Apple introduces TopoPrimer, a topological framework to improve time-series forecasting accuracy

Apple’s Machine Learning Research team introduced TopoPrimer, a framework designed to make the global topological structure of a series population an explicit input to any forecasting model. The approach precomputes topological features once per domain using persistent homology and spectral sheaf coordinates, then integrates them into models either as per-token inputs for fully-trained systems or as lightweight adapters for pre-trained backbones.

Across four public benchmarks evaluated on Chronos and TimesFM, TopoPrimer consistently improved forecasting accuracy, with the largest gain of 7.3% MSE observed on the ECL dataset. The benefits were consistent across both zero-shot and fine-tuned backbones, suggesting that topological signals and per-series training capture complementary information.

The framework’s advantages were most pronounced in difficult forecasting regimes. Under peak seasonal demand, classical and zero-shot models degraded by up to 50%, whereas TopoPrimer maintained performance within 10% of baseline. In cold-start scenarios with no item history, TopoPrimer reduced MAE by 27% compared to a topology-free baseline.

TopoPrimer’s design includes two main components: persistent homology for structural representation and spectral sheaf coordinates as the primary accuracy driver. The framework is intended to be domain-agnostic, with precomputation performed once per dataset and deployment tailored to the model’s training stage—either as a token-level input or a lightweight adapter.