AI methods, such as generative models and reinforcement learning, have recently been applied to combinatorial optimization (CO) problems, especially NP-hard ones. This paper compares such GPU-based methods with classical CPU-based methods on the Maximum Independent Set (MIS) problem. Strikingly, even on in-distribution random graphs, leading AI-inspired methods are consistently outperformed by the state-of-the-art classical solver KaMIS running on a single CPU, and some AI-inspired methods frequently fail to surpass even the simplest degree-based greedy heuristic. Even with post-processing techniques like local search, AI-inspired methods still perform worse than CPU-based solvers. To better understand the source of these failures, we introduce a novel analysis, serialization, which reveals that non-backtracking AI-inspired methods, e.g. LTFT (which is based on GFlowNets), end up reasoning similarly to the simplest degree-based greedy, and thus worse than KaMIS. More generally, our findings suggest a need for a rethinking of current approaches in AI for CO, advocating for more rigorous benchmarking and the principled integration of classical heuristics. Additionally, we also find that CPU-based algorithm KaMIS have strong performance on sparse random graphs, which appears to show that the shattering threshold conjecture for large independent sets proposed by Coja-Oghlan & Efthymiou (2015) does not apply for real-life sizes (such as 10^6 nodes).

翻译：近年来，AI方法（如生成模型和强化学习）已被应用于组合优化问题，尤其是NP难问题。本文在最大独立集问题上，将此类基于GPU的方法与基于CPU的经典方法进行了比较。令人惊讶的是，即使在同分布随机图中，领先的AI启发方法也始终被单CPU上运行的最先进经典求解器KaMIS所超越，且部分AI启发方法甚至无法超过最简单的基于度数的贪婪启发式算法。即使采用局部搜索等后处理技术，AI启发方法的性能仍逊于基于CPU的求解器。为更好理解这些失败的根源，我们引入了一种新颖的分析方法——序列化，该方法揭示了非回溯型AI启发方法（例如基于GFlowNets的LTFT）最终会表现出与最简单度数贪婪算法相似的推理方式，因此性能劣于KaMIS。更广泛而言，我们的发现表明需要重新思考当前AI用于组合优化的方法，倡导更严格的基准测试以及经典启发式算法的原则性整合。此外，我们还发现基于CPU的KaMIS算法在稀疏随机图上表现出强大性能，这似乎表明Coja-Oghlan与Efthymiou（2015）针对大独立集提出的破碎阈值猜想在实际规模（如10^6节点）中并不适用。