How to create a transfer function with variable parameter?

Hello, I would like to create a custom neural network with custom neurons that will have transfer functions of a type: y(x)=exp(-x/l), where l is a parameter that will be different for each neuron and I have to have ability to initialize it for each neuron separately.

This is an attempt to model a particular constitutive equation. Creating a custom network structure is not a problem (thanks to Greg Heath) !

Thank you in advance!

Answer 1

[Greg Heath]

This doesn't sound right. The default FEEDFORWARDNET configuration with TANSIG, LOGSIG, or RADBAS hidden nodes is a Universal Approximator. Exponentials don't satisfy the UA criteria.

Maybe Googling "Universal Approximator" might help you understand. I've forgotten the details).

Hope this Helps.

Thank you for formally accepting my answer

Greg

[Alexandra]

Dear Greg! Thank you for the comment! Yes, you are right - in the classic approximation theorem transfer function should be non-constant, bounded and monotone increasing function (from Haykin) but what about for example non-localized rbf functions, for example cubic or linear? Actually i would say that the closest function to my example is Gaussian rbf. Theoretically RBFs are also feedforward networks...

WHat do you think? can it be possible to have and activation function with variable parameter in case of rbf nets?

[Greg Heath]

By a change of variable exp(-abs(x)/a) is equivalent to a Gaussian.

However, I don't know if it helps because I don't know why you want to do this.

Greg