这项研究用强化学习解决了刚性理论中的极值搜索难题，做图论或机器人运动规划的开发者可以直接借鉴其方法。
该研究提出了一种强化学习方法，用于寻找具有异常多实现数的最小刚性图。在刚性理论中，相同边长数据可对应多种几何实现，但传统穷举搜索因候选图数量爆炸和计算成本高昂而不可行。研究者利用Henneberg移动（0-和1-扩展）逐步构建图，并通过深度交叉熵方法优化实现数不变量，策略网络采用图同构网络编码器和置换等变动作头。实验表明，该方法在平面实现数上匹配已知最优解，并在球面实现数上改进了最佳已知边界，发现了新的记录图。
Learning Minimally Rigid Graphs with High Realization Counts
For minimally rigid graphs, the same edge-length data can admit multiple realizations (up to translations and rotations). Finding graphs with exceptionally many realizations is an extremal problem in rigidity theory, but exhaustive search quickly becomes infeasible due to the super-exponential growth of the number of candidate graphs and the high cost of realization-count evaluation. We propose a reinforcement-learning approach that constructs minimally rigid graphs via 0- and 1-extensions, also known as Henneberg moves. We optimize realization-count invariants using the Deep Cross-Entropy Method with a policy parameterized by a Graph Isomorphism Network encoder and a permutation-equivariant extension-level action head. Empirically, our method matches the known optima for planar realization counts and improves the best known bounds for spherical realization counts, yielding new record graphs.