I think I have it. But I have another question. I figured out how to initialize the weights for my quadratic net in the way that I want, but I may need to constrain which ones are learnable and which are constant, and I don't know how to do that.

Here is an example of what works. There is some book keeping up front to define the sparse initialization array which might distract from the main point, but I don't have time right now to make a nicer example. I don't need to freeze a whole layer, just part of it. What I need is actually a non-linear convolution, so only certain parameters need to be frozen in the convolution kernel. Also, is NetArray the only way to add user-specified learnable parameters?

Thanks, Giulio.

I am having trouble with the syntax. How can I generalize the previous so that given an input vector x of size n, I get an output vector y of size m, where yk=Sum{i,j}[ A{kij}xi xj ]+Sumj [ B{kj} xj ]? And then the a{kij} and B{kj} are learnable parameters and can be initialized in specific ways (for example the a tensor will be sparse, with nonzero entries only for i,j close to k)?

I realize I need something with FunctionLayer and NetArray, but I am not sure of the syntax after reading the documentation. Help, please...