Topological Tabular Learning: Cross-Regime Generalisation via Riemann Surface Residual Networks

Gradient-boosted decision trees (GBDTs) are the dominant method for tabular prediction, yet they encode cyclic features; months, days of week, seasonal indicators, as scalar values on which axis-aligned splits impose trivial topology. We show that this encoding cannot represent multi-valued functions: mappings where the same cyclic input produces systematically different outputs depending on a latent regime. We propose Topological Tabular Learning (TTL), a hybrid architecture that models GBDT residuals on a learned Riemann surface. A 77-parameter genus-1 model, trained on UK property transactions from 1995–2022, correctly predicts the direction of monthly residual corrections in a completely unseen macroeconomic regime (2023–2025 rate hiking) with 10/12 accuracy (p = 0.019, binomial test). Across five-fold regime cross-validation, the topological correction outperforms optimal cross-regime lookup tables on all five folds (sign test p = 0.031), while the lookup degrades performance on every fold. These results demonstrate that monodromy—the mathematical structure connecting sheets of a Riemann surface, provides a principled basis for cross-regime generalisation on cyclic features that no existing tabular method achieves.