TopoPrimer：预测模型中缺失的拓扑上下文

摘要

我们提出 TopoPrimer 框架，该框架使序列群体的全局拓扑结构成为任何预测模型的显式输入。TopoPrimer 提升了跨不同领域的预测精度，在季节性需求高峰下稳定预测结果，并弥补了冷启动差距。通过持久同调和谱层坐标，在每个领域预计算一次后，TopoPrimer 以 token 为单位部署到完全训练的模型中，并作为轻量级适配器用于预训练主干网络。在这两个组件中，谱层坐标是主要的精度驱动因素。在 Chronos 和 TimesFM 的四个公开基准测试中，TopoPrimer 持续提升预测精度，在 ECL 数据集上 MSE 提升高达 7.3%。这一拓扑优势在零样本和微调主干网络中表现出几乎相同的幅度，表明拓扑与逐序列训练捕捉到了互补的信号。在困难情形下，增益最为显著：在季节性需求高峰时期，经典模型和零样本模型的性能下降高达 50%，而 TopoPrimer 的下降幅度保持在 10% 以内；在冷启动（无商品历史数据）时，TopoPrimer 相较于无拓扑的基线将 MAE 降低了 27%。

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.