# Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity

arXiv: https://arxiv.org/abs/2202.12482 · HTML: https://mlsanity.com/paper/2202.12482/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [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)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel](https://mlsanity.com/paper/1810.05369/) (2018)
- [On the Power and Limitations of Random Features for Understanding Neural Networks](https://mlsanity.com/paper/1904.00687/) (2019)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Mathematical Models of Overparameterized Neural Networks](https://mlsanity.com/paper/2012.13982/) (2020)
- [Group SLOPE - adaptive selection of groups of predictors](https://mlsanity.com/paper/1610.04960/) (2016)
- [A Dynamical View on Optimization Algorithms of Overparameterized Neural Networks](https://mlsanity.com/paper/2010.13165/) (2020)
- [Characterizing the SLOPE Trade-off: A Variational Perspective and the Donoho-Tanner Limit](https://mlsanity.com/paper/2105.13302/) (2021)
- [Efficient Designs of SLOPE Penalty Sequences in Finite Dimension](https://mlsanity.com/paper/2102.07211/) (2021)

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

- [Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection](https://mlsanity.com/paper/2209.09326/) (2022)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Improving Neural Additive Models with Bayesian Principles](https://mlsanity.com/paper/2305.16905/) (2023)
- [Sparsity in Continuous-Depth Neural Networks](https://mlsanity.com/paper/2210.14672/) (2022)
- [Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions](https://mlsanity.com/paper/2307.13149/) (2023)
- [Interpreting and generalizing deep learning in physics-based problems with functional linear models](https://mlsanity.com/paper/2307.04569/) (2023)
- [Higher-order Neural Additive Models: An Interpretable Machine Learning Model with Feature Interactions](https://mlsanity.com/paper/2209.15409/) (2022)
- [Identifiability Challenges in Sparse Linear Ordinary Differential Equations](https://mlsanity.com/paper/2506.09816/) (2025)
- [Regionally Additive Models: Explainable-by-design models minimizing feature interactions](https://mlsanity.com/paper/2309.12215/) (2023)
- [Differentiable Sparsity via D-Gating: Simple and Versatile Structured Penalization](https://mlsanity.com/paper/2509.23898/) (2025)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [Interpretable Prediction and Feature Selection for Survival Analysis](https://mlsanity.com/paper/2404.14689/) (2024)
- [Explainable Interface for Human-Autonomy Teaming: A Survey](https://mlsanity.com/paper/2405.02583/) (2024)
- [Transparent Networks for Multivariate Time Series](https://mlsanity.com/paper/2410.10535/) (2024)
- [Selecting Feature Interactions for Generalized Additive Models by Distilling Foundation Models](https://mlsanity.com/paper/2604.13332/) (2026)
- [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)
- [A Hessian-informed hyperparameter optimization for differential learning rate](https://mlsanity.com/paper/2501.06954/) (2025)
- [Provably Explaining Neural Additive Models](https://mlsanity.com/paper/2602.17530/) (2026)
- [HRR: Hierarchical Retrospection Refinement for Generated Image Detection](https://mlsanity.com/paper/2502.17862/) (2025)
- [dnamite: A Python Package for Neural Additive Models](https://mlsanity.com/paper/2503.07642/) (2025)
- [An Interpretable Deep Learning Model for General Insurance Pricing](https://mlsanity.com/paper/2509.08467/) (2025)
- [Sparse Deep Additive Model with Interactions: Enhancing Interpretability and Predictability](https://mlsanity.com/paper/2509.23068/) (2025)
- [Additive Large Language Models for Semi-Structured Text](https://mlsanity.com/paper/2511.11922/) (2025)
- [Interpretable and Fair Generalized Additive Neural Networks via Multi-objective Learning](https://mlsanity.com/paper/2609.05946/) (2026)

## Abstract (arXiv)

Interpretable machine learning has demonstrated impressive performance while preserving explainability. In particular, neural additive models (NAM) offer the interpretability to the black-box deep learning and achieve state-of-the-art accuracy among the large family of generalized additive models. In order to empower NAM with feature selection and improve the generalization, we propose the sparse neural additive models (SNAM) that employ the group sparsity regularization (e.g. Group LASSO), where each feature is learned by a sub-network whose trainable parameters are clustered as a group. We study the theoretical properties for SNAM with novel techniques to tackle the non-parametric truth, thus extending from classical sparse linear models such as the LASSO, which only works on the parametric truth. Specifically, we show that SNAM with subgradient and proximal gradient descents provably converges to zero training loss as t→∞, and that the estimation error of SNAM vanishes asymptotically as n→∞. We also prove that SNAM, similar to LASSO, can have exact support recovery, i.e. perfect feature selection, with appropriate regularization. Moreover, we show that the SNAM can generalize well and preserve the `identifiability', recovering each feature's effect. We validate our theories via extensive experiments and further testify to the good accuracy and efficiency of SNAM.