LLMs fail at formal proof routing without explicit verification cues
Researchers have identified a systematic routing failure in large language models when tasked with selecting proof mechanisms from formally verified algebraic structures in Lean 4. GPT-OSS-120B and Llama 3.3 70B both show significant accuracy gaps (68-80%) on blind classification tasks, but performance jumps dramatically (82-91%) when given access to Lean verification cues. This work exposes a critical limitation in how LLMs handle structured mathematical reasoning: they struggle with mechanism selection in closed domains without explicit formal guidance, suggesting that formal verification artifacts may be necessary scaffolding for reliable mathematical reasoning at scale.
Modelwire context
ExplainerThe critical detail buried in the accuracy jump: models don't lack algebraic knowledge, they fail at mechanism selection in closed domains. The 14-point floor-to-ceiling gap isn't fixed by scale or training; it's fixed by access to formal verification artifacts, suggesting LLMs need external structure to reason reliably about constrained problem spaces.
This connects directly to the FormalRx taxonomy work from last week, which mapped autoformalization failures into 28 specific error categories. Both papers expose the same underlying problem: formal reasoning pipelines fail silently when models can't diagnose which rule or mechanism applies. The routing failure here is a specific instance of the broader semantic translation breakdown that FormalRx tries to make visible. Together they suggest that opaque end-to-end evaluation masks where formal reasoning actually breaks, and that intermediate verification signals (like Lean cues) may be necessary scaffolding rather than optional polish.
If GPT-OSS-120B and Llama 3.3 70B maintain their 82-91% performance on held-out algebraic structures not seen during training, that confirms the Lean cues are teaching genuine mechanism selection rather than memorization. If performance drops below 75% on novel FiberRing variants, the improvement was brittle and the routing failure remains unsolved.
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MentionsGPT-OSS-120B · Llama 3.3 70B · Lean 4 · FiberRing
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Modelwire summarizes, we don’t republish. arXiv cs.CL originally reported this story as “Mechanism-level routing failure in LLMs over Lean-verified algebraic structures”. The full content lives on arxiv.org. If you’re a publisher and want a different summarization policy for your work, see our takedown page.