E2E音声認識の適材適所を考える

Tokyo BISH Bash #5の発表資料

紹介した論文:
[Toshniwal et al. 2018] Toshniwal, S., Kannan, A., Chiu, C.C., Wu, Y., Sainath, T.N. and Livescu, K., 2018, December. A comparison of techniques for language model integration in encoder-decoder speech recognition. In 2018 IEEE spoken language technology workshop (SLT) (pp. 369-375). IEEE.
[Variani et al. 2020] Variani, E., Rybach, D., Allauzen, C. and Riley, M., 2020, May. Hybrid autoregressive transducer (HAT). In ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 6139-6143). IEEE.
[Pundak et al. 2018] Pundak, G., Sainath, T.N., Prabhavalkar, R., Kannan, A. and Zhao, D., 2018, December. Deep context: End-to-end contextual speech recognition. In 2018 IEEE spoken language technology workshop (SLT) (pp. 418-425). IEEE.
[Zhao et al. 2019]: Zhao, D., Sainath, T.N., Rybach, D., Rondon, P., Bhatia, D., Li, B. and Pang, R., 2019. Shallow-Fusion End-to-End Contextual Biasing. In Interspeech (pp. 1418-1422).
[Jain et al. 2020] Jain, M., Keren, G., Mahadeokar, J., Zweig, G., Metze, F. and Saraf, Y., 2020. Contextual RNN-T for open domain asr. In Interspeech.

Transcript

1. Yotaro Kubo (yotaro@google.com) E2EԻ੠ೝࣝͷదࡐదॴΛߟ͑Δ Tokyo BISH Bash #5. Jun 23, 2021.
2. Self-introduction 2010 2014 2018 Waseda RW
 TH NTT CS Labs. Amazon NNԻڹϞσϧ GMMͷࣝผֶश FST for ԻڹϞσϧ 💥 DNN Impact DNNͷߴ଎Խ/ ࠷దԽ ϧʔϧϕʔεLM Voice search Voice assistant 💥 E2E Impact Multi-output ASR ٳ 
 Έ ॻ੶ࣥච/ ߍਖ਼ 📘 2021೥4݄ ͍ͭʹ׬੒
3. ػցֶशʹΑΔԻ੠ೝࣝ • E2E Impact௚લ·ͰͷԻ੠ೝࣝΛ೔ຊޠͰৄࡉʹֶ΂Δຊ 
 (ͱͳͬͯཉ͍͠ͱࢥ͍ͳ͕Βࣥචͨ͠) • Ի੠ೝࣝΛࣗ෼ͰϑϩϜɾεΫϥον࣮૷͢ΔͨΊʹ 
 ඞཁͳ஌͕ࣝશ෦ॻ͍ͯ͋Γ·͢ • ҰൠੑΛॏࢹͨ͠ͷͰઆ໌͸ந৅త͔΋???
4. ػցֶशʹΑΔԻ੠ೝࣝ • E2E Impact௚લ·ͰͷԻ੠ೝࣝΛ೔ຊޠͰৄࡉʹֶ΂Δຊ 
 (ͱͳͬͯཉ͍͠ͱࢥ͍ͳ͕Βࣥචͨ͠) • E2EԻ੠ೝࣝʹ͍ͭͯ͸खബ͕ͩ… End-to-end⾳声認識の検討は精⼒的に続けられているが，2020年現在，認識精度の観点で， 従来法を超えることができるかどうかは議論が分かれている。 また，精度の問題のみでは なく，発⾳辞書モデルや⾔語モデルなど，従来の⾳声認識では⼈⼿で挙動を変更することが 可能であった部分が，End-to-end ⾳声 認識ではブラックボックス化してしまうという問題 もある。反⾯，探索誤りの少ない点や，従来のように巨⼤なデコーディング・ネットワーク を事前に構成しなくてよい点，GPU のような⾼度に並列な計算装置が利⽤しやすい点など， 計算資源の側⾯での利点は⼤きい。さらに，End-to-end 型⾳声認識では⾳声認識のソフト ウェア構成を⼤幅に簡略化できるという利点もある。End-to-end ⾳声認識を採⽤するか 従来の⾳響/⾔語モデルを利⽤するかは，応⽤先の特性を踏まえて慎重に決定すべきである。 ຊॻͷ࠷ऴϖʔδ࠷ऴஈམΑΓ
5. ػցֶशʹΑΔԻ੠ೝࣝ • E2E Impact௚લ·ͰͷԻ੠ೝࣝΛ೔ຊޠͰৄࡉʹֶ΂Δຊ 
 (ͱͳͬͯཉ͍͠ͱࢥ͍ͳ͕Βࣥචͨ͠) • E2EԻ੠ೝࣝʹ͍ͭͯ͸खബ͕ͩ… End-to-end⾳声認識の検討は精⼒的に続けられているが，2020年現在，認識精度の観点で， 従来法を超えることができるかどうかは議論が分かれている。 また，精度の問題のみでは なく，発⾳辞書モデルや⾔語モデルなど，従来の⾳声認識では⼈⼿で挙動を変更することが 可能であった部分が，End-to-end ⾳声 認識ではブラックボックス化してしまうという問題 もある。反⾯，探索誤りの少ない点や，従来のように巨⼤なデコーディング・ネットワーク を事前に構成しなくてよい点，GPU のような⾼度に並列な計算装置が利⽤しやすい点など， 計算資源の側⾯での利点は⼤きい。さらに，End-to-end 型⾳声認識では⾳声認識のソフト ウェア構成を⼤幅に簡略化できるという利点もある。End-to-end ⾳声認識を採⽤するか 従来の⾳響/⾔語モデルを利⽤するかは，応⽤先の特性を踏まえて慎重に決定すべきである。 ຊॻͷ࠷ऴϖʔδ࠷ऴஈམΑΓ ???
6. ैདྷͷԻ੠ೝࣝثͱE2EԻ੠ೝࣝثͷҧ͍ ௨ΓɼԻૉ͸୯ޠͷҧ͍Λදݱ͢ΔԻͷ࠷খ୯ҐͰ͋Γɼೖྗ৴߸ͱ୯ޠྻͷ ؒΛऔΓ࣋ͭதؒม਺ͱͯ͠౎߹͕Α͍ɻԻૉྻ m Λಋೖ͢Δͱɼੜ੒Ϟσ ϧ͸ҎԼͷΑ͏ʹॻ͘͜ͱ͕Ͱ͖Δɻ p(X, y | D) = m p(X | m, D) ԻڹϞσϧ p(m | y, D) ൃԻࣙॻϞσϧ p(y | D) ݴޠϞσϧ . (4.2) ͜͜Ͱɼೖྗ৴߸ X ͸୯ޠྻ y ʹ͸௚઀ґଘͤͣɼԻૉྻ m ͷΈʹΑͬͯఆ ·Δͱ͍͏Ծఆ͕ಋೖ͞Εͨ͜ͱʹ஫ҙ͞Ε͍ͨɻ ࣜதʹࣔͨ͠௨Γɼp(X | m, D) ΛԻڹϞσϧɼp(m | y, D) ΛൃԻࣙॻϞ σϧɼp(y | D) ΛݴޠϞσϧͱݺͿɻ͜ͷதͰಛʹൃԻࣙॻϞσϧ͸ओʹਓख ʹΑͬͯ༻ҙ͞ΕΔͱ͍͏఺ͰಛघͰ͋Δɻ͜ΕΛػցֶशʹΑͬͯਪఆ͢Δ E2E: Conventional: <latexit sha1_base64="SqlHWtdxa4stj2qy1iIvwiiwXpM=">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</latexit> p(y | X, D) = NeuralNet(y, X; ⇥(D)) ͜͜ͷp΋Α͘ Neural Net ͜͜ͷp͸جຊ Neural Net ͜͜ͷp͸جຊతʹ 
 ϧʔϧϕʔε <latexit sha1_base64="h9b7ttjZYJz2S8aySr3nUqPBwYM=">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</latexit> z}|{ Իૉ Իૉͱ͍͏தؒදݱ͕࢖ΘΕΔ
7. E2EԻ੠ೝࣝʹର͍ͯ࣋ͬͯ͠Δݸਓతͳҹ৅ non-E2E E2E ਫ਼౓ 😃 😐→😃 ೝࣝ଎౓ ☹ 😐 ·ͨ͸ 😃 ࣮૷ن໛ ☹ 😃 ΧελϚΠζ 😃 ☹→😐 • ΧελϚΠζ͕ॏཁͳԠ༻Ͱ 
 E2EԻ੠ೝࣝΛ࢖͏ͷ͸େม 
 ͱ͍͏ҹ৅
8. ຊ೔ͷٞ୊ ैདྷͷASR͸Ͳ͏͍͏ΧελϚΠζ͕Ͱ͖Δ͔ E2EԻ੠ೝࣝث͸ͲͷΑ͏ʹΧελϚΠζͰ͖Δ͔
9. ௨ΓɼԻૉ͸୯ޠͷҧ͍Λදݱ͢ΔԻͷ࠷খ୯ҐͰ͋Γɼೖྗ৴߸ͱ୯ޠྻͷ ؒΛऔΓ࣋ͭதؒม਺ͱͯ͠౎߹͕Α͍ɻԻૉྻ m Λಋೖ͢Δͱɼੜ੒Ϟσ ϧ͸ҎԼͷΑ͏ʹॻ͘͜ͱ͕Ͱ͖Δɻ p(X, y | D) = m p(X | m, D) ԻڹϞσϧ p(m | y, D) ൃԻࣙॻϞσϧ p(y | D) ݴޠϞσϧ . (4.2) ͜͜Ͱɼೖྗ৴߸ X ͸୯ޠྻ y ʹ͸௚઀ґଘͤͣɼԻૉྻ m ͷΈʹΑͬͯఆ ·Δͱ͍͏Ծఆ͕ಋೖ͞Εͨ͜ͱʹ஫ҙ͞Ε͍ͨɻ ࣜதʹࣔͨ͠௨Γɼp(X | m, D) ΛԻڹϞσϧɼp(m | y, D) ΛൃԻࣙॻϞ σϧɼp(y | D) ΛݴޠϞσϧͱݺͿɻ͜ͷதͰಛʹൃԻࣙॻϞσϧ͸ओʹਓख ʹΑͬͯ༻ҙ͞ΕΔͱ͍͏఺ͰಛघͰ͋Δɻ͜ΕΛػցֶशʹΑͬͯਪఆ͢Δ Conventional: 😀 🙂 😐 ΧελϚΠζ͠΍͢͞ ཁ࠶ֶश ਓखͰ͍͡ΕΔ ֶशͨ͠ϞσϧΛ ૢ࡞Ͱ͖Δ
10. ASRΧελϚΠζͷඞཁੑ • ৽ޠʗ଄ޠ΁ͷରԠ • ػೳ֦ுαΠΫϧͱσʔλऩूαΠΫϧͷෆҰக 
 (υϝΠϯݻ༗ޠɼυϝΠϯݻ༗จ๏) • Ϣʔβʔݻ༗ͷޠ ʢओʹݴޠతଆ໘ʣ
11. ྫ1: ଄ޠʗ৽ޠ΁ͷରԠ • ·Εʹશ͘৽͍͠ݴ༿͕౜ಥʹग़ݱ͢Δ (Brexit΍ྩ࿨ͳͲ) ୯ޠͱൃԻͷରԠ͸ɼࣙॻΛ༻͍ͯఆٛ͢Δ͜ͱ͕Ͱ͖Δɻਤ 4.2 ʹɼલষ Ͱಋೖͨ͠Ի੠ೝࣝثʹ࢖ΘΕͨൃԻࣙॻΛࣔ͢ɻൃԻࣙॻ͸ਤͷΑ͏ʹ୯ޠ ͱରԠ͢ΔԻૉྻΛۭനͰ۠੾ͬͯදه͢ΔϑΥʔϚοτ͕ҰൠతͰ͋Δɻ ੺͍ a k a i ੨͍ a o i ྑ͍ i i Ո i e ஑ i k e ֋ k a i ΠΧ i k a ֆ e ਤ 4.2 ൃԻࣙॻͷҰྫ ͜ͷࣙॻΛݩʹਤ 3.5ʢ p.72ʣͷΑ͏ͳ FST ʹಘΔʹ͸ɼॳظঢ়ଶͱऴྃ ঢ়ଶΛ 1 ͭͣͭఆΊɼͦΕΒͷؒʹ 1 ୯ޠʹ͖ͭ 1 ͭͷύεΛߏங͢Δϓϩά ϥϜΛ༻͍Δɻ֤੒ޭύεͰ͸ରԠ͢ΔԻૉͷܥྻΛडཧ͠ɼͦͷύεͷͲ͜ ͔Ͱ୯ޠΛग़ྗ͢Δɻ୯ޠΛग़ྗ͠ͳ͔ͬͨঢ়ଶભҠͷग़ྗΞϧϑΝϕοτͱ ͯ͠͸ ε Λઃఆ͢ΔɻԻૉྻ͔ΒҰ୯ޠ΁ͷม׵Ͱ͸ͳ͘ɼ୯ޠྻ΁ͷม׵ͱ Իૉຖʹֶश͞ΕͨϞσϧΛϧʔϧϕʔεͰܨ͛Δैདྷܕ͸ ͜͏͍͏࣌ʹ༗ར
12. ྫ2: ػೳ֦ுαΠΫϧͱσʔλऩूαΠΫϧ σʔλ੔උ Ϟσϧֶश σϓϩΠ ϓϩμΫτͷ੒௕αΠΫϧͷԿॲʹ৽ػೳ֦ுΛೖΕΔ͔? ྑ͍Ϟσϧ͕ͳ͍ͱ ৽ػೳΛσϓϩΠͰ͖ͳ͍ ྑ͍σʔλ͕ͳ͍ͱ ৽ػೳͷൃ࿩ΛֶशͰ͖ͳ͍ ৽ػೳ͕࣮૷͞Ε͍ͯͳ͍ͱ 
 ద੾ͳσʔλ͕ू·Βͳ͍ ਓྗ΍ਓखσʔλΛ࢖ͬͯ 
 ͏·͘ϒʔτετϥοϓ 
 ͢Δ࢓૊Έ͕ඞཁ
13. σʔλ੔උ Ϟσϧֶश σϓϩΠ ैདྷͷԻ੠ೝࣝͰ͸Ϟσϧֶशͷޙʹ΋ਓ͕հೖͰ͖Δ ਓखʹΑΔݴޠϞσϧ (FSTจ๏) ݴޠϞσϧࠞ߹ σʔλͷॏΈ෇͚
14. ਓखʹΑΔจ๏ 0 1 <<
    >> 2 <<>> 3 4 5 6  <<
    >>  • OpenGrm ThraxͳͲͷπʔϧͰɼΑΓώϡʔϚϯɾϑϨϯυϦͳܗͰจ๏Λ࡞Δ͜ͱ͕Ͱ͖Δɻ ૝ఆ͞ΕΔग़ྗจ๏ͷϞσϧΛ࡞͓ͬͯ͘͜ͱ͕Ͱ͖Δ
15. ݴޠϞσϧࠞ߹ Wikipedia text Web ਓखͰॻ͍ͨจ๏ θ1 θ2 θ3 αϯϓϦϯά υϝΠϯจ๏σʔλ ̂ θ ॏΈௐ੔༻ σʔλ ৽ػೳͷݴޠϞσϧΛطଘͷෳ਺ͷݴޠϞσϧͷ ॏΈ෇͖࿨ʹΑͬͯද͠ɼॏΈͷΈΛௐ੔͢Δ (ॏΈ͸ਓखͰ΋ௐ੔Ͱ͖Δ)
16. ྫ3: ϢʔβʔຖͷΧελϚΠζ 0 1 <<
    >> 2 <<>> 3 4 5 6  <<
    >>  • ݻ༗໊ࢺͷ׬ᘳͳࣗ༝ೝࣝ͸ࠔ೉ 
 (ಛʹදهΛ߹ΘͤΔඞཁ͕͋Δ৔߹ɻγεςϜσβΠϯʹΑͬͯASRͰͷղܾΛආ͚Δ͜ͱ΋) • e.g. “΀Γͯ͌ɾ΢ʔϚϯ” (๜ը) vs “Pretty Woman” (༸ը) • ۂ໊ͳͲ͸ϓϨΠϦετʹؚ·ΕΔޠͷ֬཰Λ্͛Δ͜ͱͰରԠՄೳ ͜ͷΑ͏ʹͯ͠ಘͨจ๏Λࠞ߹ͨ͠Γɼจ๏͔ΒͷαϯϓϧΛ༻ֶ͍ͯशͨ͠ΓͰ͖Δ
17. E2EԻ੠ೝࣝث͸ΧελϚΠζͰ͖Δ͔? →෦෼తʹYes!!
18. E2EԻ੠ೝࣝ Τϯίʔμ σίʔμ 132 4. Ի ੠ ೝ ࣝ γ ε ς Ϝ 0 1 a:ε 2 k:֋ 3 i:ε 4 e:ֆ SIL:ε k:੺͍ 5 o:੨͍ a:ε i:ྑ͍ e:Ո 6 k:ε a:ε k:֋ i:ε e:ֆ SIL:ε i:ε a:ΠΧ e:஑ ਤ 4.4 ൃԻࣙॻΛද͢ FST (ϙʔζڐ༰; ࠷దԽ) ਤ 4.5 ೾ܗʮྑ͍ֆʯ ઢܗ࣌ෆมγεςϜ (linear time-invariant system) ͱݺ͹ΕΔγεςϜͰྑ <latexit sha1_base64="EUsov3jqKi2M5jTfU6NwWlpGo3s=">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</latexit> p(yn | X, y1:n 1 ) Ξςϯγϣϯܕ τϥϯεσϡʔαܕ Τϯίʔμ 132 4. Ի ੠ ೝ ࣝ γ ε ς Ϝ 0 1 a:ε 2 k:֋ 3 i:ε 4 e:ֆ SIL:ε k:੺͍ 5 o:੨͍ a:ε i:ྑ͍ e:Ո 6 k:ε a:ε k:֋ i:ε e:ֆ SIL:ε i:ε a:ΠΧ e:஑ ਤ 4.4 ൃԻࣙॻΛද͢ FST (ϙʔζڐ༰; ࠷దԽ) ਤ 4.5 ೾ܗʮྑ͍ֆʯ ઢܗ࣌ෆมγεςϜ (linear time-invariant system) ͱݺ͹ΕΔγεςϜͰྑ ۙ͘ࣅͰ͖ΔɽԻ੠ೝࣝγεςϜ͕࣮ࡍʹ؍ଌ͢Δ৴߸͸ɼൃ࿩ऀ͔Β์ࣹ͞ ϓϨσΟΫγϣϯ ωοτ ઌߦ୯ޠྻ ઌߦ୯ޠྻ δϣΠϯτ 
 ωοτ <latexit sha1_base64="Ow/kAhK/45uuHlk3tq1TXitFb2g=">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</latexit> p(zn,t | X, y1:n 1 ) (FSTͱͷࠞಉʹ஫ҙ!!)
19. Τϯίʔμ σίʔμ 132 4. Ի ੠ ೝ ࣝ γ ε ς Ϝ 0 1 a:ε 2 k:֋ 3 i:ε 4 e:ֆ SIL:ε k:੺͍ 5 o:੨͍ a:ε i:ྑ͍ e:Ո 6 k:ε a:ε k:֋ i:ε e:ֆ SIL:ε i:ε a:ΠΧ e:஑ ਤ 4.4 ൃԻࣙॻΛද͢ FST (ϙʔζڐ༰; ࠷దԽ) ਤ 4.5 ೾ܗʮྑ͍ֆʯ ઢܗ࣌ෆมγεςϜ (linear time-invariant system) ͱݺ͹ΕΔγεςϜͰྑ <latexit sha1_base64="EUsov3jqKi2M5jTfU6NwWlpGo3s=">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</latexit> p(yn | X, y1:n 1 ) Ξςϯγϣϯܕ ઌߦ୯ޠྻ • ୯ޠͷ֬཰Λ௚઀ਪఆ͢Δ 
 γϯϓϧͳߏ଄ • σίʔμ͸ΞςϯγϣϯػߏͰ 
 Τϯίʔμग़ྗΛಡΈͱΔ 
 RNNݴޠϞσϧͷҰछ
20. τϥϯεσϡʔαܕ Τϯίʔμ 132 4. Ի ੠ ೝ ࣝ γ ε ς Ϝ 0 1 a:ε 2 k:֋ 3 i:ε 4 e:ֆ SIL:ε k:੺͍ 5 o:੨͍ a:ε i:ྑ͍ e:Ո 6 k:ε a:ε k:֋ i:ε e:ֆ SIL:ε i:ε a:ΠΧ e:஑ ਤ 4.4 ൃԻࣙॻΛද͢ FST (ϙʔζڐ༰; ࠷దԽ) ਤ 4.5 ೾ܗʮྑ͍ֆʯ ઢܗ࣌ෆมγεςϜ (linear time-invariant system) ͱݺ͹ΕΔγεςϜͰྑ ۙ͘ࣅͰ͖ΔɽԻ੠ೝࣝγεςϜ͕࣮ࡍʹ؍ଌ͢Δ৴߸͸ɼൃ࿩ऀ͔Β์ࣹ͞ ϓϨσΟΫγϣϯ 
 ωοτ ઌߦ୯ޠྻ δϣΠϯτ 
 ωοτ <latexit sha1_base64="Ow/kAhK/45uuHlk3tq1TXitFb2g=">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</latexit> p(zn,t | X, y1:n 1 ) • ͸ΞϥΠϯϝϯτ • : ઌߦ୯ޠ͕ ͷ࣌ɼ 
 ࣌ࠁ Ͱ͸Կ΋ग़ྗ͠ͳ͍ • : ઌߦ୯ޠ͕ ͷ࣌ɼ 
 ࣌ࠁ Ͱ୯ޠ Λग़ྗ • ͔Β୯ޠྻΛ෮ݩ͢Δʹ͸ 
 ViterbiΞϧΰϦζϜ͕ඞཁ • ֶश࣌͸ ͷपล֬཰ΛٻΊΔ 
 લ޲͖ޙ޲͖ΞϧΰϦζϜ͕ඞཁ zn,t zn,t = ϕ y1:n−1 t zn,t = y′  y1:n−1 t y′  zn,t zn,t (FSTͱͷࠞಉʹ஫ҙ!!)
21. E2EԻ੠ೝࣝ <latexit sha1_base64="SqlHWtdxa4stj2qy1iIvwiiwXpM=">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</latexit> p(y | X, D) = NeuralNet(y, X; ⇥(D)) • جຊతʹ͸ϖΞσʔλͰͷֶश͕ඞཁ • ݴޠϞσϧʢΒ͖͠෦෼ʣͱԻڹϞσϧʢΒ͖͠෦෼ʣʹ෼͔Ε͍ͯΔ͕ ෼୲͸໌֬Ͱͳ͍ (༷ʑͳݚڀใࠂ͕ɼΤϯίʔμ͕૝ఆҎ্ʹ͍Ζ͍Ζ΍ͬͯΔ͜ͱΛ͍ࣔࠦͯ͠Δ)
22. External LM in attention-based ASR Shallow Fusion Deep Fusion [Toshniwal et al. 2018] Cold Fusion • σίʔμग़ྗͱ֎෦ݴޠϞσϧͷੵΛ࣍୯ޠͷ༧ଌ෼෍ͱͯ͠࢖͏ • σίʔμͷӅΕ૚ग़ྗͱ֎෦ݴޠϞσϧͷӅΕ૚ग़ྗΛܨ͛ͯɼ 
 ৽ͨͳग़ྗ૚Λֶशͤ͞Δ͜ͱͰ༥߹ • σίʔμग़ྗΛ࢖͏͔֎෦LMΛ࢖͏͔Λબ͹ͤΔήʔτͱASRΛಉ࣌ʹֶश
23. External LM in attention-based ASR Shallow Fusion Deep Fusion [Livescu et al. 2018] Cold Fusion • σίʔμग़ྗͱ֎෦ݴޠϞσϧͷੵΛ࣍୯ޠͷ༧ଌ෼෍ͱͯ͠࢖͏ • σίʔμͷӅΕ૚ग़ྗͱ֎෦ݴޠϞσϧͷӅΕ૚ग़ྗΛܨ͛ͯɼ 
 ৽ͨͳग़ྗ૚Λֶशͤ͞Δ͜ͱͰ༥߹ • σίʔμग़ྗΛ࢖͏͔֎෦LMΛ࢖͏͔Λબ͹ͤΔήʔτͱASRΛಉ࣌ʹֶश Ϟσϧͷ࠶ֶश͕ෆཁͰ͔༷ͭʑͳλΠϓͷݴޠϞσϧΛ 
 ߹੒Ͱ͖ΔͨΊ޿͘༻͍ΒΕ͍ͯΔ
24. Shallow Fusion • σίʔμग़ྗͱ֎෦ݴޠϞσϧͷੵΛ࣍୯ޠͷ༧ଌ෼෍ͱͯ͠࢖͏ ʢैདྷͷԻ੠ೝࣝͰݟΒΕΔʣϕΠζଇʹجͮ͘୯ޠͷࣄޙ֬཰ʹݟ͑ͳ͘΋ͳ͍͕…. ASRϞσϧͷग़ྗ͸طʹݴޠϞσϧΛؚΜͩ΋ͷͳͷͰ ݴޠϞσϧ͕μϒͬͯ͠·͍ͬͯΔ <latexit sha1_base64="Ibe8NQe/HBmLPl73mSfSD6aQNAw=">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</latexit> p(yn | X, y1:n 1 ) / exp log pDec(yn | X, y1:n 1 ) + log pExtLM(yn | y1:n 1 ) <latexit sha1_base64="LlLj+taxyb83qkamVapH8WmMFZY=">AABJR3iczVzbctvIER1vkt2Nc1lv8pgXbCRX2SlbluzcKpuk1rZkyxetZFmSZZteFUhCJC0ShAlSlkzjJ/JX+YJUnvIJeUvlJVXp6cYQg+EQ3fCmKiuWJAjoc6bn1tPdmFEz6ffS8erq3y989L3v/+DjTz794cUf/fgnP/3s0uc/O0iHk1Er2m8N+8PRYTNMo34vjvbHvXE/OkxGUTho9qNnzZO7+vmz02iU9obx3vg8iV4Nwk7cO+61wjHcOrr0JrlyfjSNs6Ax6LXhRzieHmbXgsZp1JqeZ0fTtT/E19eyq0EjGQ2T8TBIruQyBDg/ij3CZU7n6dGlpdWVVfwK5i/W8osllX/tDD9f+odqqLYaqpaaqIGKVKzGcN1XoUrh81KtqVWVwL1Xagr3RnDVw+eRytRFwE5AKgKJEO6ewM8O/PUyvxvD35ozRXQLSunD9wiQgbqcy7Th+hjv0m9dfmDJLipjitxax3P43cw5B3B3rLpwl8MZSSlO12kMGv4e69IDPRO8o2vZKtXoGH734e8x6K9/noNkBFdtQI3gqgX3+nCX7ugyRvCb2lXXvIvtHKJcBFdaJ63VCMuK1FtsnQHqHAPHFJ7tYKtOoSTqlUVyxJrhtamzbuV26c4IrnQ7Zfip4ovUGdZOzrohYE2hLTpCPiPLc3bgWspJshI9B9jfNAak+g5ELTvK+5TnNLIcp76TinuqkOZ4+yiZCnkLaY5X245Q3GtbM2mO9xRnmIzVyHKcBzU4D4Sc+s5pjd46FXDercF5t8RZxdrGOzJWI8tpul6Dc13IOcLrDq5eEl5bnuPercm9O8ddxa5XHL0+yrgfiGbXxGJ9qW7iylaUdAX+WoL1P7PYk9zWjeHZl6jLEuAydZW1ZrHY7mwKdNcr5ymsPVrvW7ne/BjRrEezWl1B3W2pCGwTzeUIPZ0MJG6xdSNdNKKTewNRqT1lel1BrThtbrLanACKNKqrw9Hc3Ufq8Qfoxo3iNvpWmaOFYWwCRnuADfTGyAfTXtt18ENX1G/gE+FMD2ay3FiJUYoveQifEK57uPpPUYNj+KuvbljXDfTX9PdyqT7LQnseY+8UutjjV9fnDK6XrZlXyJq51lDX1Hv8OcXxmeVl823wIeW7rcdrcRE8YW4EZBhZyMYm2bIGxhzHcP9lPhpH2FNdjE2qa7+4zCYwTvOacvxVJezhqPLXRscBiTU6qvz4zTmeFDWU2ERdy9OFeugZlGFNea/WtdTFHBmjxz9GP3YK8zHD65WcVY8GbhxW+XPhzN+sbu0hPlnsb5Jl0HbQRIdD1F9S+3do0YYV7H7uVeGqFYojm0Ka95Tq8K47vHq+6k+Aq1gLx6uOOgOw+6au17FNqMxgxldE7CnY/uo+0zMtdDSk2Rey9dNyTS+2KcK6sRlhWyJs24tti7CuJ0jYSIQ99mKPRVh3JBC2I8J2vdiuCNvzYnsi7Gsv9rUIe+LFnoiwfS+2L8K60QlhByKsawUJG4uwbhRA2KEI6/o/hE1E2Dde7BsR1o2NCTsSYV1bTNhUhHXXMsLyXmMT8zo+7ESEdWNswp6KsG+92Lci7JkXeybCnnux5yLsOy/2nWA115K3vejbopLveLF3RNi7XuxdEXbdi10XYTe82A0R9p4Xe0+Eve/F3hdhN73YTRH2gRf7QIR96MU+FGEfebGPRNjHXuxjEXbLi90SYb/2Yr8WYbe92G0RdseL3RFhn3ixT0TYXS92V4R96sU+FWH3vNg9EXbfi90XYQ+82AMR9pkX+0yEPfRiD0XY517scxH2hRf7Qrgy6IxMgu/EMrU4+mqU5CTRRAS6cJyFlMTnDvO71Zy2nCT60JE3r6ktJ4lLEnwP1cforZrZlZV4PiFmDORl+BESn0PSi+9q9KKET86mR7uE0ZaTtq+Ue15aEscNBcyFlCRCC6F3E5bTlpPEbiGi2yxvWVIS2U0YxoEwDohZpljIdDaLrxcxnQlj7YRlSoRMNLp4PltOEit2ZzHuIkYjI9VRwlmWlMSlOkPM23xbTqqvlHteWmKXQnZUGhlJlCy39K6sZKx2BaO1W3O88pxlSUmOkedsidmolbhap0I2fS9Cz6Oa0ZaT+Gb3hT6PLSeJq2U+jy0n8fZl6+VerZXysXgFKktKvHWu/w+Fvb/DMu0ImZ4KbdLTWtZov4b9cGUltefn5Y54Xu4I5uWOeF5uC+elLVd+Y5PiWKV3NS2Mgej99Qj9qG6+p9BEXnXe1xCbm5eju5LMHEm6uTmD57NzJOnm5wyez9CRpJujM3g+S0eSbp7O4PlMHUm6uTqD57N1JOnm6wyez9iRpJuzM3g+a0eSbt7O4PnMHUm6uTuD57N3JOnm7wyez+CRpJvDM3g+i0eSbh7P4PlMHkm6uTyD57N5JOnm8wyez+iRpJvTM3g+q0eSbl7P4PnMHkm6uT2D57N7JOnm9wyez/CRpJvjM3g+y0eSbp7P4PlMH0m6uT6D57N9JOnm+wyez/iRpJvzM3g+60eSbt7P4PnMH0m6uT+DL7J/l78jn2JN3cK9+Vuwxu2BnQyc5///T1WrD3AXEO0wt9uddn4UT3uYFaP9OtX9WGDI17B3UU1Qis4oRLgTiHaN8SXrUvndQvr6rKI25mmd2hjMt6tNuWRZbd5iZDFS7q4Q4iyeujsf15CH3wX0aG61K+/irMIe4AkUv2bFM253U4QZVLNLIMUoSp+gKfaPlZkJkaH8n1j+27jDltpe2m8hYhrqi1nfS3rKlNTDGONDSiIkX1LordMizYu9y3Lmch0WaVqHuYUxhG+XoDmHEOd9Hwv2WcSI1UzL8J2pbzyc43z/0TJYY45N73mrZiMJGVvMssU12EybLWYz+x8NW9VO2g1l7/A2u1cp163PFeg7tMO92MlanIDQT4ter9a8XFJZ4w1n9Ni7aMtlv8prFKjqPbDaQ+iooaJTcV0co62ZnDlJYEb0DfUrYNSlB3B1g6nJDnz8VtI8qcYP8zcpI3jaQyvg4/JJGW/H2EltczcgjtWaX87bhT6a7wFmWyaqCT/HwKMj7jsgvQ6YexD9bYLEQ7TsWxBLbIPuT8Cnfgoeyz7wPgP/7jn4WCHgW3l5HcwGvMbzAQOld3UnYKlHOOIm6hQ0PQO/h3bxUF/aOtm6mbrSe9xi/Pilm9giS9be24tM/9MuVNvu+vMikpGb5uvR/4KL6s1zuaNhSbTvOJ7zR8rtPO9Du226iLmHI0DPGj2fynu8iki+2ta47Vju98U4N/5KhXssYvR47FXLMIytdZdjmczWFtvemlMOZlXhNBliP9o9Y2zc+9K1e2rgvfMXv3KRZS6fHqK6XlMr8LmW21RJjx3na8n8eEqdeVuHg5s9VWy7WDv/CG8KNSKObXye5RaZzl710ZMhf1nG8kLRTv9FPKssT4J4fVpogpnXzDNSi2cS26fPNiU4S018QhZR+2xxvq708nas0qzMYzzy6WzsSJD0LjScWQwJuq/o1H+BNL39frZKczPBtGpxrroYMeb8SQr3peOu8Cco2iisyu05TyObeSfHYv5EDZ1ZUvhA9rWpf9knqnfOyOyImvc8aLTZT7n3D9qvmCzgKZ4Zjfo4Hhv5/I9VH7n7uOprH4XaN8jvBjhKg5L8Im3IxsZoSbQnFLAeYjyba0Yr0qcoS+utNdvF8UxzO5jN7QBnpbZfesYX/39imD81ctwbEu2jmf99kPf+F3/5gBHUxrYPS3PeXe3XVWH1A9C8l2vZgZqEsxZv4/yo7vdCzl5nzMyyvbogPyN7VTUs1PzZRLp30/IDu+h1kN/xbbTtLtC2njZ2nQP0yeltWIgrj+6rUzwTNcY9TTHTfqGj0y1BC36Js/9WzZas1qM4o1acyiuuaR7/EWT+LPByIiHbDSGfttwnAj6SKxir7az+/ypdy17aNreHu7YinEUTlNGj7avcK4tyq0h7HHT/Lys6j6czbX1cq1Jc9ShqXstP93Zy/y+yMnIpekY9Vl/ynmhXoy9KrLu3kqzDAGeW5tPn7y8eXVpac/+/z/zFwc2Vtd+u3Hzy66Wv7uT/++dT9Qv1Sxida+p30EqbEEHuQ5l/U/+58PGFTzb/uvnPzX9t/ptEP7qQY36uSl8PLvwX9iOIfA==</latexit> p(yn | X, y1:n 1 ) / p(X | yn, y1:n 1 )p(yn | y1:n 1 )
25. Hybrid auto-regressive transducer [Variani et al. 2020] Τϯίʔμ 132 4. Ի ੠ ೝ ࣝ γ ε ς Ϝ 0 1 a:ε 2 k:֋ 3 i:ε 4 e:ֆ SIL:ε k:੺͍ 5 o:੨͍ a:ε i:ྑ͍ e:Ո 6 k:ε a:ε k:֋ i:ε e:ֆ SIL:ε i:ε a:ΠΧ e:஑ ਤ 4.4 ൃԻࣙॻΛද͢ FST (ϙʔζڐ༰; ࠷దԽ) ϓϨσΟΫγϣϯ 
 ωοτ ઌߦ୯ޠྻ δϣΠϯτ 
 ωοτ <latexit sha1_base64="XsMd3vZnk30zKJ69lbxLdGdN0+c=">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</latexit> z }| { ୯ޠͷग़ྗ֬཰ ʮ࣍ͷ࣌ࠁΛݟʹߦ͔͘ʯ ͷબ୒ γάϞΠυʢ== D=2ͷSoftmaxʣͰਪఆ ޠኮ਺ͱಉ͡αΠζͷSoftmaxͰਪఆ ͜ͷ෼ղʹΑͬͯɼΤϯίʔμग़ྗʹґଘ͠ͳ͍ 
 ࣍୯ޠͷ༧ଌ෼෍ Λۙࣅతʹ ಘΔ͜ͱ͕Ͱ͖Δ (→಺෦ݴޠϞσϧ) p(yn ∣ y1:n−1 )
26. Hybrid auto-regressive transducer [Variani et al. 2020] • ಺෦ݴޠϞσϧΛΩϟϯηϧ͢Δ͜ͱͰɼݴޠϞσϧͷೋॏΛ๷͙ <latexit sha1_base64="FuuxFqSdLGvedzSUYzH4lkF+66M=">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</latexit> p(yn | X, y1:n 1 ) / exp 1 log pDec(yn | X, y1:n 1 ) 2 log pIntLM(yn | y1:n 1 ) + log pExtLM(yn | y1:n 1 ) Shallow Fusion͸ ʹ૬౰͢Δ͕ɼ ͕࠷ྑͰ͋Δ͜ͱ͕ࣔ͞Εͨ → Shallow FusionʹΑΔೋॏݴޠϞσϧ͸΍͸Γ໰୊͕͋Δ??? λ2 = 0 λ2 ≃ 1
27. Shallow-fusion with FSA [Pundak et al. 2018][Zhao et al. 2019] FSTݴޠϞσϧͷShallow Fusionͱ 
 E2EϞσϧͷϏʔϜαʔνͷ૬ੑ͕ѱ͍
28. ෮श: ϏʔϜαʔν • ϏʔϜαʔν 
 = ෯༏ઌ୳ࡧ 
 + ώϡʔϦεςΟοΫͳࢬמΓ • ίετͷ௿͍ʢ→֬཰ͷߴ͍ʣ 
 ग़ྗܥྻΛݟ͚ͭΔΞϧΰϦζϜ • ׬શʹࢬמΓ͞Εͯ͠·ͬͨ 
 ϓϨϑΟοΫε͸΋͏ग़ͯ͜ͳ͍ 308 Ҿ ༻ ɾ ࢀ ߟ จ ݙ i = 1 2 3 . . . ֤୯ޠ਺ຖͷ࠷େԾઆ਺
    W ࢬמΓ w 3,r
    
    w 3,1 + B or w 3,r
    
    f 1 + B or
    w 3,r
    
    f N ιʔτ͞ΕͨԾઆ܈ ྦྷੵॏΈɿߴ ྦྷੵॏΈɿ௿ ऴྃԾઆ ྦྷੵॏΈɿf 5 ྦྷੵॏΈɿw 3,1 σίʔμʔঢ়ଶɿh 3,1 ग़ྗγϯϘϧ
    y 3,1 ਤ 8.7 ୯ޠಉظϏʔϜ୳ࡧͷσʔλߏ଄ Schwenk, H. and Bengio, Y.: Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation, in Proc. Empirical
29. Shallow-fusion with FSA [Pundak et al. 2018][Zhao et al. 2019] FSTݴޠϞσϧͷShallow Fusionͱ 
 E2EϞσϧͷϏʔϜαʔνͷ૬ੑ͕ѱ͍ the biasing candidates in the beam. However, the authors only explored the idea using grapheme subword units. In addition, the authors never explored results with “anti-context”, to ensure that biasing does not affect recognition quality if all biasing phrases are not relevant. The following sections introduce improvements to shallow-fusion E2E biasing to address theses concerns. 0 1 c:c/-0.25 ε:ε/0.25 2 a:a/-0.25 ε:ε/0.5 3 t:t/-0.25 ε:ε/0.75 4 <space>:<space>/-0.25 Figure 1: Contextual FST for the word “cat”, represented at the subword unit level with backoff arcs. 2.3. Shallow Fusion Improvements ϖφϧςΟͷۉ౳෼഑ Failure Arcͷಋೖ εϩοτ͚ͩͰ͸ͳ͘ 
 จ຺΋ϞσϧԽ etc…
30. Contextual LASͳͲ [Pundak et al. 2020] [Jain et al. 2020] Τϯίʔμ σίʔμ 132 4. Ի ੠ ೝ ࣝ γ ε ς Ϝ 0 1 a:ε 2 k:֋ 3 i:ε 4 e:ֆ SIL:ε k:੺͍ 5 o:੨͍ a:ε i:ྑ͍ e:Ո 6 k:ε a:ε k:֋ i:ε e:ֆ SIL:ε i:ε a:ΠΧ e:஑ ਤ 4.4 ൃԻࣙॻΛද͢ FST (ϙʔζڐ༰; ࠷దԽ) ਤ 4.5 ೾ܗʮྑ͍ֆʯ ઢܗ࣌ෆมγεςϜ (linear time-invariant system) ͱݺ͹ΕΔγεςϜͰྑ <latexit sha1_base64="EUsov3jqKi2M5jTfU6NwWlpGo3s=">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</latexit> p(yn | X, y1:n 1 ) ઌߦ୯ޠྻ ֎෦৘ใ 
 Τϯίʔμ ϢʔβͷϓϨΠϦετ AppϦετͳͲ • Ϣʔβ৘ใΛΤϯίʔυͨ͠΋ͷΛ 
 ΞςϯγϣϯػߏͰσίʔμʹ౉͢ • Attention-basedͷσίʔμͷΈͰ͸ͳ͘ɼ Transducerʹ௥Ճͯ͠࢖͏͜ͱ΋Ͱ͖Δɻ 
 [Jain et al. 2020]
31. ·ͱΊ
32. E2EԻ੠ೝࣝͱैདྷܕͷΧελϚΠζੑͷൺֱ • E2EԻ੠ೝࣝͷݴޠϞσϧͷΧελϚΠζ͸࣮֬ʹਐΜͰ͖͍ͯΔ • ҰํɼൃԻࣙॻͷΧελϚΠζ͸೉͍͠ 
 
 → E2EԻ੠ೝࣝ͸ൃԻࣙॻΛ༻͍ͳ͍ͷͰ౰ͨΓલ 
 → όοΫΤϯυ͕දهͷҧ͍ʹහײͳ৔߹ɼE2E͸࢖͍ͮΒ͍ 
 (୯७ʹԻૉͱ୯ޠͷ྆ํΛE2Eͷ࿮૊ΈͰग़ྗ͢Δͱ͍͏ࢼΈ΋͋Δ)
33. ΧελϚΠζੑ͸ඞཁͳͷ͔ • ԻڹϞσϧͷΧελϚΠζʢϞσϧదԠʣ͸͋·Γ࢖ΘΕͳ͘ͳ͖ͬͯͨ 
 (Ή͠ΖEncoder pretrainingɼ͢ͳΘͪେྔͷΦʔσΟΦσʔλͰ൚༻ΤϯίʔμΛ࡞Δํ޲͕੝Γ্͍ͬͯΔɻ) • ݴޠϞσϧ΋ʮ௒ߴਫ਼౓ͷ൚༻Ϟσϧ͕Ұͭ͋Ε͹ྑ͍ʯͱ͍͏ํ޲ʹͳΔ͔? • ΦϯσόΠεASRͷΑ͏ʹܭࢉྔͱͷ݉Ͷ߹͍ͰΧελϚΠζ͕ඞཁͳ͜ͱ΋
34. ల๬ • CTCͷల։ɿCTC͸E2Eٕज़ͱͯ͠ఏҊ͞Ε͕ͨɼԻڹϞσϧͱͯ͠΋ߴਫ਼౓ • E2EͷͨΊʹల։͞Εٕͨज़͕ɼԻڹϞσϧٕज़ͱͯ͠ར༻͞ΕΔ͜ͱ΋ 
 (CTC/ SpecAug/ Transformer/ etc…) 
 • ߴ͍ΧελϚΠζੑͱE2EͷԸܙΛཱ྆͢ΔͨΊ 
 E2Eٕज़ͱैདྷͷԻڹʗݴޠϞσϧٕज़ͷ༥߹ʹ΋ظ଴
35. Thank you Yotaro Kubo @ Google Tokyo