TopoPrimer：預測模型中缺失的拓撲上下文

摘要

我們引入了 TopoPrimer，這是一個將序列群體的全局拓撲結構作為任何預測模型明確輸入的框架。TopoPrimer 在多個領域提升了預測準確性，穩定了季節性需求高峰下的預測，並縮小了冷啟動差距。透過持續同調與譜層坐標，每個領域只需預先計算一次，TopoPrimer 可針對完全訓練的模型以每個 token 的方式部署，同時也作為預訓練主幹的輕量級適配器。在這兩個組件中，譜層坐標是提升準確性的主要驅動力。在基於 Chronos 和 TimesFM 的四個公開基準測試中，TopoPrimer 持續提升了預測準確性，在 ECL 資料集上的 MSE 提升高達 7.3%。拓撲優勢在零樣本與微調主幹上以近乎相同的幅度持續存在，這表明拓撲與每個序列的訓練捕捉了互補的信號。在困難場景下，其增益尤為顯著。在季節性需求高峰時，傳統與零樣本模型性能下降高達 50%，而 TopoPrimer 則保持在 10% 以內。在缺乏項目歷史記錄的冷啟動情況下，TopoPrimer 相比無拓撲的基線降低了 27% 的 MAE。

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.