TopoPrimer: The Missing Topological Context in Forecasting Models

TL;DR

TopoPrimer introduces a topological framework that enhances forecasting models by explicitly incorporating the global topological structure of data, leading to improved accuracy and stability across various challenging scenarios.

Contribution

It presents a novel method to embed topological information into forecasting models using persistent homology and spectral sheaf coordinates, significantly boosting performance.

Findings

Up to 7.3% MSE improvement on ECL benchmark.

Maintains accuracy gains during seasonal spikes and cold-start scenarios.

Reduces MAE by 27% at cold start compared to baseline.

Abstract

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.