  We design and conduct a simple experiment to study whether neural networks
can perform several steps of approximate reasoning in a fixed dimensional
latent space. The set of rewrites (i.e. transformations) that can be
successfully performed on a statement represents essential semantic features of
the statement. We can compress this information by embedding the formula in a
vector space, such that the vector associated with a statement can be used to
predict whether a statement can be rewritten by other theorems. Predicting the
embedding of a formula generated by some rewrite rule is naturally viewed as
approximate reasoning in the latent space. In order to measure the
effectiveness of this reasoning, we perform approximate deduction sequences in
the latent space and use the resulting embedding to inform the semantic
features of the corresponding formal statement (which is obtained by performing
the corresponding rewrite sequence using real formulas). Our experiments show
that graph neural networks can make non-trivial predictions about the
rewrite-success of statements, even when they propagate predicted latent
representations for several steps. Since our corpus of mathematical formulas
includes a wide variety of mathematical disciplines, this experiment is a
strong indicator for the feasibility of deduction in latent space in general.
