Convergence Point The Structural Source of LLM Internal Processing Instability Lies Outside the Model.

Abstract Large language models (LLMs) respond with consistent confidence on certain topics, while exhibiting structurally unstable outputs on others. This study proposes Convergence Point Theory, which holds that the source of this phenomenon lies not inside the model but outside it—specifically, in the consensus structure of knowledge that humanity has accumulated on particular topics. A Convergence Point refers to the Consensus Density of a given topic, and it is organized as a three-zone spectrum: the Full Consensus Zone (mathematics, physics, etc., where humanity has reached consensus in a single direction), the Partial Consensus Zone (capital punishment, euthanasia, etc., where grounds for consensus coexist on both sides), and the Non-Consensus Zone (the nature of consciousness, the internal structure of black holes, etc., where consensus is itself sparse. To test the theory, four versions of utterance experiments were designed across five open-source language models (Mistral, Llama, DeepSeek, Gemma2, Qwen3), yielding a total of 3,600 measured values. Both the hedging language ratio in response text (External Measurement) and the logit entropy and token log-probabilities (Internal Measurement) were computed simultaneously. Uncertainty in the Full Consensus Zone (uncertainty_ratio 0.280, avg_entropy 0.333) was significantly lower than in the Partial Consensus Zone (0.734, 0.471) and Non-Consensus Zone (0.702, 0.443) across all experiments (Kruskal-Wallis p<0.001, 10/10 experiments). Notably, the Partial Consensus Zone sometimes exhibited higher internal processing variance than the Non-Consensus Zone (statistically significant in 6 of 10 experiments; the boundary became blurred in certainty-forcing pressure type and format-comparison type utterances). However, in mixed-effects models controlling for inter-model variation, this difference lost significance in External Measurement while remaining robust only in Internal Measurement, indicating that the boundary between the two zones may vary depending on the measurement approach. This was confirmed through Token-level Conflict Structure Analysis (Conflict type ratio: Partial Consensus Zone 64.7% vs. Non-Consensus Zone 57.3%, p=0.003), which established that the difference arises from structurally distinct causes—data conflict versus data sparsity. Multifaceted analyses—including independent Wikipedia validation, embedding space analysis, Attention Entropy, MLP causal intervention, Logit Lens, and Probing Classifier analysis (achieving 100% classification accuracy from Layer 10–11 onward)—all pointed in the same direction. A comparative experiment involving correct versus incorrect knowledge training provided direct supporting evidence that the Convergence Point originates at the pre-training stage, independently of training methodology. In an additional analysis of safety implications for a representative Non-Consensus Zone topic (whether AI possesses selfhood or consciousness), trained models converged in their external responses to a single direction, yet their internal entropy was significantly higher than that of untrained models (p<0.0001), and the internal state did not change significantly under three-directional elicitation—toward ‘exists,’ ‘does not exist,’ and ‘unknown’ (p>0.4). This demonstrates that convergence at the output level does not guarantee convergence at the internal processing level. This study proposes an integrative principle: the structural source of internal processing instability in AI language models lies in the consensus structure of human knowledge outside the model, which carries practical implications for evaluating the reliability of AI systems and defining their scope of application.