# MonoKAN: Certified Monotonic Kolmogorov-Arnold Network

arXiv: https://arxiv.org/abs/2409.11078 · HTML: https://mlsanity.com/paper/2409.11078/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 17 Sep 2024.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)
- [Counterexample-Guided Learning of Monotonic Neural Networks](https://mlsanity.com/paper/2006.08852/) (2020)
- [Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementation](https://mlsanity.com/paper/2407.17790/) (2024)
- [How to Incorporate Monotonicity in Deep Networks While Preserving Flexibility?](https://mlsanity.com/paper/1909.10662/) (2019)
- [Deontological Ethics By Monotonicity Shape Constraints](https://mlsanity.com/paper/2001.11990/) (2020)
- [A mathematical certification for positivity conditions in Neural Networks with applications to partial monotonicity and Trustworthy AI](https://mlsanity.com/paper/2406.08525/) (2024)

## Built on by (most cited first, 4 of 4)

- [Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models](https://mlsanity.com/paper/2602.17750/) (2026)
- [Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias](https://mlsanity.com/paper/2606.17886/) (2026)
- [Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functions](https://mlsanity.com/paper/2602.06737/) (2026)
- [Fitting scattered data with optional monotonicity constraints on GPU: LipFit package](https://mlsanity.com/paper/2606.04670/) (2026)

## Abstract (arXiv)

Artificial Neural Networks (ANNs) have significantly advanced various fields by effectively recognizing patterns and solving complex problems. Despite these advancements, their interpretability remains a critical challenge, especially in applications where transparency and accountability are essential. To address this, explainable AI (XAI) has made progress in demystifying ANNs, yet interpretability alone is often insufficient. In certain applications, model predictions must align with expert-imposed requirements, sometimes exemplified by partial monotonicity constraints. While monotonic approaches are found in the literature for traditional Multi-layer Perceptrons (MLPs), they still face difficulties in achieving both interpretability and certified partial monotonicity. Recently, the Kolmogorov-Arnold Network (KAN) architecture, based on learnable activation functions parametrized as splines, has been proposed as a more interpretable alternative to MLPs. Building on this, we introduce a novel ANN architecture called MonoKAN, which is based on the KAN architecture and achieves certified partial monotonicity while enhancing interpretability. To achieve this, we employ cubic Hermite splines, which guarantee monotonicity through a set of straightforward conditions. Additionally, by using positive weights in the linear combinations of these splines, we ensure that the network preserves the monotonic relationships between input and output. Our experiments demonstrate that MonoKAN not only enhances interpretability but also improves predictive performance across the majority of benchmarks, outperforming state-of-the-art monotonic MLP approaches.