# Random Vector Functional Link Networks for Function Approximation on Manifolds

arXiv: https://arxiv.org/abs/2007.15776 · HTML: https://mlsanity.com/paper/2007.15776/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2020.

## Built on by (most cited first, 19 of 19)

- [Random vector functional link network: recent developments, applications, and future directions](https://mlsanity.com/paper/2203.11316/) (2022)
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- [Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine](https://mlsanity.com/paper/2204.11375/) (2022)
- [Random vector functional link neural network based ensemble deep learning for short-term load forecasting](https://mlsanity.com/paper/2107.14385/) (2021)
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- [Solving Partial Differential Equations with Random Feature Models](https://mlsanity.com/paper/2501.00288/) (2024)
- [Weighting and Pruning based Ensemble Deep Random Vector Functional Link Network for Tabular Data Classification](https://mlsanity.com/paper/2201.05809/) (2022)
- [Randomly Initialized Subnetworks with Iterative Weight Recycling](https://mlsanity.com/paper/2303.15953/) (2023)
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- [Enhanced Feature Based Granular Ball Twin Support Vector Machine](https://mlsanity.com/paper/2410.05786/) (2024)
- [CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks](https://mlsanity.com/paper/2605.12580/) (2026)
- [Incremental Online Learning of Randomized Neural Network with Forward Regularization](https://mlsanity.com/paper/2412.13096/) (2024)
- [Efficient uniform approximation using Random Vector Functional Link networks](https://mlsanity.com/paper/2306.17501/) (2023)
- [Partially Randomizing Transformer Weights for Dialogue Response Diversity](https://mlsanity.com/paper/2311.10943/) (2023)
- [Eigenvalues of Autoencoders in Training and at Initialization](https://mlsanity.com/paper/2201.11813/) (2022)
- [HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation](https://mlsanity.com/paper/2501.18199/) (2025)
- [Residual-Guided Randomized Neural Networks](https://mlsanity.com/paper/2608.28267/) (2026)

## Abstract (arXiv)

The learning speed of feed-forward neural networks is notoriously slow and has presented a bottleneck in deep learning applications for several decades. For instance, gradient-based learning algorithms, which are used extensively to train neural networks, tend to work slowly when all of the network parameters must be iteratively tuned. To counter this, both researchers and practitioners have tried introducing randomness to reduce the learning requirement. Based on the original construction of Igelnik and Pao, single layer neural-networks with random input-to-hidden layer weights and biases have seen success in practice, but the necessary theoretical justification is lacking. In this paper, we begin to fill this theoretical gap. We provide a (corrected) rigorous proof that the Igelnik and Pao construction is a universal approximator for continuous functions on compact domains, with approximation error decaying asymptotically like O(1/√n) for the number n of network nodes. We then extend this result to the non-asymptotic setting, proving that one can achieve any desired approximation error with high probability provided n is sufficiently large. We further adapt this randomized neural network architecture to approximate functions on smooth, compact submanifolds of Euclidean space, providing theoretical guarantees in both the asymptotic and non-asymptotic forms. Finally, we illustrate our results on manifolds with numerical experiments.