# DIM: Enforcing Domain-Informed Monotonicity in Deep Neural Networks

arXiv: https://arxiv.org/abs/2509.21666 · HTML: https://mlsanity.com/paper/2509.21666/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Counterexample-Guided Learning of Monotonic Neural Networks](https://mlsanity.com/paper/2006.08852/) (2020)
- [How to Incorporate Monotonicity in Deep Networks While Preserving Flexibility?](https://mlsanity.com/paper/1909.10662/) (2019)
- [Testing Monotonicity of Machine Learning Models](https://mlsanity.com/paper/2002.12278/) (2020)
- [Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularization](https://mlsanity.com/paper/2404.14701/) (2024)
- [Model-Agnostic Graph Regularization for Few-Shot Learning](https://mlsanity.com/paper/2102.07077/) (2021)
- [Smoothness and monotonicity constraints for neural networks using ICEnet](https://mlsanity.com/paper/2305.08807/) (2023)

## Built on by (most cited first, 1 of 1)

- [AMBIT: Augmenting Mobility Baselines with Interpretable Trees](https://mlsanity.com/paper/2512.22466/) (2025)

## Abstract (arXiv)

While deep learning models excel at predictive tasks, they often overfit due to their complex structure and large number of parameters, causing them to memorize training data, including noise, rather than learn patterns that generalize to new data. To tackle this challenge, this paper proposes a new regularization method, i.e., Enforcing Domain-Informed Monotonicity in Deep Neural Networks (DIM), which maintains domain-informed monotonic relationships in complex deep learning models to further improve predictions. Specifically, our method enforces monotonicity by penalizing violations relative to a linear baseline, effectively encouraging the model to follow expected trends while preserving its predictive power. We formalize this approach through a comprehensive mathematical framework that establishes a linear reference, measures deviations from monotonic behavior, and integrates these measurements into the training objective. We test and validate the proposed methodology using a real-world ridesourcing dataset from Chicago and a synthetically created dataset. Experiments across various neural network architectures show that even modest monotonicity constraints consistently enhance model performance. DIM enhances the predictive performance of deep neural networks by applying domain-informed monotonicity constraints to regularize model behavior and mitigate overfitting