Are neural networks able to deal with non-normalised inputs?
Normalization helps to eliminate scale factors that might exist between variables in your data. Take, for example, the classic problem of predicting home prices. If you represent the square footage of your home in square millimeters, a large change in this value will have a relatively small effect on home price, implying a small gradient on this variable. If you represent that value in square kilometers, a small numerical change will have a large impact on price, implying a large gradient. Normalization isn't necessarily required, but can help to balance the problem by making all variables have "equal weight" in your model. If you were to include both the square millimeter and square kilometer variables in your training data, the neural network would likely spend a lot of effort optimizing on the square kilometer variable, since it is numerically more important. You can still do training with un-normalized data, but it will likely take longer, and possibly have worse output if your important variables are numerically smallest.