  In this paper, we present an approach to integer factorization using
distributed representations formed with Vector Symbolic Architectures. The
approach formulates integer factorization in a manner such that it can be
solved using neural networks and potentially implemented on parallel
neuromorphic hardware. We introduce a method for encoding numbers in
distributed vector spaces and explain how the resonator network can solve the
integer factorization problem. We evaluate the approach on factorization of
semiprimes by measuring the factorization accuracy versus the scale of the
problem. We also demonstrate how the proposed approach generalizes beyond the
factorization of semiprimes; in principle, it can be used for factorization of
any composite number. This work demonstrates how a well-known combinatorial
search problem may be formulated and solved within the framework of Vector
Symbolic Architectures, and it opens the door to solving similarly difficult
problems in other domains.
