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 $IVOLӝ߈Ѩ࢝੉ۆ $IVOLա־ӝ $IVOLѨ࢝ೞӝ $IVOLѨ࢝੹റ୊ܻ 4FSWJOH4USVDUVSF 1P$%FNP 2"

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 $IVOL - CBTFE3FUSJFWBM

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 ৵ଂѐջ  --.җदݔ౮Ѩ࢝ীࢲ઺ਃ  ׹߸੄ҙ۲ࢿ߂੿ഛبী૒੽੸৔ೱ ೞա੄ޙࢲח  ׮নೠࣗ઱ઁܳ૑צױۅਵ۽ҳࢿ\ױۅU ]U¸UPQJDT^  ࢎਊ੗੄૕ޙীо੢೙ਃೠ੿ࠁחয٣ী 8IZ$IVOL

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 ޙױ 1BSBHSBQI  ҳઑоੜ٘۞դޙࢲܳ׮ܙٸਬਊ  ౠ੿ѐ֛੉ա઱ઁীҙೠࣗѐషۿਸ׸ӝীਬਊ  ੘ࢿ੗о੄بೠࢤп੄൒ܴ੹ജ߈৔ೞӝী੸೤ -> ੘ࢿ੗ࢤп੄ҳઑ  ױੌ઱ઁ৔৉੉ޙױࠁ׮௼ӝب੘ӝبೣ 
 -> ৈ۞઱ઁܳݽইҳࢿೞѢա ೠо૑઱ઁ੄ӟӖਸૣ਷ഐ൚ਵ۽ա־ӝبೣ 8IZ$IVOL

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 ӡ੉оӡݶ  ੄޷࢚੄/PJTFૐо -> ઱ઁо࠙࢑غযੌҙࢿ੷ೞ  Ѩ࢝੐߬٬ಿ૕੷ೞ -> ૕੄৬੿ഛ൤ੌ஖ೞחޙࢲܳ଺ӝয۰਑  ׹߸ীࠛ೙ਃೠղਊ -> )BMMVDJOBUJPOૐо ӡ੉оૣਵݶ  ੹୓ݓۅਬप  ೧׼ఫझ౟੄੄޷৵ҋ־ۅ 8IZ$IVOL

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 $IVOLա־ӝ

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 8IBUJT$IVOLJOH .JMMFSsT-BX .JMMFSsT.BHJD/VNCFS  ಣӐ੸ੋࢎۈ੄ױӝӝর۱ೠ҅ח‚ѐ  .FNPSZTQBO ӝর੄ױਤ ™$IVOL  $IVOLۆ  ઱য૓Ӗীࢲੋधೡࣻ੓ח୭؀੄޷ױਤ  ࢎۈ݃׮$IVOL੄ӡ੉о׮ܴ  ं੗ ױয ҳ੺ j  Ӓۢஹೊఠח   .JMMFS ("  5IFNBHJDBMOVNCFSTFWFO QMVTPSNJOVTUXP4PNFMJNJUTPOPVSDBQBDJUZGPSQSPDFTTJOHJOGPSNBUJPO1TZDIPMPHJDBM3FWJFX   m

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 $IVOL੄੿੄  ୭ࣗೠ੄ز૕੸ੋ੄޷۽ޘਸࣻ੓ח୭؀ױਤ  ੄޷ ز૕ࢿ ஏ੿ߑߨ਷ $IVOLJOH੉ۆ  ௾ޙࢲܳ੄޷࢚ਵ۽Ӑੌೠױਤ۽࠙ೡೞח੘স  ઱ઁ੄ੌҙࢿਸਬ૑ೞח୭؀ೠ੄ޙ੢૘೤  Ѩ࢝ޙࢲղ*OGPSNBUJPO/PJTFܳ୭ࣗച 8IBUJT$IVOLJOH (PUP"QQFOEJY

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 ӝ؀ബҗ  दݔ౮Ѩ࢝ಿ૕ীѾ੿੸৉ೡ  ઁೠػ$POUFYU8JOEPXղীࢲ --.੉ղਊਸऔҊ੿ഛ൤੉೧  ױੌ઱ઁ઺बਵ۽ъೞѱ'PDVTػѨ࢝Ѿҗ যڌѱଂѐջ  যڃӡ੉۽  ୭੸੄$IVOLTJ[Fח೦࢚ੌ੿ೞ૑ঋ਺ 8IBUJT$IVOLJOH

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  'JYFE - TJ[F$IVOLJOH  3FDVSTJWF$IVOLJOH ҳ࠙੗۽࠙ೡ)JFSBSDIJDBM*UFSBUJWF  %PDVNFOU4QFDJ fi D$IVOLJOH ҳઑх૑ -PHJDBM4FDUJPO .BSLEPXO )5.- j  4FNBOUJD$IVOLJOH Ѩ࢝ಿ૕ࠁ੢ ৮Ѿࢿ ੌҙࢿ וܿ ޙ੢ BODIPS  8JOEPX -> ੐߬٬  "HFOUJD$IVOLJOH)PXIVNBOTEP ୐ޙ੢੉୐ޙױ -> ׮਺ޙ੢ਸ੍Ҋখޙױী߽೤ৈࠗѾ੿ -> ՘ө૑ $IVOLJOH.FUIPET

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ޙࢲ 5PP-POH $IVOLT "*.PEFM "VUIPS *OEFY ҳઑх૑ ✂︎ ޙ੢ױਤ 4FNBOUJD 'FBUVSFT $IVOLJOH.FUIPET 

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$IVOLJOH.FUIPET Ѩ࢝ߑध 4UBUJD %ZOBNJD അ੤ -FYJDBM 9 ޙࢲױਤ )JHIMJHIU৔৉઱߸5FYU 4FNBOUJD 7FDUPS Ӑ١࠙ೡ 'JYFE-FOHUI 5FYU0WFSMBQ 9 4FNBOUJD$IVOL -FYJDBM ੄޷࠙ೡ ޙ੢ױਤ ߭ఠਬࢎب 9 4FNBOUJD 7FDUPS 9 ష௾ױਤ੐߬٬೙ਃ -> $PM#&35 

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 $IVOLJOH"1* 4FNBOUJD$IVOLJOH  &NCFEEJOH&-&$53"  0QFSBUJPO-FWFM4FOUFODF  -PHJDਬࢎب߂ਬࢎب߸ചਯх૑  ੄޷߸ചਯীٮܲ0WFSMBQبੑ  ҕҕؘ੉ఠ߂য়೑ࣗझؘ੉ఠ೟ण ୹୊IUUQT XXXLBLBPDPSQDPNQBHFEFUBJM

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 $IVOL"1*ӝמౠ૚  ޙࢲղҳઑ߈৔  ੄޷ӝ߈  ޙ੢ױਤ0QFSBUJPO  $IVOLӡ੉ઁೠ ୹୊IUUQT XXXCCDDPNLPSFBOBSUJDMFTDXQYKQP $IVOLJOH"1* CBDL

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 $IVOLѨ࢝ೞӝ

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 $IVOL3FUSJFWBM ޙࢲױਤѨ࢝җח׮ܰ׮  ࢎۈٜ਷$IVOLܳ੘ࢿ9  ޙࢲઙࣘ੸ౠࢿ 
 -> ઁݾ ஠పҊܻ $MJDL - -PH١  ೠޙࢲղ$IVOLр੄ޙݓҙ҅ਬप 
 -> ৘दtߡۅয়߄݃޷؀ా۸਷jӒחোࢸীࢲ૑૑੗ٜীѱju

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 $IVOL3FUSJFWBM $IVOLױਤѨ࢝ীࢲ೙ਃೠѪٜ  ઁݾ $IVOL5JUMF  ҙ۲૕੄ $BOEJEBUF2VFTUJPOT 
 -> ੉$IVOLחযڃ૕ޙਸ೧Ѿ೧઴ࣻ੓ਸө  ਗېޙࢲ߂׮ܲ$IVOL৬੄ҙ҅ 1BSFOU - $IJME)JFSBSDIZ 
 -> ೠޙࢲղ$IVOLр੄ҙ҅ب  Ѩ࢝ਊ੐߬٬'JOF5VOF 
 -> $IVOLܻ࠙ਊ&NCFEEJOHীࢲ࠙ച

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 )ZCSJE3FUSJFWBM  $IVOL੄੢ױ੼ 
 -> 'PDVTFE5PQJD -PTU$POUFYU  ޙࢲ߹.FUB$IVOLبੑ 
 -> ਃড$IVOL ૑धӒې೐ 1BSFOU - $IJME)JFSBSDIZ j  ׮ࣻ੄઺ࠂ$IVOL۽ੋೠѨ࢝ಿ૕੷ೞߑ૑ 
 -> ৘زੌೠղਊ੄׏झӝࢎ $IVOL3FUSJFWBM

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 $IVOL5JUMF  Ѩ࢝ಿ૕ী઺ਃ࠺઺  ޙࢲઁݾ߆ীহחؘ   ਃডUBTLܳ߸ഋ೧ࢤࢿ -> 5ള۲ $IVOL'FBUVSFT

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 $BOEJBUF2VFTUJPOT  )Z%& )ZQPUIFUJDBM%PDVNFOU&NCFEEJOH  ࢎਊ੗૕੄ -> --.੉о࢚੄׹߸੘ࢿ -> ਬࢎޙࢲѨ࢝ WFDUPS  -> --.׹߸ࣻ੿  --.੄׹߸җਬࢎೠղਊ੄Ӗ੉ইפݶ଺૑ޅೡࣻ੓਺  )Z2& )ZQPUIFUJDBM2VFTUJPO&NCFEEJOH  $IVOL੍ܳҊ׹߸ೡࣻ੓ח૕ޙറࠁܳೣԋ࢝ੋ  ૕ޙࢤࢿ -> 5ള۲ $IVOL'FBUVSFT

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 1P$%FNP$IVOLJOH"1*

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 $IVOL'FBUVSFT৘द ӝসҔਸ؀࢚ਵ۽݄दߧ਍৔ਸद੘ೠةੌ਷࢜۽਍ਃੋী઱ݾೞҊ੓׮ "*оࡅܲࣘب۽֢زഅ੢ীبੑغҊ੓חѪযڃ੹ޙоٜ਷"*о઱ੌӔޖઁഛ࢑оࣘചೡѪ੉ۄҊ݈ೠ׮ ݈֙৔Ҵ੄׏झ߂೯ࢎ੿ࠁӝসrప௼௏ UFDIDP sоࣻ૘ೠ੗ܐب੉ّܳ߉ஜೠ׮ ੉ഥࢎחr֙ӝࣿਸా೧׳ۄ૕֢زജ҃sਸ੹ݎೞӝਤ೧޷Ҵ੄࠺ૉפझܻ؊ৈݺীѱࢸޙਸपद೮׮ ࢸޙѾҗ઱ੌӔޖઁܳद೯ೞחઑ૒੄חഥࢎ਍৔ী"*ܳҟߧਤೞѱഝਊ઺੉঻׮ ୁ(15э਷ࢤࢿഋ"*೐۽Ӓ۔ਵ۽਍৔ਸрࣗചೞҊ੓঻؍Ѫ੉׮߈ݶ઱ੌӔޖӝস઺ূ݅"*ܳ੉੿بࣻળਵ۽ࢎਊೞҊ੓঻׮ $IVOL5JUMF $BOEJEBUF2VFTUJPOT 2VFSZ3FXSJUF "*о֢زഅ੢ী بੑغח੉ਬ ਬۣীࢲח"*оযڌѱ֢زഅ੢ীبੑغҊ੓աਃ ਬۣ"*֢زഅ੢بੑ ֙৔Ҵ੄ప௼௏ীࢲࣻ૘ೠؘ੉ఠחޖ঺ੋоਃ ֙৔Ҵప௼௏ؘ੉ఠ ઱ੌӔޖઁܳद೯ೞחઑ૒਷ݻ੉ݴ ੉ٜ਷ഥࢎ਍৔ী"*ܳযڌѱഝਊೞҊ੓աਃ ઱ੌӔޖઁઑ૒"*ഝਊ TMJEF

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 $IVOL'FBUVSFT৘द ই౵౟ ౠࣻѤޛ ੄ࣗਬ੗חӒѤޛ੄ച੤۽ੋೞৈఋੋ੉ࢎݎೞѢա࢚ࠗਸੑ঻ਸٸژח׮ܲࢎۈ੄੤ޛীࣚ೧оߊࢤೠٸীחҗप੉হח҃਋ীبࠁ೷Ә ঘ੄ߧਤীࢲӒࣚ೧ܳߓ࢚ೡ଼੐੉੓णפ׮੉҃਋|पച଼੐ীҙೠߨܫ}ীبࠛҳೞҊই౵౟੄ࣗਬ੗ীѱ҃җप੉੓ח҃਋ীبӒࣚ೧ܳߓ࢚ೡ଼੐੉ ੓णפ׮ |ച੤۽ੋೠ੤೧ࠁ࢚җࠁ೷оੑীҙೠߨܫ}ઁઑઁ೦ ই౵౟ ౠࣻѤޛ ࣗਬ੗੄ࣚ೧ߓ଼࢚੐ীҙೞৈח|ച੤۽ੋೠ੤೧ࠁ࢚җࠁ೷оੑী ҙೠߨܫ}ীࢲӏ੿ೞחѪ৻ীח|޹ߨ}ীٮܵפ׮ |ച੤۽ੋೠ੤೧ࠁ࢚җࠁ೷оੑীҙೠߨܫ}ઁઑઁ೦  œౠࣻѤޛҴਬѤޛ䡪ҕਬѤޛ䡪Үਭदࢸ䡪ߔച੼䡪द੢䡪੄ܐदࢸ䡪൜೯੢䡪ࣼ߅সࣗ䡪׮઺੉ਊসࣗ䡪਍ࣻदࢸ䡪ҕ੢䡪ҕز઱ఖӒ߆ীৈ۞ࢎۈ੉୹ੑژחӔޖೞѢաѢ઱ ೞחѤޛ۽ࢲച੤੄ਤ೷੉աѤޛ੄ݶ੸١ਸҊ۰ೞৈ|ച੤۽ੋೠ੤೧ࠁ࢚җࠁ೷оੑীҙೠߨܫद೯۸}ઁઑীࢲ੿ೞחѤޛਸ݈ೣ |ച੤۽ੋೠ੤೧ ࠁ࢚җࠁ೷оੑীҙೠߨܫ}ઁઑઁഐ $IVOL5JUMF $BOEJEBUF2VFTUJPOT 2VFSZ3FXSJUF ই౵౟ച੤द ࣚ೧ߓ଼࢚੐ rपച଼੐ীҙೠߨܫীبࠛҳೞҊই౵౟੄ࣗਬ੗оࠁ೷Әঘ੄ߧਤীࢲࣚ೧ܳߓ࢚೧ঠೞ ח੉ਬחޖ঺ੋоਃ ই౵౟ࣗਬ੗ࠁ೷Әঘ ࣚ೧ߓ࢚੉ਬ ച੤۽ੋೠ੤೧ࠁ࢚җࠁ೷оੑীҙೠߨܫ਷যڃ҃਋ী੸ਊغաਃ ച੤੤೧ࠁ࢚ࠁ೷оੑߨܫ ౠࣻѤޛীחযڃѪٜ੉੓աਃ ౠࣻѤޛ ୹୊ߨઁ୊<଺ӝए਍ࢤഝߨ۸੿ࠁ>

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 ࢎਊػࢤࢿݽ؛  5ӝ߈  ؘ੉ఠ.4 - ."3$0 "* - )VC ଺ӝए਍ࢤഝߨ۸੿ࠁ ߨઁ୊  .VMUJ - UBTLള۲  5JUMF  $BOEJEBUF2VFTUJPOT  2VFSZ3FXSJUF  ݽ؛ೞա۽ৈ۞ӝמઁҕ 
 -> (16੗ਗബਯ੸ഝਊ  0//9 - "DDFMFSBUFE୶ۿࢲߡ $IVOL'FBUVSFT

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 $IVOL3FUSJFWBM4VNNBSZ $IVOLJOH  $IVOLJOH.PEFM&-&$53"  %FEJDBUFE$IVOL&NCFEEJOH3P#&35B  $IVOL5JUMF5  $BOEJEBUF2VFTUJPO5 3FUSJFWBM  2VFSZ3FXSJUF5  )JFSBSDIJDBM3FUSJFWBM5SVF  --. - 3FSBOL5SVF --. - 3FSBOL'BMTF --. - 3FSBOL5SVF   ࠄߊ಴おؘݽदোীࢲחয়೑ࣗझ--.ࢎਊೣ

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 1SF1PTU3FUSJFWBMJO3"( $IVOLѨ࢝੹റ୊ܻ

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 1SF1PTU3FUSJFWBM 2VFSZ3FXSJUF 23  Ѩ࢝ਊ૕੄WT؀ച୓૕ޙ ,FZXPSETWT4FOUFODF  5.VMUJ - UBTLള۲ ؀ചഋ૕ޙ Ѩ࢝ਊ૕੄ ࣗ੢ਸ੘ࢿೡٸ যڃ੿ࠁܳನೣ೧ঠೞաਃ ࣗ੢੘ࢿ੿ࠁ ੌਊӔ۽੗੄੿੄חޖ঺ੋоਃ ੌਊӔ۽੗੿੄ ੗׮оযӵޡ஘ѱৌൗ૩উಽܻ֎যڃ਍ز੉જਸө যӵޡ஘Ѫಽ਍ز

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 3F3BOL  --.੉ࠁӝী੸೤ೠࣽࢲ۽Ѩ࢝ޙࢲ੤ߓ஖ (FOFSBUF  )BMMVDJOBUJPO୭ࣗച 
 -> ੗ܐ݅ࠁҊ؀׹೧ۄ  ӝࠄ࢚धҗ)BMMVDJOBUJPOр҃҅ݽഐ 
 -> ઁѢࠛо 1SF1PTU3FUSJFWBM .PEFM" .PEFM# \tDIVOL@DPOUFOUutࣗই݃࠺חj೐ۘ௿ܽ%ܖझ߰౟୊ۢࢿੋੌٸѦܻח҃਋بju^ ೐ۘ௿ܽ%ܖૉ߰౟ -> ؀ా۸

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 4FSWJOH4USVDUVSF

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4FSWJOH4USVDUVSF"*4FBSDICFUB 2 ࢎਊ੗૕੄ 6* 23 2VFSZ3FXSJUF Ѩ࢝ ޙࢲࣻ૘ ؘؘ࢚੉ఠࣻ૘ ୶оਢޙࢲ௼܀ --.੐੄੄য়೑ࣗझݽ؛ࢎਊоמ 1SPNQU --. "HFOU 4ZTUFN ݽ؛݂ ࢝ੋ $IVOLJOH 2s 3"($PSF PO,BLBP$MPVE Ѩ࢝Ѿҗ ୹୊ઁҕ 0O,BLBP$MPVE $IVOLӝ߈ 
 ࢝ੋݽ؛݂ݽٕ ୭ઙ׹߸ 0O,BLBP$MPVE $POUFYU߈৔ 8୹୊ ޙࢲѨ࢝Ѿҗ

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 4FSWJOH4USVDUVSF"*4FBSDICFUB

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 1P$%FNP

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 1P$%FNP$IVOLJOH"1*

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 1P$%FNP$IVOLJOH"1*

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 $SFEJUT  Ѩ࢝$*$  Ѩ࢝ࢲ࠺झ౱  Ѩ࢝୶ୌݽ؛݂౱  Ѩ࢝೒ۖಬ౱  "*਽ਊѨ࢝౱  Ѩ࢝ӝദ౱  Ѩ࢝दझమ౱ ୓೷ഋੋఢभ೐۽Ӓ۔ъইഅש  ޙࢲղҳઑх૑۽૒ѐߊ߂Ҋبച 
 -> Ҋಿ૕$IVOLࢤ࢑ 0QFO4PVSDF%BUB  ߨઁ୊t଺ӝए਍ࢤഝߨ۸੿ࠁu  धড୊tधಿউ੹աۄu t੄ডಿউ੹աۄu ,PXPSLFS୓೷ࠗझ 3"(POࢎղࠂ૑߂সޖXJLJޙࢲ 4FSWJOH4USVDUVSF"*4FBSDICFUB

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 5PXIPNJUNBZDPODFSOj  ѐੋ੸ਵ۽਍৔ೞח࠶۽Ӓաҳઑചػѱद౸ޙࢲ۽3"(ܳҳࢿೞҊर਷ؘয۵૑ঋਸө  ഥࢎࢎղޙࢲ۽3"(ܳҳࢿೞ۰חؘ"*ܳੜݽܰח૒ਗ੉Әߑೡࣻ੓ਸө  ࠁউޙઁ۽$IBU(15"1*э਷৻ࠗࢲ࠺झী੄ઓೞ૑ঋҊ3"(ܳࢎղীࢲҳ୷ೡࣻ੓ਸө

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 2"

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 4FNBOUJD$POTJTUFODZ  ࠺तೠ੄޷੄ޙ੢ٜ੉߭ఠҕр࢚ীࢲઑ޻ೞѱݽৈ੓যঠೣ    Loss1 = 𝔼 [d(vtitle , vchunk sent. )] Loss2 = Var[vchunk sent. ] Loss3 = 𝔼 [d(vtitle1 , vchunk1 sent. )] + 𝔼 [d(vtitle2 , vchunk2 sent. )] d(vtitle1 , vtitle2 ) + ϵ ( ≪ 1) "QQFOEJY TMJEF

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 4FNBOUJD$PIFSFODF  4NPPUIBOE-PHJDBM'MPXPGB%PDVNFOU  ޙࢲ੹୓੉ঠӝ൒ܴ੉֤ܻ੸੉Ҋ੗োझۣѱൗ۞Ѿۿী੉ܴ  Loss = (θsent1 , sent2 + θsent2 , sent3 − θsent1 , sent3 )2 2 "QQFOEJY TMJEF

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 &0%