通过两阶段框架统一时间序列共性并保留特异性，提升高维时序预测精度。
Hopformer: Homogeneity-Pursuit Transformer for Time Series Forecasting
- 先提取共性低方差趋势，再用微调变压器建模残差依赖
- 在合成与真实数据上平均降低MASE 6.56%
- 理论保证偏差-方差最优，适合多变量时序预测任务
高维协变量下的多时间序列预测面临核心挑战：既要统一共同的时间模式，又要保留有意义的序列特异性信息。我们提出Hopformer（同质性追求变压器），一种两阶段框架。第一阶段采用稀疏模式聚合（SPA）方案，提取融合协变量的共同低方差趋势，作为同质化层；第二阶段使用LoRA微调的Transformer建模残差中的复杂依赖关系。方法具有理论基础：我们证明了SPA通过奥拉克不等式实现近似最优的偏差-方差权衡，并在依赖时间序列数据下给出了第二阶段的泛化界。在合成与真实世界基准测试中，Hopformer实现了新的性能上限，平均降低MASE 6.56%。
原文摘要 · Abstract (English)
Forecasting multiple time-series with high-dimensional covariates presents a core challenge: unifying common temporal patterns while retaining meaningful series-specific information. We introduce Hopformer (Homogeneity-Pursuit Transformer), a two-stage framework that addresses this challenge. In the first stage, we perform a Sparsity Pattern Aggregation (SPA) scheme extracting a common low-variance trend that incorporates the covariates. This acts as a homogenization layer. In the second stage, a LoRA-fine-tuned Transformer models the remaining complex dependencies in the residual. Our method is theoretically grounded. We prove that SPA achieves a near-optimal bias-variance trade-off via an oracle inequality. We also provide generalization bounds for the second stage under dependent time series data. Hopformer sets a new state of the art, improving MASE by an average of 6.56% across synthetic and real-world forecasting benchmarks.
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