From 67b37e68188dbe2a76a25d741533afe7d7eb921e Mon Sep 17 00:00:00 2001 From: seunghan96 Date: Thu, 5 Oct 2023 18:16:29 +0900 Subject: [PATCH] update --- _posts/2023-10-05-(CL_paper100)Nonst_Trans.md | 128 ++++++++++++++++-- _posts/non-stationary_transformer.pdf | Bin 2613070 -> 0 bytes assets/img/ts/img472.png | Bin 0 -> 68022 bytes assets/img/ts/img473.png | Bin 0 -> 344136 bytes assets/img/ts/img474.png | Bin 0 -> 145851 bytes assets/img/ts/img475.png | Bin 0 -> 199663 bytes assets/img/ts/img476.png | Bin 0 -> 73342 bytes assets/img/ts/img477.png | Bin 0 -> 143369 bytes assets/img/ts/img478.png | Bin 0 -> 89079 bytes 9 files changed, 118 insertions(+), 10 deletions(-) delete mode 100644 _posts/non-stationary_transformer.pdf create mode 100644 assets/img/ts/img472.png create mode 100644 assets/img/ts/img473.png create mode 100644 assets/img/ts/img474.png create mode 100644 assets/img/ts/img475.png create mode 100644 assets/img/ts/img476.png create mode 100644 assets/img/ts/img477.png create mode 100644 assets/img/ts/img478.png diff --git a/_posts/2023-10-05-(CL_paper100)Nonst_Trans.md b/_posts/2023-10-05-(CL_paper100)Nonst_Trans.md index 21f9cbe97435..e21d7924e137 100644 --- a/_posts/2023-10-05-(CL_paper100)Nonst_Trans.md +++ b/_posts/2023-10-05-(CL_paper100)Nonst_Trans.md @@ -17,6 +17,19 @@ https://github.com/thuml/Nonstationary_Transformers. 0. Abstract 0. Introduction +0. Related Works + 0. Deep Models for TSF + 0. Stationarization for TSF + +0. Non-stationary Transformers + 0. Series Stantionarization + 0. De-stationary Attention + +0. Experiments + 0. Experimental Setups + 0. Main Results + 0. Ablation Study +
@@ -24,7 +37,7 @@ https://github.com/thuml/Nonstationary_Transformers. Previous studies : use stationarization to attenuate the non-stationarity of TS -$\rightarrow$ can be less instructive for real-world TS +$$\rightarrow$$ can be less instructive for real-world TS
@@ -52,7 +65,7 @@ Non-stationarity of data However, non-stationarity is the inherent property -$\rightarrow$ also good guidance for discovering temporal dependencies +$$\rightarrow$$ also good guidance for discovering temporal dependencies
@@ -62,7 +75,7 @@ Example) Figure 1 - ( Figure 1 (b) ) Transformers trained on the stationarized series tend to generate indistinguishable attentions - $\rightarrow$ ***over-stationarization*** problem + $$\rightarrow$$ ***over-stationarization*** problem - unexpected side-effect ... makes Transformers fail to capture eventful temporal dependencies @@ -166,27 +179,122 @@ De-stationary Attention mechanism
-Self-Attention: $\operatorname{Attn}(\mathbf{Q}, \mathbf{K}, \mathbf{V})=\operatorname{Softmax}\left(\frac{\mathbf{Q K}^{\top}}{\sqrt{d_k}}\right) \mathbf{V}$. +Self-Attention: $$\operatorname{Attn}(\mathbf{Q}, \mathbf{K}, \mathbf{V})=\operatorname{Softmax}\left(\frac{\mathbf{Q K}^{\top}}{\sqrt{d_k}}\right) \mathbf{V}$$. Bring the vanished non-stationary information back to its calculation - approximate the - - positive scaling scalar $\tau=\sigma_{\mathbf{x}}^2 \in \mathbb{R}^{+}$ - - shifting vector $\boldsymbol{\Delta}=\mathbf{K} \mu_{\mathbf{Q}} \in \mathbb{R}^{S \times 1}$, + - positive scaling scalar $$\tau=\sigma_{\mathbf{x}}^2 \in \mathbb{R}^{+}$$ + - shifting vector $$\boldsymbol{\Delta}=\mathbf{K} \mu_{\mathbf{Q}} \in \mathbb{R}^{S \times 1}$$, which are defined as de-stationary factors. -- try to learn de-stationary factors directly from the statistics of unstationarized $\mathbf{x}, \mathbf{Q}$ and $\mathbf{K}$ by MLP +- try to learn de-stationary factors directly from the statistics of unstationarized $$\mathbf{x}, \mathbf{Q}$$ and $$\mathbf{K}$$ by MLP
-$\log \tau=\operatorname{MLP}\left(\sigma_{\mathbf{x}}, \mathbf{x}\right)$. +$$\log \tau=\operatorname{MLP}\left(\sigma_{\mathbf{x}}, \mathbf{x}\right)$$. -$\boldsymbol{\Delta}=\operatorname{MLP}\left(\mu_{\mathbf{x}}, \mathbf{x}\right)$. -$\operatorname{Attn}\left(\mathbf{Q}^{\prime}, \mathbf{K}^{\prime}, \mathbf{V}^{\prime}, \tau, \boldsymbol{\Delta}\right)=\operatorname{Softmax}\left(\frac{\tau \mathbf{Q}^{\prime} \mathbf{K}^{\prime}+\mathbf{1} \boldsymbol{\Delta}^{\top}}{\sqrt{d_k}}\right) \mathbf{V}^{\prime}$. +$$\boldsymbol{\Delta}=\operatorname{MLP}\left(\mu_{\mathbf{x}}, \mathbf{x}\right)$$. +$$\operatorname{Attn}\left(\mathbf{Q}^{\prime}, \mathbf{K}^{\prime}, \mathbf{V}^{\prime}, \tau, \boldsymbol{\Delta}\right)=\operatorname{Softmax}\left(\frac{\tau \mathbf{Q}^{\prime} \mathbf{K}^{\prime}+\mathbf{1} \boldsymbol{\Delta}^{\top}}{\sqrt{d_k}}\right) \mathbf{V}^{\prime}$$.
# 4. Experiments +## (1) Experimental Setups + +### a) Datasets + +- Electricity +- ETT datasets +- IExchange +- ILI +- Traffic +- Weather + +
+ +### b) Degree of stationarity + +Augmented Dick-Fuller (ADF) test statistic + +- small value = high stationarity + +![figure2](/assets/img/ts/img472.png) + +
+ +### c) Baselines + +- pass + +
+ +## (2) Main Results + +### a) Forecasting + +MTS Forecasting + +![figure2](/assets/img/ts/img473.png) + +
+ +UTS Forecasting + +![figure2](/assets/img/ts/img474.png) + +
+ +### b) Framework Generality + +![figure2](/assets/img/ts/img475.png) + +Conclusion: Non-stationary Transformer is an **effective and lightweight** framework that can be widely **applied to Transformer-based models** and enhances their non-stationary predictability + +
+ +## (3) Ablation Study + +### a) Quality evaluation + +Dataset: ETTm2 + +Models: + +- vanilla Transformer +- Transformer with only Series Stationarization +- Non-stationary Transformer + +
+ +![figure2](/assets/img/ts/img476.png) + +
+ +### b) Quantitative performance + +![figure2](/assets/img/ts/img477.png) + +
+ +## (3) Model Analysis + +### a) Over-stationarization problem + +Transformers with .... + +- v1) Transformer + Ours ( = Non-stationary Transformer ) +- v2) Transformer + RevIN +- v3) Transformer + Series Stationarization + +
+ +![figure2](/assets/img/ts/img478.png) + +Result + +- v2 & v3) tend to output series with unexpected high degree of stationarity + diff --git a/_posts/non-stationary_transformer.pdf b/_posts/non-stationary_transformer.pdf deleted file mode 100644 index efa297187131ceb53104237d5c52a0d3077a779c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 2613070 zcmeFYV{~mzw=EoJ$2NDeW81dvWXHB`J3F>*+qP}ncE0TMyyx8a-tYXlzwWQIT3fB! zs9AHYsy_Q{t@kymh-3wYspzPgAc?x3az7y%nVIov@vZgDAUQelX(Uap40Y{H-3$%z z>AoX;dS*HXS{7P-8c}==e0mmIR(wV}Hhe978X0`XzuiLkbSw;v^vw7)()e@?_%w=t z@1UinrN`&yhBUM?_?s91|HtHBosBdlXJ?x)WR@ctb9{(>20@fCemR9!oO!zdic7_I~`VQ81-?x9S37Y`&XBd^Hmj6iW z^e?Cw{ttL)#02p*IO!Sm>F8-0j93g=n3!3O=-60T4E2rlnOSui=~!3|*|<6B*ywbP z=vnE%(Wn1z=@|8mm{<+y_2^g(b!qikSh%(RJ_CCPJ40PdNSAbdJp-L>V;wym9aac} zmhzr+Vfc}HbV2%CU(roOc(OZK!P^$U;d21^5j$8x`YEAeG)myuh?hCu^HewZ6MR6# z8+Q;r4IchuJ>O%Xa9V-kA)UJ=T3WhKi81iD0AJg9Y$7tEmLs@!EMc+tUwfCn&V8h8 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