# q-RBFNN:A Quantum Calculus-based RBF Neural Network

arXiv: https://arxiv.org/abs/2106.01370 · HTML: https://mlsanity.com/paper/2106.01370/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 60 references that are in the map.
- First posted on arXiv 2 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [A Novel Adaptive Kernel for the RBF Neural Networks](https://mlsanity.com/paper/1905.03546/) (2019)
- [A Robust Variable Step Size Fractional Least Mean Square (RVSS-FLMS) Algorithm](https://mlsanity.com/paper/1711.04973/) (2017)
- [Enhanced q-Least Mean Square](https://mlsanity.com/paper/1801.00410/) (2018)
- [q-LMF: Quantum Calculus-based Least Mean Fourth Algorithm](https://mlsanity.com/paper/1812.02588/) (2018)
- [Shallow Neural Network can Perfectly Classify an Object following Separable Probability Distribution](https://mlsanity.com/paper/1904.09109/) (2019)
- [Quantum Calculus-based Volterra LMS for Nonlinear Channel Estimation](https://mlsanity.com/paper/1908.02510/) (2019)
- [Chaotic Time Series Prediction using Spatio-Temporal RBF Neural Networks](https://mlsanity.com/paper/1908.08389/) (2019)
- [AFP-CKSAAP: Prediction of Antifreeze Proteins Using Composition of k-Spaced Amino Acid Pairs with Deep Neural Network](https://mlsanity.com/paper/1910.06392/) (2019)

## Abstract (arXiv)

In this research a novel stochastic gradient descent based learning approach for the radial basis function neural networks (RBFNN) is proposed. The proposed method is based on the q-gradient which is also known as Jackson derivative. In contrast to the conventional gradient, which finds the tangent, the q-gradient finds the secant of the function and takes larger steps towards the optimal solution. The proposed q-RBFNN is analyzed for its convergence performance in the context of least square algorithm. In particular, a closed form expression of the Wiener solution is obtained, and stability bounds of the learning rate (step-size) is derived. The analytical results are validated through computer simulation. Additionally, we propose an adaptive technique for the time-varying q-parameter to improve convergence speed with no trade-offs in the steady state performance.