用可学习权重自动差分,提升长时间序列预测精度。
Learning to Difference: Adaptive Reversible Differencing (AdaRDiff) for Time Series Forecasting

- 通过可学习加权差分消除趋势与周期性,简化时间序列。
- 在8个真实数据集上达到顶尖预测精度,参数开销极小。
- 可插拔模块,适配各类模型,显著提升线性模型到Transformer性能。
可靠的长时序预测是重要但困难的问题。趋势和季节性引入复杂的时间结构,挑战基于学习的预测模型。传统差分法通过减去邻近历史值来去除这些结构,但依赖人工设定阶数与周期,难以融入现代深度架构。本文提出自适应可逆差分(AdaRDiff),一种通用差分方法,使用可学习权重对先前时刻进行加权差分,以简化序列。在此基础上进行预测,再通过自回归方式重建被移除成分,实现趋势与季节性的联合建模。该重建过程具有闭式卷积表达式,可在GPU上并行化,相比朴素递归实现提速达33.7倍。此外,采用两阶段训练策略,分离结构发现与重建学习,依据线性模型下的梯度理论分析设计。AdaRDiff在涵盖电力、气象、交通和能源的8个基准上取得最优预测表现,参数成本几乎可忽略。其作为即插即用模块,能有效提升8种不同骨干模型(从线性模型到Transformer)的性能,线性模型提升最高达25.9%,iTransformer提升最高达18.3%。
原文摘要 · Abstract (English)
Reliable long-horizon time series forecasting is an important yet difficult problem. Trends and seasonality introduce complex temporal structure that challenges learning-based forecasting models. Differencing, which subtracts nearby past values to remove such structure, is the classical remedy, but its reliance on hand-picked orders and periods has kept it largely absent from recent deep architectures. We propose \textbf{\underline{Ada}}ptive \textbf{\underline{R}}eversible \textbf{\underline{Diff}}erencing \textbf{(AdaRDiff)}, a generalized differencing approach that uses learnable weights to simplify the series through weighted differencing with previous time instants. This yields stabilized residuals on which forecasting is performed, after which the removed components are restored autoregressively to reconstruct the forecast, capturing trend and seasonality jointly through a single operator. This reconstruction admits a closed-form convolutional expression, which parallelizes on GPU and yields up to $33.7\times$ speedup over the naive recurrence. We furthermore rely on a two-phase training schedule that separates temporal structure discovery from reconstruction learning, as suggested by a theoretical analysis of the gradient when using a linear forecasting model. AdaRDiff attains state-of-the-art forecast accuracy across eight benchmarks spanning electricity, weather, traffic, and energy, at negligible parameter cost. Furthermore, it is designed as a plug-and-play module: integrating AdaRDiff improves eight diverse backbones, from linear models to Transformers, in the large majority of cases, by up to $25.9\%$ with a linear backbone and $18.3\%$ with iTransformer.
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