# ETSformer: Exponential Smoothing Transformers for Time-series Forecasting

论文地址：

* <https://arxiv.org/abs/2202.01381>

## 整体思路以及计算方式

针对时间序列问题的特点，提出了Exponential Smoothing Attention和Frequency Attention，这里主要讨论Exponential Smoothing Attention。

* 输入：$$V\in \mathbb R^{n\times d}$$
* 输出：$${A}*{\mathrm{ES}} \cdot\left\[\begin{array}{c} \mathbf {v}*{0}^{\top} \ {V} \end{array}\right]\in \mathbb R^{n\times d}$$，其中

  $$
  {A}\_{\mathrm{ES}}=\left\[\begin{array}{cccccc} (1-\alpha)^{1} & \alpha & 0 & 0 & \ldots & 0 \ (1-\alpha)^{2} & \alpha(1-\alpha) & \alpha & 0 & \ldots & 0 \ (1-\alpha)^{3} & \alpha(1-\alpha)^{2} & \alpha(1-\alpha) & \alpha & \ldots & 0 \ \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \ (1-\alpha)^{n} & \alpha(1-\alpha)^{n-1} & \ldots & \alpha(1-\alpha)^{j} & \ldots & \alpha \end{array}\right]
  $$

利用论文提出的算法，可以再$$O(nd\log n)$$中完成。

## 时间复杂度

$$O(nd\log n)$$。

## 训练以及loss

不变。

## 代码

* <https://github.com/lucidrains/ETSformer-pytorch>

## 实验以及适用场景

本文主要讨论的是时间序列问题，实验部分忽略。

## 细节

暂无。

## 简评

本质上还是一种相对位置编码的思路，可以在$$O(nd\log n)$$时间内完成，可以进行尝试。


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