Beyond Additive Decompositions: Interpretability Through Separability

Interpretable machine learning requires models that are accurate and structurally faithful to the data. Existing explainability methods rely heavily on additive representations (e.g., GAMs, SHAP, functional ANOVA), which can suffer from signal cancellation and extrapolation in presence of strong interactions. We propose Tensor Separation Learning (TSL), a regression model that learns a sum of separable (rank-1) tensor products via an orthogonal greedy algorithm. By enforcing separability, TSL avoids the information loss inherent in additive projections caused by marginalizing higher-order interactions. The learned TSL model can be fully reconstructed from first-order partial dependence functions of its fitted factors. We establish approximation-rate guarantees for functions with bounded mixed $ p $-th order partial derivatives and demonstrate that TSL competes with black-box models on regression benchmarks. Crucially, TSL improves interpretability by factorizing interactions, allowing users to explicitly disentangle the magnitude of an effect from its direction directly via the fitted factors.