DIM: Enforcing Domain-Informed Monotonicity in Deep Neural Networks

2025-09-25

AI Summary

Deep neural networks (DNNs) often suffer from degraded generalization due to overfitting, especially when training data is noisy. To address this, we propose a domain-knowledge-driven monotonicity regularization method: leveraging a linear reference model to explicitly encode prior monotonic relationships, we define monotonicity violations as deviations from this reference and formulate a differentiable penalty term integrated into the loss function. Our approach requires no architectural modifications and is compatible with arbitrary DNN architectures. Experiments on both synthetic and real-world datasets demonstrate that moderate monotonicity constraints effectively mitigate overfitting—enhancing model robustness and interpretability without sacrificing predictive accuracy. The core contribution is a principled, end-to-end trainable monotonicity regularization framework grounded in a linear reference model, enabling effective synergy between domain knowledge and deep learning.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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

Problem

• Preventing overfitting in deep neural networks
• Enforcing domain-informed monotonicity constraints
• Improving generalization through regularization methods

Innovation

• Enforces domain-informed monotonicity in neural networks
• Penalizes violations relative to a linear baseline
• Integrates monotonicity constraints into training objective