Feeling of Knowing in Large Language Models
Zichuan Fu, Xian Wu, Jingtong Gao, Wenlin Zhang, Jiaxuan Li, Binhao Wang, Yimin Deng, Guojing Li, Xiaopeng Li, Derong Xu, Yefeng Zheng, Xiangyu Zhao
Abstract
Post-training updates change what large language models (LLMs) can answer, but may leave their answerability judgments misaligned. We study this knowledge-judgment desynchronization through functional feeling of knowing (FoK), which supports selective generation, retrieval triggering, and model routing without implying subjective experience. We propose two trainable channels: a knowledge channel that changes answerability and a FoK channel that judges the current knowledge state. Three stages train them: on-policy supervised fine-tuning (OP-SFT) updates knowledge from corrected on-policy answers; knowledge-delta FoK training (K$Δ$-FT) adapts judgments across intermediate knowledge states; and FoK-guided policy optimization (FGPO) trains the subsequent answer or explanation. Factual-QA experiments, cross-dataset evaluation, and three sequential updates show that explicit FoK alignment improves judgment quality on updated knowledge. MMLU and ARC-Easy separately assess capability preservation.