# Beyond Additive Decompositions: Interpretability Through Separability

arXiv: https://arxiv.org/abs/2605.31200 · HTML: https://mlsanity.com/paper/2605.31200/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 19 of 19)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Unifying local and global model explanations by functional decomposition of low dimensional structures](https://mlsanity.com/paper/2208.06151/) (2022)
- [Simple algorithms for optimization on Riemannian manifolds with constraints](https://mlsanity.com/paper/1901.10000/) (2019)
- [A least-squares method for sparse low rank approximation of multivariate functions](https://mlsanity.com/paper/1305.0030/) (2013)
- [Random Planted Forest: a directly interpretable tree ensemble](https://mlsanity.com/paper/2012.14563/) (2020)
- [Fast Estimation of Partial Dependence Functions using Trees](https://mlsanity.com/paper/2410.13448/) (2024)
- [Tensor Product Neural Networks for Functional ANOVA Model](https://mlsanity.com/paper/2502.15215/) (2025)

## Abstract (arXiv)

Interpretable machine learning requires models that are accurate and structurally faithful to the data. Existing explainability methods rely heavily on additive representations (e.g., Generalized Additive Models (GAMs), SHapley Additive exPlanations (SHAP), functional ANOVA), which can suffer from signal cancellation and off-support extrapolation in the presence of strong interactions. We propose Tensor Separation Learning (TSL), a regression model that learns a sum of rank-1 products of univariate per-feature functions via a stagewise greedy procedure with orthogonal refitting. 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, up to constant factors. This stage-wise correspondence ensures that the resulting visualizations are faithful to the fitted components. 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.