# Scalable Interpretability via Polynomials

arXiv: https://arxiv.org/abs/2205.14108 · HTML: https://mlsanity.com/paper/2205.14108/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 81 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Metrics for Explainable AI: Challenges and Prospects](https://mlsanity.com/paper/1812.04608/) (2018)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Benchmarking Representation Learning for Natural World Image Collections](https://mlsanity.com/paper/2103.16483/) (2021)
- [Post-hoc Interpretability for Neural NLP: A Survey](https://mlsanity.com/paper/2108.04840/) (2021)
- [ParlAI: A Dialog Research Software Platform](https://mlsanity.com/paper/1705.06476/) (2017)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [Invertible Concept-based Explanations for CNN Models with Non-negative Concept Activation Vectors](https://mlsanity.com/paper/2006.15417/) (2020)
- ["How do I fool you?": Manipulating User Trust via Misleading Black Box Explanations](https://mlsanity.com/paper/1911.06473/) (2019)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Pi-nets: Deep Polynomial Neural Networks](https://mlsanity.com/paper/2003.03828/) (2020)
- [PolyGAN: High-Order Polynomial Generators](https://mlsanity.com/paper/1908.06571/) (2019)

## Built on by (most cited first, 25 of 25)

- ["Help Me Help the AI": Understanding How Explainability Can Support Human-AI Interaction](https://mlsanity.com/paper/2210.03735/) (2022)
- [Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Mean](https://mlsanity.com/paper/2301.11862/) (2023)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Beyond Linear Probes: Dynamic Safety Monitoring for Language Models](https://mlsanity.com/paper/2509.26238/) (2025)
- [Backpack Language Models](https://mlsanity.com/paper/2305.16765/) (2023)
- [Regularization of polynomial networks for image recognition](https://mlsanity.com/paper/2303.13896/) (2023)
- [Curve Your Enthusiasm: Concurvity Regularization in Differentiable Generalized Additive Models](https://mlsanity.com/paper/2305.11475/) (2023)
- [Multilinear Operator Networks](https://mlsanity.com/paper/2401.17992/) (2024)
- [Multi-Objective Optimization of Performance and Interpretability of Tabular Supervised Machine Learning Models](https://mlsanity.com/paper/2307.08175/) (2023)
- [FocusLearn: Fully-Interpretable, High-Performance Modular Neural Networks for Time Series](https://mlsanity.com/paper/2311.16834/) (2023)
- [A Survey of Explainable AI in Deep Visual Modeling: Methods and Metrics](https://mlsanity.com/paper/2301.13445/) (2023)
- [A Tensor Decomposition Perspective on Second-order RNNs](https://mlsanity.com/paper/2406.05045/) (2024)
- [A Training Framework for Optimal and Stable Training of Polynomial Neural Networks](https://mlsanity.com/paper/2505.11589/) (2025)
- [Transparent Networks for Multivariate Time Series](https://mlsanity.com/paper/2410.10535/) (2024)
- [Beyond Black-Box Predictions: Identifying Marginal Feature Effects in Tabular Transformer Networks](https://mlsanity.com/paper/2504.08712/) (2025)
- [Selecting Feature Interactions for Generalized Additive Models by Distilling Foundation Models](https://mlsanity.com/paper/2604.13332/) (2026)
- [UFO: A unified method for controlling Understandability and Faithfulness Objectives in concept-based explanations for CNNs](https://mlsanity.com/paper/2303.15632/) (2023)
- [Neural Additive Image Model: Interpretation through Interpolation](https://mlsanity.com/paper/2405.02295/) (2024)
- [How Video Meetings Change Your Expression](https://mlsanity.com/paper/2406.00955/) (2024)
- [GAMformer: Bridging Tabular Foundation Models and Interpretable Machine Learning](https://mlsanity.com/paper/2410.04560/) (2024)
- [Generalized Sparse Additive Model with Unknown Link Function](https://mlsanity.com/paper/2410.06012/) (2024)
- [Tensor Polynomial Additive Model](https://mlsanity.com/paper/2406.02980/) (2024)
- [LIT-LVM: Structured Regularization for Interaction Terms in Linear Predictors using Latent Variable Models](https://mlsanity.com/paper/2506.15492/) (2025)
- [The Impact of Concept Explanations and Interventions on Human-Machine Collaboration](https://mlsanity.com/paper/2512.00015/) (2025)
- [The Quadrilateral Loss: Additivity as a Measurable Behavior of Dense Neural Networks](https://mlsanity.com/paper/2607.20201/) (2026)

## Abstract (arXiv)

Generalized Additive Models (GAMs) have quickly become the leading choice for inherently-interpretable machine learning. However, unlike uninterpretable methods such as DNNs, they lack expressive power and easy scalability, and are hence not a feasible alternative for real-world tasks. We present a new class of GAMs that use tensor rank decompositions of polynomials to learn powerful, em inherently-interpretable models. Our approach, titled Scalable Polynomial Additive Models (SPAM) is effortlessly scalable and models em all higher-order feature interactions without a combinatorial parameter explosion. SPAM outperforms all current interpretable approaches, and matches DNN/XGBoost performance on a series of real-world benchmarks with up to hundreds of thousands of features. We demonstrate by human subject evaluations that SPAMs are demonstrably more interpretable in practice, and are hence an effortless replacement for DNNs for creating interpretable and high-performance systems suitable for large-scale machine learning. Source code is available at https://github.com/facebookresearch/nbm-spam.