Probing Neural Combinatorial Optimization Models

TL;DR

This paper pioneers the interpretation of neural combinatorial optimization models by analyzing their internal representations with novel probing tools, revealing how they encode information and generalize, which can inform improvements.

Contribution

It introduces Coefficient Significance Probing (CS-Probing), a new method for analyzing NCO models, and provides systematic insights into their learned representations and biases.

Findings

NCO models encode both low-level and high-level information.

Probing reveals model biases and factors influencing generalization.

Minor modifications can improve model generalization.

Abstract

Neural combinatorial optimization (NCO) has achieved remarkable performance, yet its learned model representations and decision rationale remain a black box. This impedes both academic research and practical deployment, since researchers and stakeholders require deeper insights into NCO models. In this paper, we take the first critical step towards interpreting NCO models by investigating their representations through various probing tasks. Moreover, we introduce a novel probing tool named Coefficient Significance Probing (CS-Probing) to enable deeper analysis of NCO representations by examining the coefficients and statistical significance during probing. Extensive experiments and analysis reveal that NCO models encode low-level information essential for solution construction, while capturing high-level knowledge to facilitate better decisions. Using CS-Probing, we find that prevalent NCO models impose varying inductive biases on their learned representations, uncover direct evidence related to model generalization, and identify key embedding dimensions associated with specific knowledge. These insights can be potentially translated into practice, for example, with minor code modifications, we improve the generalization of the analyzed model. Our work represents a first systematic attempt to interpret black-box NCO models, showcasing probing as a promising tool for analyzing their internal mechanisms and revealing insights for the NCO community. The source code is publicly available.