Do I need to standardize my one hot encoded labels? I'm trying to do a simple softmax regression where I have features  (2 columns) and a one hot encoded vector of labels (two categories: left = 1  and Right = 0). Do I need to standardize just the vector of features or also the vector of labels? when I do that all my zeros and ones transform in different numbers and also I don't know how to identify who is the Left or the Right category. I'm using mxnet and gluon.
Here is how I standardize:
labels = (labels - labels.mean()) / (labels.max() - labels.min())

labels before standardization:
[0. 1. 1. 1. 1. 1.

labels after standardization:
[-0.5633803   0.43661973  0.43661973  0.43661973  0.43661973  0.43661973 ...

How can I  after identify (with strings) if my prediction is actually giving me Left or Right?
NO, you do not standardize labels
The purpose of standardization is to bring features with disparate ranges into a standard range. When the data is not standardized, features with large numerical values will tend to have a larger influence (weight) than those that are smaller numerically.

Consider the Automobile Data Set (https://archive.ics.uci.edu/ml/datasets/automobile)  from UC Irvine. Among the features, it has height, lenght, width, weight, # cylinders, along with a number of other label and numerical features. Height ranges from from 47.8 to 59.8 and weight ranges from 1488 to 4066. You'll want to standardize them, but not label features such as body-style or engine-type.