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Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?

arXiv:2603.02462v1 Announce Type: new Abstract: A key challenge in deriving unified neural solvers for combinatorial optimization (CO) is efficient generalization of models between a given set of tasks to new tasks not used during the initial training process. To address it, we first establish a new model, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves high performance (often comparable with state-of-the-art results) 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 lead

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Semih Cant\"urk, Thomas Sabourin, Frederik Wenkel, Michael Perlmutter, Guy Wolf · · 1 min read · 13 views
#cs.LG #cs.AI

arXiv:2603.02462v1 Announce Type: new Abstract: A key challenge in deriving unified neural solvers for combinatorial optimization (CO) is efficient generalization of models between a given set of tasks to new tasks not used during the initial training process. To address it, we first establish a new model, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves high performance (often comparable with state-of-the-art results) 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 reduction 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 .

Executive Summary

This article explores the potential of computational reducibility to lead to transferable models for graph combinatorial optimization. The authors present a new model that achieves high performance across multiple CO tasks when trained individually and propose pretraining and fine-tuning strategies that transfer effectively between tasks. The findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with informed pretraining strategies. The study demonstrates the effectiveness of this approach in a multi-task learning setting and provides an open-source implementation of their work. The results have significant implications for the development of foundational models for neural CO, enabling more efficient generalization of models between tasks.

Key Points

  • ▸ The authors propose a new model that uses a GCON module for expressive message passing and energy-based unsupervised loss functions.
  • ▸ The model achieves high performance across multiple CO tasks when trained individually.
  • ▸ Pretraining and fine-tuning strategies informed by computational reducibility lead to effective transfer between tasks.

Merits

Strength in Model Performance

The proposed model achieves high performance across multiple CO tasks, often comparable with state-of-the-art results, demonstrating its effectiveness in individual task settings.

Transferability

The study demonstrates the effectiveness of pretraining and fine-tuning strategies in transferring knowledge between tasks, particularly in a multi-task learning setting.

Demerits

Limited Task Set

The study focuses on a specific set of graph CO problems, and its applicability to a broader range of tasks remains to be explored.

Lack of Theoretical Analysis

The article does not provide a comprehensive theoretical analysis of the proposed model and its pretraining strategies, which may limit its generalizability and scalability.

Expert Commentary

The article presents a significant contribution to the field of graph combinatorial optimization, demonstrating the effectiveness of computational reducibility in transferring knowledge between tasks. However, the study's limitations, such as its focus on a specific set of tasks and the lack of theoretical analysis, highlight the need for further research to generalize and scale the proposed approach. Nevertheless, the results have significant implications for the development of foundational models for neural CO and can inform the design of more efficient and effective neural network architectures.

Recommendations

  • ✓ Future research should aim to generalize the proposed approach to a broader range of graph CO tasks and explore its applicability to other domains.
  • ✓ A comprehensive theoretical analysis of the proposed model and its pretraining strategies is necessary to understand its scalability and generalizability.

Sources

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