计算可约性能否导致图组合优化的可迁移模型？
Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?
AI总结：
本文提出了一种基于计算可约性的方法，通过表达性消息传递和预训练策略，在图组合优化中实现跨任务的可迁移模型。
摘要：
在推导统一神经求解器用于组合优化（CO）时，一个关键挑战是模型在给定任务集之间高效泛化到未在初始训练过程中使用的任务。为了解决这个问题，我们首先建立了一个新模型，该模型使用GCON模块作为表达性消息传递的形式，结合基于能量的无监督损失函数。当单独在每个任务上训练时，该模型在多个CO任务上实现了高性能（通常与最先进的结果相当）。然后，我们利用计算可约性文献中的知识，提出预训练和微调策略，这些策略能够有效（a）在MVC、MIS和MaxClique之间转移，以及（b）在多任务学习设置中还结合MaxCut、MDS和图着色。此外，在留一法多任务学习设置中，我们发现预训练所有但一个任务几乎总能导致微调时在剩余任务上更快收敛，同时避免负迁移。我们的发现表明，通过使用表达性消息传递和受多项式约简文献启发的预训练策略，学习多个图CO问题中的共同表示是可行的，从而在神经CO的基础模型开发方面迈出了重要一步。我们通过https://github.com/semihcanturk/COPT-MT提供了我们的工作开源实现。
英文摘要：
A key challenge in developing unified neural solvers for combinatorial optimization (CO) is the efficient generalization of models from a given set of tasks to new tasks unseen during initial training. To address this, we first establish a new GNN encoder, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves highly competitive performance across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies that transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning, while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reducibility literature, thereby taking an important step towards enabling the development of foundational models for neural CO. We provide an open source implementation of our work at https://github.com/semihcanturk/COPT-MT.
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。
