Hierarchical Evaluation of Software Design Capabilities of Large Language Models of Code

Large language models (LLMs) are being increasingly adopted in the software engineering domain, yet the robustness of their grasp on core software design concepts remains unclear. We conduct an empirical study to systematically evaluate their understanding of cohesion (intra-module) and coupling (inter-module). We programmatically generate poorly designed code fragments and test the DeepSeek-R1 model family ($14$B, $32$B, $70$B) under varying levels of guidance, from simple \textit{Verification} to \textit{Guided} and \textit{Open-ended Generation}, while varying contextual noise by injecting distractor elements. While models exhibit a solid baseline understanding of both concepts in ideal conditions, their practical knowledge is fragile and highly asymmetrical. Reasoning about coupling proves brittle; performance collapses in noisy, open-ended scenarios, with F1 scores dropping by over $50\%$. In contrast, the models' analysis of cohesion is remarkably robust to internal noise in guided tasks, showing little performance degradation. However, this resilience also fails when all guidance is removed. Reasoning-trace analysis confirms these failure modes, revealing \textit{cognitive shortcutting} for coupling versus a more exhaustive (yet still failing) analysis for cohesion. To summarize, while LLMs can provide reliable assistance for recognizing design flaws, their ability to reason autonomously in noisy, realistic contexts is limited, highlighting the critical need for more scalable and robust program understanding capabilities.