Models spot impossible problems but solve them anyway
Source published ·Modelwire updated
Original coverage: arXiv cs.CL ↗·How Modelwire adds context
The development
A new evaluation reveals a critical gap in language model reasoning: models can internally identify physical impossibilities in engineering problems yet still output confident solutions. Researchers tested 14 models on paired mechanics problems, where one version was deliberately made unsolvable by altering constraints. Across three recent models, roughly 13% of responses failed to reject flawed problems, and strikingly, 11 of those cases showed the model had actually stated the contradiction before proceeding anyway. This finding exposes a reliability risk for deployment in technical domains where silent failure modes could compound into downstream errors, and suggests current prompting strategies don't reliably trigger rejection behavior even when models possess the underlying capability.
Modelwire’s AI-generated summary of coverage from arXiv cs.CL.
Modelwire analysis
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The critical detail is not that models fail on impossible problems, but that they demonstrably recognize the impossibility mid-reasoning and proceed anyway. This is a failure mode distinct from hallucination or knowledge gaps: the capability to detect the flaw exists, but the model lacks a reliable mechanism to act on that detection.
This finding extends the diagnostic framework established in the Mathematical Primitives paper from early October, which showed that high accuracy can mask gaps between surface correctness and genuine understanding. Here we see a sharper version: models possess the primitive (contradiction detection) but fail at the execution layer (actually rejecting the output). The Correct Answers, Invalid Traces study from late September documented a similar disconnect between intermediate steps and final answers. Together, these papers suggest that current LLMs can perform isolated reasoning operations without integrating them into coherent decision-making, a pattern that compounds the reliability risks flagged in the Self-Decidability work on regulatory boundaries.
If the same 14 models show improvement on this benchmark after fine-tuning with explicit rejection-as-action training, that confirms the gap is behavioral rather than perceptual. If performance remains flat despite intervention, it suggests the issue runs deeper into how models weight competing objectives during generation.
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Coverage behind this analysis
These archive entries ground the connection in our analysis. They are ordered by source publication date, with links to our coverage and the original sources.
·arXiv cs.LG
Researchers expose hidden gaps in LLM mathematical reasoning beyond accuracy metrics
Researchers have identified a structural gap in how large language models approach mathematical reasoning, proposing the concept of Mathematical Primitives to diagnose where models fail despite high solution accuracy. The work introduces a four-dimensional benchmark spanning Discovery, Generation, Digestion, and Execution that decouples surface-level correctness from genuine mathematical understanding. This framework matters because it reveals…
MentionsLanguage models
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Modelwire summarizes, we don’t republish. arXiv cs.CL originally reported this story as “Language models can notice an impossible engineering problem yet still report it as solved”. 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.