  Sparsity is regarded as a desirable property of representations, especially
in terms of explanation. However, its usage has been limited due to the gap
with dense representations. Most NLP research progresses in recent years are
based on dense representations. Thus the desirable property of sparsity cannot
be leveraged. Inspired by Fourier Transformation, in this paper, we propose a
novel Semantic Transformation method to bridge the dense and sparse spaces,
which can facilitate the NLP research to shift from dense space to sparse space
or to jointly use both spaces. The key idea of the proposed approach is to use
a Forward Transformation to transform dense representations to sparse
representations. Then some useful operations in the sparse space can be
performed over the sparse representations, and the sparse representations can
be used directly to perform downstream tasks such as text classification and
natural language inference. Then, a Backward Transformation can also be carried
out to transform those processed sparse representations to dense
representations. Experiments using classification tasks and natural language
inference task show that the proposed Semantic Transformation is effective.
