q-RBFNN:A Quantum Calculus-based RBF Neural Network
This work addresses convergence speed issues in neural network training for researchers and practitioners, representing an incremental improvement over existing methods.
The paper tackles the problem of slow convergence in radial basis function neural networks by proposing a q-gradient based stochastic gradient descent method, which achieves faster convergence without compromising steady-state performance through an adaptive q-parameter technique.
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.