  In this paper, we propose SCANING, an unsupervised framework for paraphrasing
via controlled noise injection. We focus on the novel task of paraphrasing
algebraic word problems having practical applications in online pedagogy as a
means to reduce plagiarism as well as ensure understanding on the part of the
student instead of rote memorization. This task is more complex than
paraphrasing general-domain corpora due to the difficulty in preserving
critical information for solution consistency of the paraphrased word problem,
managing the increased length of the text and ensuring diversity in the
generated paraphrase. Existing approaches fail to demonstrate adequate
performance on at least one, if not all, of these facets, necessitating the
need for a more comprehensive solution. To this end, we model the noising
search space as a composition of contextual and syntactic aspects and sample
noising functions consisting of either one or both aspects. This allows for
learning a denoising function that operates over both aspects and produces
semantically equivalent and syntactically diverse outputs through grounded
noise injection. The denoising function serves as a foundation for learning a
paraphrasing function which operates solely in the input-paraphrase space
without carrying any direct dependency on noise. We demonstrate SCANING
considerably improves performance in terms of both semantic preservation and
producing diverse paraphrases through extensive automated and manual evaluation
across 4 datasets.
