Interpreting Neural Combinatorial Optimization via Evolving Programmatic Bottlenecks

Researchers introduce Evolving Programmatic Bottlenecks (EPB), a novel framework for interpreting Neural Combinatorial Optimization models by distilling them into human-readable program portfolios. The method uses large language models to autonomously evolve interpretable programs while maintaining performance comparable to the original black-box models, addressing a critical gap in AI explainability for complex sequential decision-making systems.

The interpretability crisis in neural combinatorial optimization represents a significant bottleneck for real-world deployment of advanced AI systems. Neural networks excel at solving complex optimization problems but operate as black boxes, making it difficult for practitioners to understand why models make specific decisions or diagnose failures. This opacity creates regulatory and safety concerns, particularly as these systems move into critical applications.

EPB addresses this challenge through an innovative two-block architecture that iteratively distills neural policies into human-understandable program ensembles. The framework leverages large language models to evolve a bank of interpretable programs while using gradient-based optimization to train a router that selects which program applies at each step. By coupling numerical gradients for routing decisions with textual gradients for program refinement, EPB bridges symbolic and neural approaches to achieve interpretability without sacrificing performance.

The implications extend beyond academic interest. Organizations deploying optimization-based systems in supply chain, logistics, and resource allocation face growing pressure to explain algorithmic decisions to stakeholders and regulators. EPB's ability to distill complex neural policies into recognizable heuristic variants enables practitioners to validate model behavior against domain expertise and identify failure modes. The research demonstrates that NCO behavior varies across optimization stages and can be decomposed into classic algorithmic patterns—insights that inform both model design and operational understanding.

Future work should focus on scaling EPB to larger problem instances and evaluating its effectiveness across diverse optimization domains. Integration with existing model cards and explainability frameworks could accelerate adoption in production systems.

• →EPB distills black-box neural combinatorial optimization models into human-readable program portfolios without significant performance loss
• →The framework reveals that neural optimization policies shift across problem stages and approximate compositions of classic heuristics
• →Hybrid textual-numerical gradients enable simultaneous optimization of routing decisions and interpretable program evolution
• →Dynamic capacity adaptation through fault-targeted expansion and redundancy pruning improves portfolio efficiency
• →This work establishes a practical pathway for interpretable sequential decision-making beyond traditional concept bottleneck approaches