Scale-invariant representation of machine learning

The success of machine learning stems from its structured data representation. Similar data have close representation as compressed codes for classification or emerged labels for clustering. We observe that the frequency of the internal representation follows power laws in both supervised and unsupervised learning. The scale-invariant distribution implies that machine learning largely compresses frequent typical data, and at the same time, differentiates many atypical data as outliers. In this study, we derive how the power laws can naturally arise in machine learning. In terms of information theory, the scale-invariant representation corresponds to a maximally uncertain data grouping among possible representations that guarantee pre-specified learning accuracy.