# Curve Your Enthusiasm: Concurvity Regularization in Differentiable Generalized Additive Models

arXiv: https://arxiv.org/abs/2305.11475 · HTML: https://mlsanity.com/paper/2305.11475/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Reducing Overfitting in Deep Networks by Decorrelating Representations](https://mlsanity.com/paper/1511.06068/) (2015)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [How Interpretable and Trustworthy are GAMs?](https://mlsanity.com/paper/2006.06466/) (2020)
- [Regularizing CNNs with Locally Constrained Decorrelations](https://mlsanity.com/paper/1611.01967/) (2016)
- [Scalable Interpretability via Polynomials](https://mlsanity.com/paper/2205.14108/) (2022)
- [NeuralProphet: Explainable Forecasting at Scale](https://mlsanity.com/paper/2111.15397/) (2021)

## Built on by (most cited first, 12 of 12)

- [Challenges in interpretability of additive models](https://mlsanity.com/paper/2504.10169/) (2025)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [NBMLSS: probabilistic forecasting of electricity prices via Neural Basis Models for Location Scale and Shape](https://mlsanity.com/paper/2411.13921/) (2024)
- [Beyond Black-Box Predictions: Identifying Marginal Feature Effects in Tabular Transformer Networks](https://mlsanity.com/paper/2504.08712/) (2025)
- [Neural Additive Image Model: Interpretation through Interpolation](https://mlsanity.com/paper/2405.02295/) (2024)
- [Generalized Sparse Additive Model with Unknown Link Function](https://mlsanity.com/paper/2410.06012/) (2024)
- [LucidAtlas: Learning Uncertainty-Aware, Covariate-Disentangled, Individualized Atlas Representations](https://mlsanity.com/paper/2502.08445/) (2025)
- [Breaking the Black Box: Inherently Interpretable Physics-Constrained Machine Learning With Weighted Mixed-Effects for Imbalanced Seismic Data](https://mlsanity.com/paper/2508.19031/) (2025)
- [ADHAM: Additive Deep Hazard Analysis Mixtures for Interpretable Survival Regression](https://mlsanity.com/paper/2509.07108/) (2025)
- [From Distributional to Quantile Neural Basis Models: the case of Electricity Price Forecasting](https://mlsanity.com/paper/2509.14113/) (2025)
- [The Quadrilateral Loss: Additivity as a Measurable Behavior of Dense Neural Networks](https://mlsanity.com/paper/2607.20201/) (2026)
- [Controlling for Omitted Variable Bias in Deep Neural Networks](https://mlsanity.com/paper/2608.25930/) (2026)

## Abstract (arXiv)

Generalized Additive Models (GAMs) have recently experienced a resurgence in popularity due to their interpretability, which arises from expressing the target value as a sum of non-linear transformations of the features. Despite the current enthusiasm for GAMs, their susceptibility to concurvity - i.e., (possibly non-linear) dependencies between the features - has hitherto been largely overlooked. Here, we demonstrate how concurvity can severly impair the interpretability of GAMs and propose a remedy: a conceptually simple, yet effective regularizer which penalizes pairwise correlations of the non-linearly transformed feature variables. This procedure is applicable to any differentiable additive model, such as Neural Additive Models or NeuralProphet, and enhances interpretability by eliminating ambiguities due to self-canceling feature contributions. We validate the effectiveness of our regularizer in experiments on synthetic as well as real-world datasets for time-series and tabular data. Our experiments show that concurvity in GAMs can be reduced without significantly compromising prediction quality, improving interpretability and reducing variance in the feature importances.