Small Language Models Show Promise in Graph Algorithm Execution.

Researchers explored the capabilities of small language models (SLMs) in executing complex graph algorithms, treating it as a closed-loop prediction task. The models were tasked with repeatedly selecting actions based on the current graph state and algorithmic progress. This setup allowed for a comprehensive evaluation of how SLMs perform when making a series of dependent decisions, moving beyond simple next-step predictions. The evaluation framework covered various classical graph procedures, synthetic graph families, and robust testing partitions. Key metrics included step accuracy, exact rollout accuracy, constraint validity, and partial solution quality. The results revealed that while SLMs can be adapted to reliably execute structural algorithms like graph traversal and coloring, their performance significantly degrades with weighted algorithms. This degradation is primarily attributed to the accumulation of errors over multiple steps, highlighting a critical challenge where strong local prediction doesn't guarantee reliable global execution.