  The paper [1] shows that simple linear classifier can compete with complex
deep learning algorithms in text classification applications. Combining bag of
words (BoW) and linear classification techniques, fastText [1] attains same or
only slightly lower accuracy than deep learning algorithms [2-9] that are
orders of magnitude slower. We proved formally that fastText can be transformed
into a simpler equivalent classifier, which unlike fastText does not have any
hidden layer. We also proved that the necessary and sufficient dimensionality
of the word vector embedding space is exactly the number of document classes.
These results help constructing more optimal linear text classifiers with
guaranteed maximum classification capabilities. The results are proven exactly
by pure formal algebraic methods without attracting any empirical data.
