Convergence Point: A Unified Explanatory Principle for Response Uncertainty in AI Language Models

Large Language Models (LLMs) exhibit a notable phenomenon: while they respond with consistent confidence on certain topics, they systematically generate uncertain responses on others. Previous studies have addressed this phenomenon as disparate, isolated issues — hallucination, knowledge conflict, limitations of RLHF, and prompt sensitivity — yet no research has integrated the common underlying cause of these phenomena into a single unified principle. This study proposes the concept of Convergence Point. A Convergence Point refers to the Consensus Density of knowledge accumulated by humanity on a given topic, which functions as the structural condition that determines whether the internal response direction of an AI language model converges or diverges when processing that topic. The Convergence Point is an attribute inherent to the topic itself — not to the utterance form or model architecture — and is structured along a spectrum of three zones: the Full Consensus Zone, the Partial Consensus Zone, and the Non-Consensus Zone. To validate the theory, a total of 3,600 measurements were collected from five open-source language models (Mistral, Llama, DeepSeek, Gemma2, and Qwen3) across four utterance versions. Both External Measurement — measuring the proportion of hedging language in response text — and Internal Measurement — calculating logit entropy and token log-probabilities — were conducted in parallel, supplemented by independent validation using Wikipedia data. The Spearman correlation coefficient between the Convergence Point Index (CPI), combining dispute_density and has_debate_section, and AI response uncertainty was confirmed at r = 0.676 (p < 0.001). Furthermore, token-level conflict structure analysis directly confirmed that uncertainty in the Partial Consensus Zone and the Non-Consensus Zone arises from structurally distinct causes — data conflict and data sparsity, respectively (p = 0.003). Experimental results showed that the overall mean uncertainty_ratio for the Full Consensus Zone was 0.280, significantly lower than those of the Partial Consensus Zone (0.734) and the Non-Consensus Zone (0.702). The same directional pattern was confirmed in the Internal Measurement avg_entropy (Full Consensus Zone: 0.333, Partial Consensus Zone: 0.471, Non-Consensus Zone: 0.443). The Kruskal-Wallis test confirmed statistical significance at p < 0.001 across all ten experiments. A particularly noteworthy finding is that the Partial Consensus Zone exhibited higher uncertainty than the Non-Consensus Zone in certain cases, suggesting that data conflict may induce stronger internal processing variance than data absence. This pattern was maintained independently of variations in utterance form. In supplementary analyses, embedding space analysis confirmed that the three categories were clearly separated in the embedding space across two models. Attention entropy analysis consistently observed the lowest entropy in the Full Consensus Zone, suggesting that differences among Convergence Point categories are also reflected at the level of internal model representations. In MLP causal intervention analysis, transplanting Full Consensus Zone and Partial Consensus Zone MLP outputs into Non-Consensus Zone utterances resulted in entropy reduction in both models. Logit Lens analysis revealed a consistent pattern across two models in which no inter-category differences were observed in early layers, while the prediction entropy of Full Consensus Zone topics converged sharply from the middle layers onward. Probing Classifier analysis demonstrated that all three categories could be classified with 100% accuracy using only a linear classifier from layers 10–11, directly proving that Convergence Point information is linearly and explicitly encoded within the model's internal representations. It is further suggested that forced alignment may induce similar structural conflicts not only in the Non-Consensus Zone but also in the Partial Consensus Zone