Integer Factorization with Compositional Distributed Representations

TL;DR

This paper introduces a novel method for integer factorization using distributed vector representations and neural networks, enabling potential implementation on neuromorphic hardware and generalization to various composite numbers.

Contribution

It presents a new encoding scheme and neural network approach for integer factorization within Vector Symbolic Architectures, expanding the applicability of such methods.

Findings

Accurate factorization of semiprimes demonstrated

Method generalizes to any composite number

Potential for parallel neuromorphic hardware implementation

Abstract

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.