normalization/denormalization for linear regression problem My question is simple actually, I have two features that have big difference in scale. So I used a simple normalization by dividing the scale=np.max(array) for both data and lables. Then after prediction, I mulitiplied this scale value back.

But since I used a DNN, wouldn't the nonlinear change the scale so make the multiply not valid? e.g.

given input data: X, label: y;
y' = y/scale
X' = X/scale
predicted = f(X')
predicted_update = predicted * scale


Anyone could provide some advice on whether I could do this or it's actually not correct? How do we handle this kind of problem?
I think it is ok, as long as your training and test data have the same maximum values for every feature, approximately. The idea is that the scaling has to be done with the training set (remember that using the test set for anything that is not testing is illegal, not even for scaling).

So, you actually fit $y'$ as a function of $X'$, and you have a model that maps properly $y' = f(X')$. When you get your test data, you just obtain the predictions by doing $f(X_{test}')$. As the paragraph before states, if you have that $scale \approx scale_{test}$, then you can just recover $y_{test}$ by doing $y_{test} = scale \cdot f(X_{test}')$.

Edit: Don't worry about nonlinearities

Even if the function $f$ is highly nonlinear, it is a function capable of mapping $X'$ to $y'$. If you trust this function and trust the fact that $y = y' \cdot scale$, then there is no need to worry about the way $f$ acts, as function composition makes sense for all kind of functions, both linear and nonlinear.