Discrete Denoising Diffusion Approach to Integer Factorization
Karlis Freivalds Emils Ozolins Guntis Barzdins
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.