用于组合优化的递归模型计算时间缩放

中文摘要 AI 辅助

我们提出了用于组合优化的微型递归模型（\nours{}），这是一种通用的神经方法，用于组合优化，它同时扩展了深度（我们递归调用网络的频率）和宽度（我们并行采样的数量）。两者对于组合优化都是基础性的：困难的实例需要大量的计算，而小网络对于避免过拟合和捕捉优化的算法本质至关重要。特别是，我们的方法由一个图感知的微型递归模型组成，该模型在潜在状态上迭代，具有自适应停止，并且只需要一个轻量级的特定于问题的解码器。与以前基于热图的通用神经求解器相比，它在旅行商问题（TSP）和最大独立集（MIS）问题上都实现了解决方案质量和推理速度之间更好的平衡，并且与结合了神经组件和针对每个问题的特定启发式的混合方法相比，仍具有竞争力。对于这两个任务使用相同的骨干架构，\nours{}在TSP上从500到10,000个城市，以更低的推理成本优于每个基于扩散的求解器，并且在标准的Erdős--Rényi-[700-800] MIS基准上，它超越了除那些仅对MIS有效的神经求解器之外的所有神经求解器。然后我们探索了用于自监督训练的自我重新标记。我们定期用模型自身更好的解决方案替换当前的训练标签集，作为替代训练信号。自我重新标记可以在放弃接近最优解的监督的同时，仍然产生同等质量的结果。

英文摘要

We propose Tiny Recursive Models for Combinatorial Optimization (\ours{}), a general neural method for combinatorial optimization that scales both depth (how often we recursively invoke our network) and width (how much we sample in parallel). Both are fundamental for combinatorial optimization: hard instances demand a large amount of compute, while a small network is essential to avoid overfitting and capture the algorithmic essence of optimization. In particular, our method consists of a graph-aware tiny recursive model that iterates on a latent state with adaptive halting and needs only a lightweight problem-specific decoder. Compared with previous heatmap-based general neural solvers, it achieves a better balance between solution quality and inference speed on both the Traveling Salesman Problem~(TSP) and the Maximum Independent Set~(MIS) problem, and remains competitive with hybrid methods that combine neural components with heuristics specific to each problem. With the same backbone architecture for both tasks, \ours{} outperforms every diffusion-based solver on TSP from 500 to 10,000 cities at a lower inference cost, and on the standard Erdős--Rényi-[700-800] MIS benchmark it surpasses all neural solvers except those that only work well on MIS. We then explore self-relabeling for self-supervised training. We periodically replace the current set of training labels with the model's own better solutions, as an alternative training signal. Self-relabeling can, while forgoing supervision from near-optimal solutions, still result in on-par quality.

发表机构

• Heinrich Heine University Düsseldorf（杜塞尔多夫海因里希·海涅大学）

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