用拓扑结构提升时间序列预测精度，尤其在冷启动和旺季更稳定。
TopoPrimer: The Missing Topological Context in Forecasting Models
- 将系列群体的全局拓扑结构作为显式输入，通过谱沙坐标增强模型理解。
- 在ECL数据集上最高降低7.3% MSE，季节高峰时误差比传统方法低50%。
- 适用于零样本与微调场景，特别适合缺乏历史数据的冷启动问题。
我们提出TopoPrimer框架，将系列群体的全局拓扑结构作为任何预测模型的显式输入。通过持久同调和谱沙坐标预计算一次，该框架可按标记部署于全训练模型或作为轻量级适配器用于预训练主干网络。其中，沙坐标是提升准确率的主要因素。在Chronos和TimesFM的四个公开基准上，TopoPrimer持续提升预测性能，于ECL数据集上最大降低7.3% MSE。该拓扑优势在零样本与微调模型中均保持近似一致，表明拓扑信息与个体训练信号具有互补性。在困难场景下表现尤为突出：季节性需求高峰时，传统与零样本模型误差最多上升50%，而TopoPrimer仅增加10%；在无物品历史的冷启动场景下，其MAE比无拓扑基线降低27%。
原文摘要 · Abstract (English)
We introduce TopoPrimer, a framework that makes the global topological structure of the series population an explicit input to any forecasting model. TopoPrimer improves accuracy across diverse domains, stabilizes forecasts under seasonal demand spikes, and closes the cold-start gap. Precomputed once per domain via persistent homology and spectral sheaf coordinates, TopoPrimer deploys per token for fully-trained models and as a lightweight adapter for pre-trained backbones. Of these two components, sheaf coordinates are the primary accuracy driver. Across four public benchmarks on Chronos and TimesFM, TopoPrimer consistently improves forecasting accuracy, with gains of up to 7.3% MSE on ECL. The topology advantage persists with near-identical magnitude across zero-shot and fine-tuned backbones, suggesting topology and per-series training capture complementary signals. The gains are most pronounced in difficult regimes. Under peak seasonal demand, classical and zero-shot models degrade by up to 50%, while TopoPrimer stays within 10%. At cold start with no item history, TopoPrimer reduces MAE by 27% over a topology-free baseline.
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