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Research questionHow can mathematical-reasoning LLMs learn to construct counterexamples that reveal conceptual understanding?A model can produce a correct answer by repeating familiar solution patterns without understanding why they work. Counterexamples make the boundaries of a claim explicit, providing a demanding way to train or assess conceptual reasoning.
AI
Evaluation & Benchmarks
LLM Pretraining & Post-training
Reasoning
Latest papersRecent research connected to this question, newest first.INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical ReasoningThe source proposes staged preference training that first supports example-based reasoning and then emphasizes correctness. Evidence covers multiple model scales and families, including out-of-distribution mathematical evaluations; no broader architecture or deployment conditions are established.research paper · Sep 4, 2026
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How can we tell whether LLMs follow coherent, human-like prerequisite relationships in mathematical reasoning?How can large reasoning models explore complex research problems while maintaining proof rigor?How can LLMs interleave reasoning with reliable step-level self-critique without a separate verifier?How can we evaluate LLM reasoning quality beyond final-answer accuracy across deployment contexts?