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論文紹介 "Informer: Beyond Efficient Transformer for Long SequenceTime-Series Forecasting"
AAAI2021"Informer: Beyond Efficient Transformer for Long SequenceTime-Series Forecasting"の論文紹介用のスライドです。
taichi_murayama
August 14, 2021
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52 slides
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2 Title: Informer: Beyond Efficient Transformer for Long Sequence Time-Series
Forecasting Author: Haoyi Zhou1, Shanghang Zhang2, Jieqi Peng1, Shuai Zhang1, Jianxin Li1, Hui Xiong3, Wancai Zhang4 (1 Beihang University (ژߤۭߤఱେֶ), 2 UC Berkeley, 3 Rutgers University, 4 SEDD Company) Conference: AAAI 2021 (Thirty-Fifth AAAI Conference on Artificial Intelligence) AAAI-21 Outstanding Paper! Bibliographic Information -
3 • ਓೳܥͷࠃࡍձٞͷτοϓΧϯϑΝϨϯε AAAIͷOutstanding Paper (͢͝ ͍ձٞͷதͰ͍͢͝จ) • ظతͳܥྻ༧ଌΛऔΓѻͬͨจ •
TransformerͱͲ͏͍͏ͷ͔Λཧղ Purpose: Why I choose this paper. ҰݴͰݴ͏ͱ… ʮظతͳܥྻ༧ଌΛతͱͨ͠ɼܭࢉίετϝϞϦίετΛ ݮͨ͠TransformerͷมछΛఏҊ͠༧ଌੑೳΛ্ʯ • ܥྻ༧ଌλεΫʹ͓͍ͯTransformer(ଞͷਂ ֶशϞσϧؚΉ)͕ۤखͳͲ͜ͳͷ ͔ʁͲ͏͍͏ղܾࡦ͕͋Δ͔ʹ͍ͭͯཧղ -
4 Motivation • աڈͷܥྻ͔Βظతͳকདྷͷܥྻ ྫ͑ϙΠϯτઌि ؒઌͷܥྻ Λ༧ଌ • ӳޠͰ಄จࣈΛऔͬͯ-45'ͱݺশ •
طଘͷϞσϧͰࠔ ྫ-45.ʹΑΔܥྻ༧ଌ औΓΈ͍ͨ՝ظతͳܥྻ༧ଌ -POH4FRVFODF5JNFTFSJFT'PSFDBTUJOH MSE score: ⻑期先の予測で 予測精度が低下 Inference speed :推論速度の低下 -
5 Motivation • 5BTLաڈͷܥྻ͔ΒظతͳকདྷͷܥྻΛ༧ଌ͢Δͱ͍͏ܥྻ ༧ଌ • *OQVU𝑋! = 𝑥" !,
𝑥# !, … , 𝑥$ ! 𝑥% ! ∈ ℝ&!} • 0VUQVU𝑌! = 𝑦" !, 𝑦# !, … , 𝑦$ ! 𝑦% ! ∈ ℝ&"} औΓΈ͍ͨ՝ظతͳܥྻ༧ଌ -POH4FRVFODF5JNFTFSJFT'PSFDBTUJOH -
7 -45'ʹର͢Δ5SBOTGPSNFS׆༻ͷ՝ • 5SBOTGPSNFSͷॴ • ࣗવݴޠॲཧը૾ॲཧͳͲʹݶΒͣܥྻ༧ଌʹ͓͍ͯߴ͍ਫ਼Λୡ [Wu, 2020], [Yu, 2020]
• ظܥྻͷೖྗͰͷؔΞϥΠϝϯτΛͱΔ͜ͱ͕Մೳ • 5SBOTGPSNFSͷॴ • ظܥྻͷೖྗग़ྗͷܭࢉϝϞϦͷίετ͕ߴ্͘ख͍͔͘ͳ͍ • ظܥྻͷਪʹ͕͔͔࣌ؒΔ Motivation -
8 -45'ʹର͢Δ5SBOTGPSNFS׆༻ͷ՝ • 5SBOTGPSNFSͷॴ • ࣗવݴޠॲཧը૾ॲཧͳͲʹݶΒͣܥྻ༧ଌʹ͓͍ͯߴ͍ਫ਼Λୡ [Wu, 2020], [Yu, 2020]
• ظܥྻͷೖྗͰͷؔΞϥΠϝϯτΛͱΔ͜ͱ͕Մೳ • 5SBOTGPSNFSͷॴ • ظܥྻͷೖྗग़ྗͷܭࢉϝϞϦͷίετ͕ߴ্͘ख͍͔͘ͳ͍ • ظܥྻͷਪʹ͕͔͔࣌ؒΔ Motivation ͦͦ5SBOTGPSNFSͱԿ͔ʁ -
9 5SBOTGPSNFSͱʁ • (PPHMF͕ʮ"UUFOUJPOJTBMMZPVOFFEʯͰఏҊ [Vaswani, 2017] • ໊લͷͱ͓Γɼ"UUFOUJPO͕ओཁͳߏཁૉ • ࣗવݴޠॲཧ
/-1 ͚ͩͰͳ͘ɼ࠷ۙͰ$7 ͳͲͷଞͰ༷ʑͳݚڀͰ׆༻ FY#&35 (15 7J5 • 5SBOTGPSNFSҎલ$//ͱ3//͕த৺ What’s Transformer? -
16 5SBOTGPSNFSͷத What’s Transformer? • جຊ&ODPEFS%FDPEFSϞσϧ • 1PTJUJPOBM&ODPEJOHͱ͍͏֤ೖྗͷ ҐஔใΛϕΫτϧͰදݱ •
&ODPEFS %FDPEFSͱʹ .VMUJIFBEBUUFOUJPOͱ'FFE'PSXBSEͰ ߏ͞Εͨ5SBOTGPSNFS#MPDLͷੵΈॏͶ Transformer Block -
19 5SBOTGPSNFS#MPDL What’s Transformer? • &ODPEFSɼ%FDPEFSͱͱʹ5SBOTGPSNFS #MPDLͷੵΈॏͶͰߏ • 5SBOTGPSNFS#MPDLͷߏ .VMUJ)FBE4FMGBUUFOUJPO
3FTJEVBM$POOFDUJPO ࠩଓ -BZFS/PSNBMJ[BUJPO 1PTJUJPOXJTF'FFE'PSXBSE %SPQPVU Transformer Block -
20 4FMGBUUFOUJPO What’s Transformer? ⼊⼒系列の 潜在表現 系列⻑ × 次元数 Key
: K Query: Q 𝑊' 𝑊( Value: V Attention Map : M 系列⻑ × 系列⻑ 𝑊) 𝑊*+! Output 𝑠𝑜𝑓𝑡𝑚𝑎𝑥( 𝑄𝐾, 𝑑 ) -
21 4FMGBUUFOUJPO What’s Transformer? Value: V Attention Map : M
系列⻑ × 系列⻑ 𝑊*+! Output 𝑠𝑜𝑓𝑡𝑚𝑎𝑥( 𝑄𝐾, 𝑑 ) -
23 -45'ʹର͢Δ5SBOTGPSNFS׆༻ͷ՝ ࠶ܝ • 5SBOTGPSNFSͷॴ • ࣗવݴޠॲཧը૾ॲཧͳͲʹݶΒͣܥྻ༧ଌʹ͓͍ͯߴ͍ਫ਼Λୡ [Wu, 2020], [Yu,
2020] • ظܥྻͷೖྗͰͷؔΞϥΠϝϯτΛͱΔ͜ͱ͕Մೳ • 5SBOTGPSNFSͷॴ • ظܥྻͷೖྗग़ྗͷܭࢉϝϞϦͷίετ͕ߴ্͘ख͍͔͘ͳ͍ • ظܥྻͷਪʹ͕͔͔࣌ؒΔ Motivation ఏҊख๏*OGPSNFSͰղܾ -
24 5SBOTGPSNFSͷ$PNQVUBUJPOBM$PNQMFYJUZ Method Complexity per Layer Convolutional 𝑂 𝐾 /
𝐷! / 𝐿 Recurrent 𝑂 𝐿 / 𝐷! Self-attention (Transformer) 𝑂 𝐿! / 𝐷 Method: • ظܥྻͰͳ͚Ε %-ͱͳΓܭࢉ࣌ؒͦ͜·Ͱͳ͍͕ɼ ظܥྻΛೖྗͱ͢Δͱɼ-%ͱͳΓܭࢉ࣌ؒϝϞϦ͕ʹ • ߋʹɼ-BZFSΛੵΈॏͶΔ͜ͱͰܭࢉ͕࣌ؒ/ഒʹ K: the length of filter D: dimensionality of space L: input length N: Number of layers Computational Complexityは 𝑶 𝑵×(𝑳𝟐 & 𝑫) -
25 *OGPSNFSʹΑΔ$PNQMFYJUZݮ Method: ̎ͭͷ$PNQMFYJUZݮख๏ΛఏҊ • 1SPC4QBSTFॏཁͷߴ͍"UUFOUJPO.BQͷΈΛར༻ 𝑂 𝐿) # 𝐷
ˠ 𝑂 𝐿 log 𝐿 # 𝐷 ʹݮ • 4FMGBUUFOUJPO%JTUJMMJOH ηϧϑΞςϯγϣϯΛग़Δ ܥྻͷ͕͞ʹͳΔΑ͏ৠཹ 𝑂 N # ⋯ ˠ 𝑂 2 − 𝜖 # ⋯ ʹݮ -
26 4FMGBUUFOUJPO ࠶ܝ Method: ProbSparse ⼊⼒系列の 潜在表現 Key : K
Query: Q 𝑊' 𝑊( Value: V Attention Map : M 系列⻑ × 系列⻑ 𝑊) 𝑊*+! Output 系列⻑(L) × 次元数(D) 𝑠𝑜𝑓𝑡𝑚𝑎𝑥( 𝑄𝐾, 𝐷 ) -
27 1SPC4QBSTF Method: ProbSparse ⼊⼒系列の 潜在表現 系列⻑(L) × 次元数(D) Key
: K Query: 2 𝑄 𝑊' 𝑊( Value: V Attention Map : M 系列⻑ × 系列⻑ 𝑊) 𝑊*+! Output 𝑠𝑜𝑓𝑡𝑚𝑎𝑥( 8 𝑄𝐾, 𝐷 ) 上位u件のQuery のみを利⽤ -
28 1SPC4QBSTF Method: ProbSparse ⼊⼒系列の 潜在表現 系列⻑(L) × 次元数(D) Key
: K Query: 2 𝑄 𝑊' 𝑊( Value: V Attention Map: M 系列⻑ × 系列⻑ 𝑊) 𝑊*+! Output 𝑠𝑜𝑓𝑡𝑚𝑎𝑥( 8 𝑄𝐾⊺ 𝐷 ) 上位u件のQuery のみを利⽤ 1: その上位はどのように選択するのか? 2: 計算効率はどれぐらい良くなるの? -
29 1SPC4QBSTFॏཁͷߴ͍2VFSZͷબ Method: ProbSparse 2VFSZ2ͷߦϕΫτϧ𝑞* ʹର͢Δ"UUFOUJPO.BQͷॏΈ ͜ͷॏΈ͕Ұ༷͔Βҳ͍ͯ͠Δ΄Ͳɼ ॏཁ͕ߴ͍4QBSTJUZNFBTVSFNFOUͰࢉग़ Query: 2
𝑄 Attention Map : M 系列⻑ × 系列⻑ 9 5 𝑒𝑥𝑝 𝑞% , 𝑘5 𝐷 ∑6 𝑒𝑥𝑝 𝑞%, 𝑘6 𝐷 正規化項 -
32 1SPC4QBSTFॏཁͷߴ͍2VFSZͷબ Method: ProbSparse 4QBSTJUZNFBTVSFNFOU Ұ༷ͱ"UUFOUJPO.BQͷ,VMMCBDL-FJCMFSڑʹج͍ͮͨई ͜ͷईͷʹج͍ͮͯɼ্ҐV݅ͷRVFSZͷΈΛར༻ 𝑀 𝑞! ,
𝐾 = 𝑙𝑛 ( "#$ % 𝑒 &!'" ⊺ ( − 1 𝐿) ( "#$ % 𝑞! 𝑘" ⊺ 𝐷 -
33 1SPC4QBSTFॏཁͷߴ͍2VFSZͷબ Method: ProbSparse 𝐾𝐿 𝑞 𝑝 = 1 𝐿
9 57" $ 𝑙𝑜𝑔 1 𝐿8" − 𝑙𝑜𝑔𝑍% + 𝑞%𝑘5 𝐷 = 𝑙𝑜𝑔 1 𝐿8" − 𝑙𝑜𝑔𝑍% + 1 𝐿 9 57" $ 𝑞%𝑘5 𝐷 = 𝑙𝑜𝑔 1 𝐿8" − 𝑙𝑜𝑔 9 57" $ exp( 𝑞%𝑘5 𝐷 ) + 1 𝐿 9 57" $ 𝑞%𝑘5 𝐷 ⼀様分布とAttention MapのKL距離 𝑞 = 1 𝐿 𝑝 = 𝑒𝑥𝑝 𝑞"𝑘# 𝐷 ∑$ 𝑒𝑥𝑝 𝑞", 𝑘$ 𝐷 = 𝑒𝑥𝑝 𝑞"𝑘# & 𝐷% & ' 𝑍" ⼀様分布 Query 𝒒𝒊 における Attention Map 𝑀 𝑞", 𝐾 = 𝑙𝑛 ; #(& )! 𝑒 *"+# ⊺ , − 1 𝐿- ; #(& )! 𝑞"𝑘# ⊺ 𝐷 Sparsity Measurement 定数項 -1 × Sparsity Measurement ref: https://cookie-box.hatenablog.com/entry/2021/02/11/195 -
34 1SPC4QBSTFܭࢉޮͷ Method: ProbSparse 4QBSTJUZ.FBTVSFNFOUͷܭࢉࣗମ͕𝑶 𝑳𝟐 ͜ͷܭࢉࣜΛҎԼͷΑ͏ʹLFZWFDUPS͔ΒαϯϓϦϯάʹΑΔۙࣅ Λߦ͏͜ͱͰ 𝑂 L
log 𝐿 Λୡ (Max − mean Measurementͷܗ) 𝑀 𝑞% , 𝐾 = 𝑙𝑛 9 57" $# 𝑒 :$;% ⊺ & − 1 𝐿' 9 57" $# 𝑞% 𝑘5 ⊺ 𝐷 L 𝑀 𝑞% , 𝐾 = max 5 𝑞% 𝑘5 ⊺ 𝐷 − 1 𝐿' 9 57" $# 𝑞% 𝑘5 ⊺ 𝐷 -
35 ,-ڑ≥ 0Ͱ͋Δ͜ͱ͔Βɼ𝐾𝐿 𝑞 𝑝 = 𝑙𝑜𝑔 > ?!" −
𝑀 𝑞* , 𝐾 ΑΓ ·ͨҎԼͷࣜʹΑΓ 1SPC4QBSTFܭࢉޮͷ Method: ProbSparse 𝑀 𝑞%, 𝐾 = 𝑙𝑛 9 57" $# 𝑒 :$;% ⊺ & − 1 𝐿' 9 57" $# 𝑞% 𝑘5 ⊺ 𝐷 ≤ 𝑙𝑛 𝐿 P max 5 𝑒 :$;% ⊺ & − 1 𝐿' 9 57" $# 𝑞% 𝑘5 ⊺ 𝐷 = 𝑙𝑛𝐿 + max 5 :$;% ⊺ & − " $# ∑ 57" $# :$;% ⊺ & 𝑙𝑜𝑔𝐿 ≤ 𝑀 𝑞! , 𝐾 = G 𝑀 𝑞* , 𝐾 : Sparsity Measurementの近似解 -
36 1SPC4QBSTFΞϧΰϦζϜ Method: ProbSparse Sampling Sparsity Measurement Select Top-u from
Q Calculate Attention Map -
37 *OGPSNFSʹΑΔ$PNQMFYJUZݮ ࠶ܝ Method: ̎ͭͷ$PNQMFYJUZݮख๏ΛఏҊ • 1SPC4QBSTFॏཁͷߴ͍"UUFOUJPO.BQͷΈΛར༻ 𝑂 𝐿) #
𝐷 ˠ 𝑂 𝐿 log 𝐿 # 𝐷 ʹݮ • 4FMGBUUFOUJPO%JTUJMMJOH ηϧϑΞςϯγϣϯΛग़Δ ܥྻͷ͕͞ʹͳΔΑ͏ৠཹ 𝑂 N # ⋯ ˠ 𝑂 2 − 𝜖 # ⋯ ʹݮ -
39 Self-attention Distilling Method: Self-attention Distilling K൪ͷK ൪ͷϨΠϠʔʹೖྗ͢Δͱ͖ʹɼ$POWE LFSOFMXJEUI ͱ.BY1PPMJOHΛ௨͢͜ͱͰܥྻΛѹॖ
ϨΠϠʔ͔ΒഒҎԼͷ$PNQMFYJUZʹѹॖ 𝑂 N # ⋯ ˠ 𝑂 2 − 𝜖 # ⋯ 𝑋@A> B = 𝑀𝑎𝑥𝑃𝑜𝑜𝑙 𝐸𝐿𝑈 𝐶𝑜𝑛𝑣1𝑑 𝑋@ B -
40 Method: Decoder Outputs through one forward "VUPSFHSFTTJWFʹΑΔਪ [Chen, 2019]
/POBVUPSFHSFTTJWFʹΑΔਪ ճؼʹΑΒͳ͍ਪ -
41 Method: Decoder Outputs through one forward "VUPSFHSFTTJWFʹΑΔਪ [Chen, 2019]
/POBVUPSFHSFTTJWFʹΑΔਪ ճؼʹΑΒͳ͍ਪ Informerはこれを採⽤ 推論が早くなるというメリット -
42 Experiment: Dataset • &5'தࠃͷͭͷҬͷిྗڙڅͷσʔλ BVUIPSTDPMMFDU • ͭͷܥྻ •
࣌ؒ୯Ґͱ୯Ґͷه • 5SBJOWBMUFTUNPOUIT • &$-ਓͷిྗফඅͷσʔλ [Li, 2019] • ࣌ؒ୯Ґͷه • 5SBJOWBMUFTUNPOUIT • 8FBUIFSΞϝϦΧ߹ऺࠃͷͷؾީσʔλ • ࣌ؒ୯Ґͷه • 5SBJOWBMUFTUNPOUIT -
43 Experiment: Baseline and Evaluation Metric • #BTFMJOF • ARIMA
• Prophet [Taylor, 2018] • LSTMa [Bahdanau, 2014] • LSTnet [Lai, 2018] • DeepAR [Salinas, 2020] • LogTrans [Li, 2019] • Reformer [Kitaev, 2019] • &WBMVBUJPO.FUSJDT • Mean Squared Error (MSE): " < ∑%7" < 𝑦 − Q 𝑦 # • Mean Absolute Error (MAE): " < ∑%7" < 𝑦 − Q 𝑦 -
44 Result: Univariate Time-series Forecasting • Informerが多くのデータセット+ 予測先において⾼い精度を達成 (特に⻑期予測) •
Query Sparsityを採⽤しなかったInformerと⽐べても,Informerが⾼い精度を達成 Attentionが着⽬する場所を制限することの効果を⽰す -
51 • ظతͳܥྻ༧ଌΛతͱͨ͠ɼܭࢉίετϝϞϦίετΛ ݮͨ͠Transformerͷมछ: InformerΛఏҊ͠༧ଌੑೳΛ্ • ॏཁͷߴ͍෦ͷΈΛAttention͢ΔProbSparseͱৠཹख๏Λ׆ ༻ͨ͠Self-attention DistillingʹΑͬͯϝϞϦίετΛݮ •
Non-autoregressiveͳग़ྗΛߦ͏͜ͱͰظ༧ଌʹ͓͍ͯਫ਼ Λҡ࣋ͨ͠ૣ͍ਪΛ࣮ݱ • ిྗσʔλؾީσʔλͳͲͷσʔλͰInformerͷ༗ޮੑΛࣔ͢ Result: Summary -
52 [Wu, 2020] Wu, Neo, et al. "Deep transformer models
for time series forecasting: The influenza prevalence case." arXiv preprint arXiv:2001.08317 (2020). [Yu, 2020] Yu, Cunjun, Xiao Ma, Jiawei Ren, Haiyu Zhao, and Shuai Yi. "Spatio-temporal graph transformer networks for pedestrian trajectory prediction." In European Conference on Computer Vision, pp. 507-523. Springer, Cham, 2020. [Vaswani, 2017] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... & Polosukhin, I. (2017). Attention is all you need. In Advances in neural information processing systems (pp. 5998-6008). [Yu, 2017] Yu, Fisher, Vladlen Koltun, and Thomas Funkhouser. "Dilated residual networks." Proceedings of the IEEE conference on computer vision and pattern recognition. 2017. [Chen, 2019] Chen, Nanxin, et al. "Listen and fill in the missing letters: Non-autoregressive transformer for speech recognition." arXiv preprint arXiv. [Li, 2019] Li, Shiyang, et al. "Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting." Advances in Neural Information Processing Systems 32 (2019): 5243-5253. [Taylor, 2018] Taylor, Sean J., and Benjamin Letham. "Forecasting at scale." The American Statistician 72.1 (2018): 37-45. [Bahdanau, 2014] Bahdanau, Dzmitry, Kyunghyun Cho, and Yoshua Bengio. "Neural machine translation by jointly learning to align and translate." arXiv preprint arXiv:1409.0473 (2014). [Lai, 2018] Lai, Guokun, et al. "Modeling long-and short-term temporal patterns with deep neural networks." The 41st International ACM SIGIR Conference on Research & Development in Information Retrieval. 2018. [Salinas, 2020] Salinas, David, et al. "DeepAR: Probabilistic forecasting with autoregressive recurrent networks." International Journal of Forecasting 36.3 (2020): 1181-1191. [Li, 2019] Li, S.; Jin, X.; Xuan, Y.; Zhou, X.; Chen, W.; Wang, Y.-X.; and Yan, X. 2019. Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Fore- casting. arXiv:1907.00235 . [Kitaev, 2019] Kitaev, N.; Kaiser, L.; and Levskaya, A. 2019. Reformer: The Efficient Transformer. In ICLR. Reference