TopoPrimer: The Missing Topological Context in Forecasting Models
Authors: name: Zara Zetlin, name: Kayhan Moharreri, name: Maria Safi
Organization: Apple

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.