Input normalization for ReLu?
You have to normalize your data to accelerate learning process but based on experience its better to normalize your data in the standard manner, mean zero and standard deviation one. Although mapping to other small intervals near to zero may also be fine but the latter case usually takes more time than the other. If you use ReLU, again based on experience, you have to normalize your data and use standard initialization techniques for your weights, like He or Glorot methods. The reason is that your should avoid each activation to be so large, because your net would be so much dependent to that activation, and you may have overfitting problem. When you use ReLU because there is no limit for its output, you have to normalize the input data and also use initialization techniques that avoid having large values for weights. For more information I encourage you taking a look at here and here.