Shallow Neural Net for predicting numbers other then 1 or 0? I'm not gonna lie, I'm very new to neural networks but am also so interested in them and learning the way they work and what can be made from them. So in my endeavors for learning, I stumbled upon Siraj Ravel's youtube channel and furthermore, his Github where he posted this 1 neuron neural network that predicts the output given inputs.* I looked at it and his accompanying video and got the basic gist of how it works. After running it a few times making minor adjustments to say the inputs, I decided why not try to add numbers other than 1 and 0. I made a pattern with the output being the inputs added, however, I ran into an error where the output of its test was '1.'. I assumed this was because of the sigmoid function forcing it to be in between 1 and 0.

Summary: How can I change that program so I can give it an input of patterns with different numbers than 1 and 0 and it will output correctly (examples below)

*In his program inputs were like [1, 0, 1] = 1, [0, 0, 1] = 0 and [1, 0, 0] = 1 (pattern is first column of matrix is answer) and he asked the program to give output for [1, 1, 0] and it correctly outputted 1.

*My goal for it was so given "[2, 2, 2] = 6, [1, 2, 0] = 3, and [1, 1, 2] = 4 (more training included if necassary)" as input could it get 4 as output for "[2, 2, 0]?

Code for program
Well, the main problem is that the existing code and the desired codes solve different problems.

The existing code solves a classification problem, when you predict one of certain classes. And you want to solve a regression problem, so that neural net will predict an arbitrary number.

Sigmoid function is necessary when you predict classes, you need to remove it for regression. Or in other words you need not Logistic Regression, but Linear Regression.
Here is a great article with explanations on this: http://peterroelants.github.io/posts/neural_network_implementation_part01/

I have written an example of implementation: https://gist.github.com/Erlemar/6a5cfcca423ef3b5f6e890c6bef6d5ed