Abstract: Large language models (LLMs) are increasingly trained to abstain on difficult questions by answering unknown. However, we observe that LLMs often misuse this option: they output unknown even when LLMs can actually solve the questions, or they fail to understand why questions are truly unsolvable. We formalize this mismatch between potential ability and the inclination of abstention as the Vague Perception phenomenon. We introduce the WakenLLM pipeline that (1) extracts Vague Perception samples and (2) measures how many of them can be converted to correct answers under stimulation. Based on stage-wise metrics (TCR, OCR, etc.) and the upper-bound accuracy Acc(WakenLLM), we quantify LLMs' reasoning potential beyond one-shot accuracy. Experiments on six LLMs suggest that, without further training or parameter revisions, LLMs can achieve up to a 68.53% increase in accuracy on Vague Perception samples through our designed pipeline. We further analyze how Vague Perception, Conformity and Degradation vary from model families and parameter sizes, and offer model selection strategies in multi-stage reasoning workflows. Finally, by comparing WakenLLM against mainstream reasoning baselines, both training and non-training ones, we show that existing baselines only activate a small portion of LLMs' reasoning potential, pointing to perception-aware reasoning as a promising direction for future LLM designing. Code and datasets are available at https://github.com/WakenLLMTeam/WakenLLM-toolkit.
External IDs:dblp:journals/corr/abs-2507-16199
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