# LiD-GLM: Lipschitz-constrained Deep Generalized Linear Models

arXiv: https://arxiv.org/abs/2608.16340 · HTML: https://mlsanity.com/paper/2608.16340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 17 Aug 2026.

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

- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Limitations of the Lipschitz constant as a defense against adversarial examples](https://mlsanity.com/paper/1807.09705/) (2018)
- [Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities](https://mlsanity.com/paper/2002.05777/) (2020)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [LipBaB: Computing exact Lipschitz constant of ReLU networks](https://mlsanity.com/paper/2105.05495/) (2021)
- [deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression](https://mlsanity.com/paper/2104.02705/) (2021)
- [A New PHO-rmula for Improved Performance of Semi-Structured Networks](https://mlsanity.com/paper/2306.00522/) (2023)
- [Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweighting](https://mlsanity.com/paper/2304.14963/) (2023)
- [Deeply-Learned Generalized Linear Models with Missing Data](https://mlsanity.com/paper/2207.08911/) (2022)
- [ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networks](https://mlsanity.com/paper/2602.15499/) (2026)

## Abstract (arXiv)

The combination of traditional statistical models and neural network (NN) components into semi-structured hybrid models is an intriguing approach to construct models that, ideally, combine traditional interpretability with the unprecedented flexibility of NNs. In order to preserve interpretability, it is usually necessary to restrict the NN components to prevent them from dominating the model. However, existing methods that enforce structural constraints on their NN components severely limit their models' flexibility; in contrast, methods that only enforce weak, indirect constraints lose meaningful interpretability. The method we propose therefore leverages invertible residual neural networks (i-ResNets) to equip generalized linear models with both nonlinear parameter estimation and a flexible correction of their distributional assumptions while always retaining stochastic monotonicity of the modeled distribution in the (formerly linear) predictor. The i-ResNets correspond to a controlled deviation from identity and by constraining their Lipschitz constant one can rigorously limit and quantify how far the hybrid model deviates from its traditional counterpart. This enables a user-specifiable compromise between flexibility and interpretability without limiting the structure of nonlinear and interaction effects that can be learned. Furthermore, we develop specific inherent interpretation techniques for our model and enforce model identifiability through an adapted post-hoc orthogonalization.