# Neural Low-Discrepancy Sequences

arXiv: https://arxiv.org/abs/2510.03745 · HTML: https://mlsanity.com/paper/2510.03745/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 54 references that are in the map.
- First posted on arXiv 4 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences](https://mlsanity.com/paper/2005.12564/) (2020)
- [Higher-order Quasi-Monte Carlo Training of Deep Neural Networks](https://mlsanity.com/paper/2009.02713/) (2020)
- [Deterministic Sampling-Based Motion Planning: Optimality, Complexity, and Performance](https://mlsanity.com/paper/1505.00023/) (2015)
- [Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks](https://mlsanity.com/paper/2405.15059/) (2024)
- [Improving Efficiency of Sampling-based Motion Planning via Message-Passing Monte Carlo](https://mlsanity.com/paper/2410.03909/) (2024)
- [Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators](https://mlsanity.com/paper/2410.01196/) (2024)
- [Low Stein Discrepancy via Message-Passing Monte Carlo](https://mlsanity.com/paper/2503.21103/) (2025)
- [On the optimization of discrepancy measures](https://mlsanity.com/paper/2508.04926/) (2025)
- [Robust designs for Gaussian process emulation of computer experiments](https://mlsanity.com/paper/2507.09156/) (2025)

## Built on by (most cited first, 1 of 1)

- [Optimizing Kernel Discrepancies via Subset Selection](https://mlsanity.com/paper/2511.02706/) (2025)

## Abstract (arXiv)

Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including in numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. Whereas most previous low-discrepancy constructions rely on abstract algebra and number theory, Message-Passing Monte Carlo (MPMC) was recently introduced to exploit machine learning methods for generating point sets with lower discrepancy than previously possible. However, MPMC is limited to generating point sets and cannot be extended to low-discrepancy sequences (LDS), i.e., sequences of points in which every prefix has low discrepancy, a property essential for many applications. To address this limitation, we introduce Neural Low-Discrepancy Sequences (NeuroLDS), the first machine learning-based framework for generating finite LDS. Drawing inspiration from classical LDS, we train a neural network to map indices to points such that the resulting sequences exhibit minimal discrepancy across all prefixes. To this end, we deploy a two-stage learning process: supervised approximation of classical constructions followed by unsupervised fine-tuning to minimize prefix discrepancies. We demonstrate that NeuroLDS outperforms all previous LDS constructions by a significant margin with respect to discrepancy measures. Moreover, we demonstrate the effectiveness of NeuroLDS across diverse applications, including numerical integration, robot motion planning, and scientific machine learning. These results highlight the promise and broad significance of Neural Low-Discrepancy Sequences. Our code can be found at https://github.com/camail-official/neuro-lds.