Erdos Goes Neural：一个用于图上组合优化的无监督学习框架
Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs
摘要：
组合优化问题对于神经网络来说是非常具有挑战性的，特别是在没有标记实例的情况下。这项工作提出了一个无监督学习框架CO问题的图，可以提供认证质量的整体解决方案。受Erdos概率方法的启发，我们使用神经网络来参数化集合上的概率分布。至关重要的是，我们表明，当网络优化w.r.t.一个适当选择的损失，学习的分布包含，具有受控的概率，低成本的整体解决方案，服从组合问题的约束。存在的概率证明，然后去随机化解码所需的解决方案。我们证明了这种方法的有效性，以获得有效的解决方案的最大集团问题，并进行局部图聚类。我们的方法在真实数据集和合成硬实例上都取得了有竞争力的结果。
英文摘要：
Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions. We demonstrate the efficacy of this approach to obtain valid solutions to the maximum clique problem and to perform local graph clustering. Our method achieves competitive results on both real datasets and synthetic hard instances.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
