Discrete Denoising Diffusion Approach to Integer Factorization

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.Comment: International Conference on Artificial Neural Networks ICANN 202

Goal-Aware Neural SAT Solver

Modern neural networks obtain information about the problem and calculate the output solely from the input values. We argue that it is not always optimal, and the network's performance can be significantly improved by augmenting it with a query mechanism that allows the network at run time to make several solution trials and get feedback on the loss value on each trial. To demonstrate the capabilities of the query mechanism, we formulate an unsupervised (not depending on labels) loss function for Boolean Satisfiability Problem (SAT) and theoretically show that it allows the network to extract rich information about the problem. We then propose a neural SAT solver with a query mechanism called QuerySAT and show that it outperforms the neural baseline on a wide range of SAT tasks