Custom transfer function with learnable parameters and custom initializing in shallow neural network

I would like to implement multidimensional wavelet neural networks using Matlab. The training entails training extra learnable parameters (dilation and translation parameters) in addition to the usual weights and biases. The following figure depicts a typical feedforward wavelet neural network that I want to implement. (Alexandridis and Zapranis, 2013)

Here, ψ is the mother wavelet.

I would like to know how to implement custom transfer functions (in this case the wavelet) with learnable parameters. Furthermore, since the wavelet neural networks are very sensitive to initialization (of dilation and translation parameters), I would like to implement a custom initialization function too. Could you please instruct me on how to implement custom transfer functions with learnable parameters and custom initialization functions to be used with the training functions provided with matlab?

Answer 1

[Emiliano Rosso]

I'm interested in your work,have you meet some improvement?