Time series forecasting task predicts future trends based on historical information. Recent U-Net-based methods have demonstrated superior performance in predicting real-world datasets. However, the performance of these models is lower than patch-based models or linear models. In this work, we propose a symmetric and hierarchical framework, Kernel-U-Net, which cuts the input sequence into slices at each layer of the network and then computes them using kernels. Furthermore, it generalizes the concept of convolutional kernels in classic U-Net to accept custom kernels that follow the same design pattern. Compared to the existing linear or transformer-based solution, our model contains 3 advantages: 1) A small number of parameters: the parameters size is $O(log(L)^2)$ where $L$ is the look-back window size, 2) Flexibility: its kernels can be customized and fitted to the datasets, 3) Computation efficiency: the computation complexity of transformer modules is reduced to $O(log(L)^2)$ if they are placed close to the latent vector. Kernel-U-Net accuracy was greater than or equal to the state-of-the-art model on six (out of seven) real-world datasets.

翻译：时间序列预测任务基于历史信息预测未来趋势。近期基于U-Net的方法在真实数据集预测中展现出优越性能，但这些模型的性能仍低于基于分块（patch）的模型或线性模型。本研究提出一种对称层次化框架——Kernel-U-Net，该框架在网络每一层将输入序列切分为切片，并通过核（kernel）对其进行计算。此外，该方法将经典U-Net中的卷积核概念泛化，可接纳遵循相同设计模式的自定义核。与现有线性或基于Transformer的解决方案相比，本模型具有三大优势：1）参数量少：参数规模为$O(log(L)^2)$（其中$L$为回溯窗口长度）；2）灵活性高：核可定制化并适配不同数据集；3）计算高效：若将Transformer模块置于潜向量附近，其计算复杂度可降至$O(log(L)^2)$。在七个真实数据集的六个中，Kernel-U-Net的预测精度达到或超越当前最优模型。