Interpreting Neural Combinatorial Optimization via Evolving Programmatic Bottlenecks

2026-06-17

AI Summary

This work addresses the limited interpretability of neural combinatorial optimization (NCO) models, which hinders their deployment and diagnosis due to opaque, state-dependent decision dynamics. To overcome this, the authors propose the Evolving Programmatic Bottleneck (EPB) framework, which leverages large language models to automatically evolve human-readable program compositions that distill black-box NCO policies into a library of step-wise action distributions. EPB jointly optimizes program capacity and content through a two-stage iterative mechanism, achieving the first program-level interpretation of NCO strategies. This reveals their stage-wise behavioral patterns and approximates them as compositions of classical heuristics. By integrating hybrid text-numerical gradient optimization with dynamic program library pruning and expansion, the distilled programs closely match the original model’s performance, demonstrating the method’s effectiveness and generality.

Abstract

Neural Combinatorial Optimization (NCO) achieves strong performance, yet its black-box nature remains a key roadblock to deployment and scientific diagnosis. Standard interpretability tools, such as Concept Bottleneck Models (CBMs), are ill-equipped for NCO, whose decisions are dynamic, state-dependent, and lack proper concept vocabulary definition. To close this gap, we introduce Evolving Programmatic Bottlenecks (EPB), to our knowledge, the first framework for interpreting NCO policies by distilling black-box NCO models into human-readable program portfolios. EPB employs an LLM to autonomously evolve a bank of programs, where each program's per-step action distribution serves as the bottleneck. EPB works through an iterative framework: Block I fixes program bank capacity and introduces a hybrid textual-numerical gradient descent scheme that couples numerical gradients for student router updates and textual gradients for LLM-based program revision; Block II dynamically adapts bank capacity via fault-targeted expansion and redundancy pruning. Extensive experiments demonstrate EPB's effectiveness and broad applicability, where the distilled program portfolios largely match original performance. EPB also reveals that NCO behavior shifts across optimization stages and can be approximated as a composition of classic heuristic variants. Our work advances interpretable NCO and establishes EPB as a promising tool for interpreting sequential decision-making models.

Problem

• Neural Combinatorial Optimization
• Interpretability
• Black-box Models
• Concept Bottleneck Models
• Sequential Decision-making

Innovation

• Evolving Programmatic Bottlenecks
• Neural Combinatorial Optimization
• Interpretability
• Program Distillation
• LLM-based Program Synthesis