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This study investigates the router hypothesis in large language models (LLMs) by applying structural prior injection to code security vulnerability detection, replicating and extending previous findings from formal mathematical reasoning. The authors evaluate three LLMs across various vulnerability categories and find that while structural priors significantly enhance in-distribution performance, they lead to substantial performance degradation out-of-distribution, particularly on real-world CVE data. The results underscore the need for distribution-aware training strategies, as iterative recalibration fails to improve performance on real data and can even worsen it.
Structural priors can boost semantic vulnerability recall to 100% in synthetic settings but collapse to just 48.9% on real-world data, revealing a critical cross-domain challenge in LLM performance.
Large language models (LLMs) exhibit a well-documented gap between latent capability and consistent activation: the router hypothesis posits that models possess the knowledge to solve a task but lack reliable internal routing to activate it. Prior work in formal mathematical reasoning (SAIR, C\'azares 2026) reports that structural priors (cheatsheets) raise in-distribution performance dramatically, yet collapse below the zero-shot baseline out-of-distribution (OOD) -- and that iterative recalibration amplifies rather than corrects the collapse. We test whether this phenomenon is cross-domain by reproducing the SAIR design in source-code security vulnerability detection, evaluating three LLMs (GPT-OSS-120B, Llama-3.3-70B, Gemma-4-31B) across three vulnerability categories (CWE-798, CWE-284, and the non-CWE N+1 anti-pattern) spanning syntactic, contextual, and semantic complexity, then transferring cheatsheet-augmented prompts to real-world CVE data from VUDENC (CWE-89, CWE-22). Our findings replicate and extend SAIR: (F1) structural priors lift semantic-vulnerability recall from 20.0% to 100.0% across all models; (F2) zero-shot performance degrades along a semantic complexity gradient; (F3) the same cheatsheets that saturate synthetic performance amplify distribution-shift collapse on real CVE data (CWE-89: 100% synthetic F1 to 48.9% on VUDENC, -51.1pp); (F5) iterative recalibration produces a v2 cheatsheet that performs worse than v1 on real data, mirroring SAIR's AN45c-vs-AN38 finding. These results provide evidence that the cross-distribution trade-off surface documented in SAIR generalises to code security, and that the router hypothesis is cross-domain. We argue the structural nature of the collapse motivates distribution-aware training over prompt calibration. Code and evaluation scripts: https://github.com/bytepro-ai/bitcoder-v2-research
