Discrete Denoising Diffusion Approach to Integer Factorization

TL;DR

This paper introduces a neural network-based discrete denoising diffusion method for integer factorization, capable of efficiently factoring integers up to 56 bits by reducing inference steps through training.

Contribution

It develops a novel seq2seq neural network architecture with relaxed categorical distribution and adapts the reverse diffusion process for improved accuracy in integer factorization.

Findings

Successfully factors integers up to 56 bits long

Training reduces inference steps exponentially

Approach offers a new direction for neural network-based factorization

Abstract

Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach to factorization utilizing deep neural networks and discrete denoising diffusion that works by iteratively correcting errors in a partially-correct solution. To this end, we develop a new seq2seq neural network architecture, employ relaxed categorical distribution and adapt the reverse diffusion process to cope better with inaccuracies in the denoising step. The approach is able to find factors for integers of up to 56 bits long. Our analysis indicates that investment in training leads to an exponential decrease of sampling steps required at inference to achieve a given success rate, thus counteracting an exponential run-time increase depending on the bit-length.