mlsanityData to 7 Oct 2026

Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences

arXiv 2005.12564 ↗First posted 26 May 2020cs.LG cs.NA math.NAcited by 20

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Abstract (arXiv)

We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly outperforms standard deep learning algorithms that are based on randomly chosen training data, for problems in moderately high dimensions. The proposed algorithm provides an efficient method for building inexpensive surrogates for many underlying maps in the context of scientific computing.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 May 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 3; 2023: 4; 2024: 3; 2025: 1; 2026: 5.

20 papers.

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  1. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  2. 2021On the approximation of functions by tanh neural networkscited by 81
  3. 2022Error estimates for physics informed neural networks approximating the Navier-Stokes equationscited by 63
  4. 2022wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation lawscited by 29
  5. 2021A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equationscited by 28
  6. 2021NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEscited by 10
  7. 2023On the Generalization of PINNs outside the training domain and the Hyperparameters influencing itcited by 10
  8. 2024A practical existence theorem for reduced order models based on convolutional autoencoderscited by 9
  9. 2024Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networkscited by 6
  10. 2021Physics-aware deep neural networks for surrogate modeling of turbulent natural convectioncited by 2
  11. 2026Lattice-based Deep Neural Networks: Regularity and Tailored Regularizationcited by 2
  12. 2022Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equationscited by 1
8 more
  1. 2023Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Timecited by 1
  2. 2024Using Low-Discrepancy Points for Data Compression in Machine Learning: An Experimental Comparisoncited by 1
  3. 2025Neural Low-Discrepancy Sequencescited by 1
  4. 2023Toward High-Performance Energy and Power Battery Cells with Machine Learning-based Optimization of Electrode Manufacturingcited by 0
  5. 2026A Bayesian Approach to Low-Discrepancy Subset Selectioncited by 0
  6. 2026Bit-Identical Medical Deep Learning via Structured Orthogonal Initializationcited by 0
  7. 2026Fourier Neural Operators with rank-1 lattice points and hyperbolic crosscited by 0
  8. 2026High Probability Derivative Bounds for Random tanh Neural Networks on a Hypercubecited by 0