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.

利用深层神经网络和离散去噪扩散的方法进行整数分解，通过迭代纠正部分正确解的错误来寻找整数的因子，能找到长达 56 位的整数的因子，训练投入可实现指数级减少抽样步骤以达到给定成功率，从而抵消取决于位长度的指数级运行时间增加。

离散去噪扩散方法在整数分解中的应用

Discrete Denoising Diffusion Approach to Integer Factorization

Code comment generation which aims to automatically generate natural language
descriptions for source code, is a crucial task in the field of automatic
software development. Traditional comment generation methods use
manually-crafted templates or information retrieval (IR) techniques to generate
summaries for source code. In recent years, neural network-based methods which
leveraged acclaimed encoder-decoder deep learning framework to learn comment
generation patterns from a large-scale parallel code corpus, have achieved
impressive results. However, these emerging methods only take code-related
information as input. Software reuse is common in the process of software
development, meaning that comments of similar code snippets are helpful for
comment generation. Inspired by the IR-based and template-based approaches, in
this paper, we propose a neural comment generation approach where we use the
existing comments of similar code snippets as exemplars to guide comment
generation. Specifically, given a piece of code, we first use an IR technique
to retrieve a similar code snippet and treat its comment as an exemplar. Then
we design a novel seq2seq neural network that takes the given code, its AST,
its similar code, and its exemplar as input, and leverages the information from
the exemplar to assist in the target comment generation based on the semantic
similarity between the source code and the similar code. We evaluate our
approach on a large-scale Java corpus, which contains about 2M samples, and
experimental results demonstrate that our model outperforms the
state-of-the-art methods by a substantial margin.

本文提出了一种基于 IR 技术和模板的 API 注释生成方法。该方法将机器翻译模型迁移到注释生成任务中并且通过引入仅对模板执行的代码生成步骤，使模型更加准确。在 Java 程序员中取得了 state-of-the-art 的回归结果。