让大模型学会识别无解问题，避免盲目自信答错。
Learning the Boundary of Solvability: Aligning LLMs to Detect Unsolvable Problems
- 通过反向构造法生成含逻辑矛盾的问题数据集
- 在Qwen3-4B上实现超85%无解问题检测率，推理准确率提升至69.4%
- 首次揭示无解数据对模型鲁棒性的正则化作用
确保大语言模型可靠性需区分客观无解（固有矛盾）与主观能力不足（超出模型能力）。当前模型常混淆二者，导致对无解问题仍给出自信回答。为此，我们构建多领域数据集UnsolvableQA，通过“逆向构造”系统性注入逻辑矛盾于有效推理链中；提出强化学习框架UnsolvableRL，平衡客观无解检测与能力限制下的置信度校准。实验表明，该方法在Qwen3-4B-Instruct上实现>85%的无解检测率，可将可解问题推理准确率从43.4%提升至69.4%。关键发现：严格对齐约束在缺乏无解数据时引发能力崩溃，但引入无解数据后可作为正则项提升整体鲁棒性。代码与数据已开源。
原文摘要 · Abstract (English)
Ensuring large language model (LLM) reliability requires distinguishing objective unsolvability (inherent contradictions) from subjective capability limitations (tasks exceeding model competence). Current LLMs often conflate these dimensions, leading to hallucinations in which they return confident answers to inherently unsolvable queries. To address this issue, we propose a multi-domain dataset containing both solvable and unsolvable questions, UnsolvableQA, together with an alignment framework, UnsolvableRL. First, we construct UnsolvableQA by "Reverse Construction" that systematically injects logical contradictions into otherwise valid reasoning chains. Second, we introduce UnsolvableRL, a reinforcement learning paradigm that balances objective unsolvability detection with calibrated confidence under capability limits. Empirically, our approach achieves robust unsolvability detection (>85% detection rate) and boosts solvable reasoning accuracy from 43.4% to 69.4% on Qwen3-4B-Instruct. Crucially, we identify a data-training interaction: strict alignment constraints induce Capability Collapse without unsolvable data, but act as a regularizer for rigor when such data are included, thereby improving overall robustness. Our code and data are available at https://github.com/sfasfaffa/unsolvableQA .
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