Rethinking Code Complexity Through the Lens of Large Language Models

TL;DR

This paper introduces LM-CC, a new code complexity metric based on LLMs' perceived difficulty, which outperforms traditional metrics in correlating with LLM performance and improving code understanding tasks.

Contribution

The paper proposes LM-CC, a novel complexity metric derived from LLMs' semantic processing, addressing the mismatch of classical metrics with LLM-perceived difficulty.

Findings

Traditional metrics show no consistent correlation with LLM performance.

LM-CC correlates more strongly with LLM performance than classical metrics.

Lowering LM-CC improves LLM-based code understanding tasks.

Abstract

Code complexity metrics such as cyclomatic complexity have long been used to assess software quality and maintainability. With the rapid advancement of large language models (LLMs) on code understanding and generation tasks, an important yet underexplored question arises: do these traditional complexity metrics meaningfully characterize the difficulty LLMs experience when processing code? In this work, we empirically demonstrate that, after controlling for code length, classical metrics exhibit no consistent correlation with LLM performance, revealing a fundamental mismatch with model-perceived difficulty. To address this gap, we propose LM-CC, a novel code complexity metric designed from the perspective of LLMs. The core premise of LM-CC is that LLM-perceived difficulty is driven by the nonlinearity of program semantics. Accordingly, we decompose programs into semantic units based on entropy, organize these units into a compositional hierarchy, and quantify complexity as a principled aggregation of compositional level and branching-induced divergence, capturing cumulative model uncertainty during code processing. Our extensive experiments show that LM-CC not only correlates more strongly with LLM performance than traditional metrics but also that lowering it directly enhances task performance.