Can function parameters be the output of a Deep Neural Network

Question

I'm just starting out with Tensorflow and DNNs.

My question is, can some parameters that make a function (e.g. control points that can make up a Gaussian function) be the output of a DNN?

What I'm trying to do is to train an NN with (some input, function configurations) and test it with test input data and it give me the function configurations based on what it learned.

I guess, in some sense my question is, can the output values of a neural network be treated as related values that build a whole or not? Is there a better way to make a neural network spit out functions?

Thank you. Any help is greatly appreciated.

Answer 1

Yes.

In the simplest case, say $x$ is the input, $t$ is the target value, $y(x,w)$ is the output of the network, minimizing the sum-of-squares loss $$E=\sum(t_i-y(x_i,w))^2$$ can be interpreted as maximizing the log-likelihood of $$p(\mathbf{t}|\mathbf{x},w,b)=\prod N(t_i|y(x_i,w),b)$$ under the assumption of a Gaussian noise (see any textbook for details). So in this sense the output of the network is the parameter of a Gaussian distribution.

In general the output of neural networks can be interpreted as function parameters as long as they are of the same range.