用扩散模型解决群论图中的路径寻找问题，提升寻路效率。
Diffusion Models for Cayley Graphs
- 将群作用图的路径搜索转化为扩散模型的正向探索与逆向寻路过程。
- 提出反向梯度优化策略，显著优于已有算法在寻路效率上的表现。
- 适用于数学中复杂结构如魔方群的路径求解，适合群论与算法研究者。
我们回顾了在群及其作用的凯莱图中寻找路径的问题，以魔方为例，并列出多个具有重要数学意义的实例。随后，我们将这些问题纳入扩散模型框架：图的探索通过前向过程完成，目标节点的定位则通过逆向后向过程实现。该方法系统化了相关讨论并启发多种推广。为改进探索效果，我们提出一种“反向梯度”假设，其性能显著优于先前可比算法。
原文摘要 · Abstract (English)
We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems in the framework of diffusion models. The exploration of the graph is carried out by the forward process, while finding the target nodes is done by the inverse backward process. This systematizes the discussion and suggests many generalizations. To improve exploration, we propose a ``reversed score'' ansatz which substantially improves over previous comparable algorithms.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。