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.

翻译：整数分解是一个著名的计算问题，其是否能够在多项式时间内求解尚不明确。随着深度神经网络的兴起，探究它们能否加速整数分解过程颇具意义。我们提出了一种利用深度神经网络和离散去噪扩散的分解方法，该方法通过迭代纠正部分正确解中的错误来工作。为此，我们开发了一种新的seq2seq神经网络架构，采用松弛分类分布，并调整逆向扩散过程以更好地应对去噪步骤中的不准确性。该方法能够分解长达56比特的整数。我们的分析表明，训练投入会导致推理时达到特定成功率所需的采样步骤呈指数级减少，从而抵消了因比特长度增加而带来的指数级运行时间增长。