# Integer Factorization with Compositional Distributed Representations

arXiv: https://arxiv.org/abs/2203.00920 · HTML: https://mlsanity.com/paper/2203.00920/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [Torchhd: An Open Source Python Library to Support Research on Hyperdimensional Computing and Vector Symbolic Architectures](https://mlsanity.com/paper/2205.09208/) (2022)
- [In-memory factorization of holographic perceptual representations](https://mlsanity.com/paper/2211.05052/) (2022)
- [Computing with Residue Numbers in High-Dimensional Representation](https://mlsanity.com/paper/2311.04872/) (2023)
- [On the Role of Noise in Factorizers for Disentangling Distributed Representations](https://mlsanity.com/paper/2412.00354/) (2024)

## Abstract (arXiv)

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.