TopoPrimer cuts cold-start forecasting error 27% using persistent homology

TopoPrimer is a forecasting framework that makes the global topological structure of a time-series population an explicit input to any model. Researchers Zara Zetlin, Kayhan Moharreri, and Maria Safi precompute persistent homology and spectral sheaf coordinates once per domain, then deploy them per token for fully trained models or as a lightweight adapter for pretrained backbones like Chronos and TimesFM. Sheaf coordinates drive most of the accuracy gain. Across four public benchmarks, TopoPrimer reduces MSE by up to 7.3% on the ECL electricity dataset and cuts cold-start MAE by 27% over topology-free baselines.

The approach addresses how foundation models handle time-series data. While pretrained forecasting backbones have improved zero-shot performance on new domains, they typically treat each series in isolation or rely on learned embeddings that don't explicitly encode the population's global structure. TopoPrimer computes topological features upfront—persistent homology captures multi-scale connectivity patterns across the series population, while spectral sheaf coordinates encode how local neighborhoods relate to the global manifold. Both are precomputed once per domain and injected token-by-token during inference, adding minimal overhead to existing pipelines. The topology advantage persists at near-identical magnitude in both zero-shot and fine-tuned settings, suggesting topology and per-series training capture complementary signals. Under peak seasonal demand, classical and zero-shot models degrade by up to 50%, while TopoPrimer stays within 10% of baseline accuracy.