# Deep Distributional Learning with Non-crossing Quantile Network

arXiv: https://arxiv.org/abs/2504.08215 · HTML: https://mlsanity.com/paper/2504.08215/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2025.

## Built on by (most cited first, 5 of 5)

- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [Generalized Fitted Q-Iteration with Clustered Data](https://mlsanity.com/paper/2510.03912/) (2025)
- [MBD: A Model-Based Debiasing Framework Across User, Content, and Model Dimensions](https://mlsanity.com/paper/2603.14422/) (2026)
- [ConquerNet: Convolution-Smoothed Quantile ReLU Neural Networks with Minimax Guarantees](https://mlsanity.com/paper/2605.06265/) (2026)
- [Non-Crossing Deep Quantile Regression for Distributional Survival Prediction](https://mlsanity.com/paper/2608.16864/) (2026)

## Abstract (arXiv)

In this paper, we introduce a non-crossing quantile (NQ) network for conditional distribution learning. By leveraging non-negative activation functions, the NQ network ensures that the learned distributions remain monotonic, effectively addressing the issue of quantile crossing. Furthermore, the NQ network-based deep distributional learning framework is highly adaptable, applicable to a wide range of applications, from classical non-parametric quantile regression to more advanced tasks such as causal effect estimation and distributional reinforcement learning (RL). We also develop a comprehensive theoretical foundation for the deep NQ estimator and its application to distributional RL, providing an in-depth analysis that demonstrates its effectiveness across these domains. Our experimental results further highlight the robustness and versatility of the NQ network.