne)o(gati)n(v)o(e)e(sampling,)h(as)i(proposed)d (by)i(Mik)o(olo)o(v)-150 4019 y(et)j(al.)g([)77 4020 y SDict begin H.S end 77 4020 a -1 x FF(3)118 3963 y SDict begin H.R end 118 3963 a 118 4019 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.mikolov2013) cvn H.B /ANN pdfmark end 118 4019 a FF(]:)-135 4236 y SDict begin H.S end -135 4236 a -135 4236 a SDict begin 12 H.A end -135 4236 a -135 4236 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.3) cvn /DEST pdfmark end -135 4236 a Fp(l)q(og)g(\033)s Fo(\()p Fn(h)p Fp(\036)145 4200 y Fm(0)166 4236 y Fo(\()p Fp(v)236 4200 y Fl(+)287 4236 y Fo(\))p Fp(;)13 b(\036)p Fo(\()p Fp(u)p Fo(\))p Fn(i)p Fo(\))j(+)682 4142 y Fk(K)654 4165 y Fj(X)654 4324 y Fk(k)q Fl(=1)778 4236 y Fi(E)822 4248 y Fk(v)853 4260 y Fh(k)895 4248 y Fm(\030)p Fk(P)982 4256 y Fh(n)1023 4248 y Fl(\()p Fk(v)r Fl(\))1108 4236 y Fo([)p Fp(l)q(og)29 b(\033)s Fo(\()p Fn(\000h)p Fp(\036)1469 4200 y Fm(0)1490 4236 y Fo(\()p Fp(v)1557 4245 y Fk(k)1595 4236 y Fo(\))p Fp(;)13 b(\036)p Fo(\()p Fp(u)p Fo(\))p Fn(i)p Fo(])1788 4383 y Fg(\(3\))-150 4483 y FF(where)34 b Fv(\033)s Fu(\()p Fv(x)p Fu(\))i(=)542 4450 y Fq(1)p 394 4464 329 4 v 394 4512 a(1+)p Fs(exp)p Fq(\()p Fy(\000)p Fs(x)p Fq(\))768 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