mlsanityData to 13 Oct 2026

Constrained Monotonic Neural Networks

arXiv 2205.11775 ↗First posted 24 May 2022cs.LG cs.AIcited by 31

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Abstract (arXiv)

Wider adoption of neural networks in many critical domains such as finance and healthcare is being hindered by the need to explain their predictions and to impose additional constraints on them. Monotonicity constraint is one of the most requested properties in real-world scenarios and is the focus of this paper. One of the oldest ways to construct a monotonic fully connected neural network is to constrain signs on its weights. Unfortunately, this construction does not work with popular non-saturated activation functions as it can only approximate convex functions. We show this shortcoming can be fixed by constructing two additional activation functions from a typical unsaturated monotonic activation function and employing each of them on the part of neurons. Our experiments show this approach of building monotonic neural networks has better accuracy when compared to other state-of-the-art methods, while being the simplest one in the sense of having the least number of parameters, and not requiring any modifications to the learning procedure or post-learning steps. Finally, we prove it can approximate any continuous monotone function on a compact subset of ℝn.

Key facts. Cited by 31 papers in the map (data through 13 Oct 2026). Builds on 20 of its 56 references that are in the map. First posted on arXiv 24 May 2022.

Builds on

20 of 56 references.

References · 20

  1. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,476
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  3. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,601
  4. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
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8 more
  1. 2017Deep Lattice Networks and Partial Monotonic Functionscited by 63
  2. 2018The age of secrecy and unfairness in recidivism predictioncited by 53
  3. 2020Certified Monotonic Neural Networkscited by 51
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  6. 2020Counterexample-Guided Learning of Monotonic Neural Networkscited by 34
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Citing papers per year: 2023: 2; 2024: 3; 2025: 10; 2026: 16.

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  2. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  3. 2026Monodense Deep Neural Model for Determining Item Price Elasticitycited by 3
  4. 2023A Deep Learning Analysis of Climate Change, Innovation, and Uncertaintycited by 2
  5. 2024Learning truly monotone operators with applications to nonlinear inverse problemscited by 2
  6. 2024A mathematical certification for positivity conditions in Neural Networks with applications to partial monotonicity and Trustworthy AIcited by 1
  7. 2025Aligning the Evaluation of Probabilistic Predictions with Downstream Valuecited by 1
  8. 2025On Aligning Prediction Models with Clinical Experiential Learning: A Prostate Cancer Case Studycited by 1
  9. 2026Learning to Recorrupt: Noise Distribution Agnostic Self-Supervised Image Denoisingcited by 1
  10. 2026Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Biascited by 1
  11. 2023Optimization- and AI-based approaches to academic quality quantification for transparent academic recruitment: part 1-model developmentcited by 0
  12. 2024Introducing Flexible Monotone Multiple Choice Item Response Theory Models and Bit Scalescited by 0
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  3. 2025Fast Gaussian Processes under Monotonicity Constraintscited by 0
  4. 2025MonoCon: A general framework for learning ultra-compact high-fidelity representations using monotonicity constraintscited by 0
  5. 2025Computing frustration and near-monotonicity in deep neural networkscited by 0
  6. 2025WTNN: Weibull-Tailored Neural Networks for survival analysiscited by 0
  7. 2026Efficient reformulations of ReLU deep neural networks for surrogate modelling in power system optimisationcited by 0
  8. 2026Monotone Optimisation with Learned Projectionscited by 0
  9. 2026Directed Ordinal Diffusion Regularization for Progression-Aware Diabetic Retinopathy Gradingcited by 0
  10. 2026Learning What Evaluators Value: A Reliable Approach to Modeling Evaluator Preferencescited by 0
  11. 2026Neural Slack Variables for Shape Constraintscited by 0
  12. 2026Profit-Based Counterfactual Explanations for Product Improvement: A Case Study of Manga Sales in Japancited by 0
  13. 2026LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problemscited by 0
  14. 2026Physically Constrained Federated Additive Models for O-RAN SLA-Risk Predictioncited by 0
  15. 2026CC-AOS: Cost- and Horizon-Conditioned Amortized Backward Induction for Finite-Horizon Optimal Stoppingcited by 0
  16. 2026Diagnosing Under-Development of Irreversible Processes in Video Generationcited by 0
  17. 2026Differentiable Fuzzy Inference Layer: A Monotone, Compositional Ordinal Reasoning Head for Large Language Modelscited by 0
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