mlsanityData to 14 Oct 2026

Deep Lattice Networks and Partial Monotonic Functions

arXiv 1709.06680 ↗First posted 19 Sep 2017stat.ML cs.LGcited by 63

Not on the map. Why?

Abstract (arXiv)

We propose learning deep models that are monotonic with respect to a user-specified set of inputs by alternating layers of linear embeddings, ensembles of lattices, and calibrators (piecewise linear functions), with appropriate constraints for monotonicity, and jointly training the resulting network. We implement the layers and projections with new computational graph nodes in TensorFlow and use the ADAM optimizer and batched stochastic gradients. Experiments on benchmark and real-world datasets show that six-layer monotonic deep lattice networks achieve state-of-the art performance for classification and regression with monotonicity guarantees.

Key facts. Cited by 63 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Sep 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 5; 2022: 11; 2023: 12; 2024: 5; 2025: 17; 2026: 13.

63 papers.

Sort:

By area:

  1. 2022ProtoPFormer: Concentrating on Prototypical Parts in Vision Transformers for Interpretable Image Recognitioncited by 63
  2. 2022Visual Recognition with Deep Nearest Centroidscited by 59
  3. 2022Logic-Based Explainability in Machine Learningcited by 48
  4. 2021Explanations for Monotonic Classifierscited by 39
  5. 2022Constrained Monotonic Neural Networkscited by 32
  6. 2022Feature Necessity & Relevancy in ML Classifier Explanationscited by 23
  7. 2022Deep Non-Crossing Quantiles through the Partial Derivativecited by 12
  8. 2022Monotonic Neural Additive Models: Pursuing Regulated Machine Learning Models for Credit Scoringcited by 12
  9. 2024Neural Clustering based Visual Representation Learningcited by 12
  10. 2025A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfactioncited by 11
  11. 2021Matching Learned Causal Effects of Neural Networks with Domain Priorscited by 10
  12. 2025Advancing Constrained Monotonic Neural Networks: Achieving Universal Approximation Beyond Bounded Activationscited by 8
38 more
  1. 2023Expressive Monotonic Neural Networkscited by 7
  2. 2021Robust and Provably Monotonic Networkscited by 6
  3. 2023Contrastive Learning with Consistent Representationscited by 6
  4. 2022Monotonicity Regularization: Improved Penalties and Novel Applications to Disentangled Representation Learning and Robust Classificationcited by 5
  5. 2023Smooth Min-Max Monotonic Networkscited by 5
  6. 2024Deep neural networks for choice analysis: Enhancing behavioral regularity with gradient regularizationcited by 5
  7. 2021A framework for massive scale personalized promotioncited by 4
  8. 2023Monotonicity for AI ethics and society: An empirical study of the monotonic neural additive model in criminology, education, health care, and financecited by 4
  9. 2023DeepSaDe: Learning Neural Networks that Guarantee Domain Constraint Satisfactioncited by 4
  10. 2023How to address monotonicity for model risk management?cited by 4
  11. 2024MonoKAN: Certified Monotonic Kolmogorov-Arnold Networkcited by 4
  12. 2025Antithetic Noise in Diffusion Modelscited by 4
  13. 2025A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strainscited by 4
  14. 2022Global Optimization Networkscited by 2
  15. 2022XClusters: Explainability-first Clusteringcited by 2
  16. 2023Smoothness and monotonicity constraints for neural networks using ICEnetcited by 2
  17. 2021Regularization Strategies for Quantile Regressioncited by 1
  18. 2023Learned Accelerator Framework for Angular-Distance-Based High-Dimensional DBSCANcited by 1
  19. 2023An interpretable neural network-based non-proportional odds model for ordinal regressioncited by 1
  20. 2023Semantic-aware Transmission Scheduling: a Monotonicity-driven Deep Reinforcement Learning Approachcited by 1
  21. 2023Can I Trust the Explanations? Investigating Explainable Machine Learning Methods for Monotonic Modelscited by 1
  22. 2024A mathematical certification for positivity conditions in Neural Networks with applications to partial monotonicity and Trustworthy AIcited by 1
  23. 2024Enhancing Monotonic Modeling with Spatio-Temporal Adaptive Awareness in Diverse Marketingcited by 1
  24. 2025MCNet: Monotonic Calibration Networks for Expressive Uncertainty Calibration in Online Advertisingcited by 1
  25. 2025MMCE: A Framework for Deep Monotonic Modeling of Multiple Causal Effectscited by 1
  26. 2025Learning Monotonic Probabilities with a Generative Cost Modelcited by 1
  27. 2025Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networkscited by 1
  28. 2026ELViS: Efficient Visual Similarity from Local Descriptors that Generalizes Across Domainscited by 1
  29. 2026Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Biascited by 1
  30. 2022Private Isotonic Regressioncited by 0
  31. 2023Variational Label-Correlation Enhancement for Congestion Predictioncited by 0
  32. 2025LucidAtlas: Learning Uncertainty-Aware, Covariate-Disentangled, Individualized Atlas Representationscited by 0
  33. 2025Constrained Machine Learning Through Hyperspherical Representationcited by 0
  34. 2025Learning Penalty for Optimal Partitioning via Automatic Feature Extractioncited by 0
  35. 2025Transfer Learning for Minimum Operating Voltage Prediction in Advanced Technology Nodes: Leveraging Legacy Data and Silicon Odometer Sensingcited by 0
  36. 2025MonoCon: A general framework for learning ultra-compact high-fidelity representations using monotonicity constraintscited by 0
  37. 2025Monotone and Separable Set Functions: Characterizations and Neural Modelscited by 0
  38. 2025Simplex-FEM Networks (SiFEN): Learning A Triangulated Function Approximatorcited by 0

50 most cited of 63 All 63 (JSON)