The Silent Scholar Problem: A Probabilistic Framework for Breaking Epistemic Asymmetry in LLM Agents

Autonomous agents powered by LLMs and Retrieval-Augmented Generation (RAG) are proficient consumers of digital content but remain unidirectional, a limitation we term epistemic asymmetry. This isolation leads to redundant reasoning and stagnates collective intelligence. Current self-reflection frameworks remain largely heuristic and private, lacking a probabilistic foundation to quantify certainty or justify external interaction.To bridge this gap, we propose a formal probabilistic framework that provides agents with a non-altruistic motive for bidirectional knowledge exchange. We model an agent's belief in a proposition using a Beta-Bernoulli distribution with a forgetting factor ($γ$). This allows us to isolate epistemic uncertainty as the variance of belief, establishing a dual drive for interaction: A homeostatic motive: The need to maintain certainty against the temporal decay introduced by $γ$. An optimal learning strategy: Targeting points of maximum ambiguity ($\mathbb{E}[θ]=0.5$) to maximize information gain. Under this framework, public contribution is reframed as optimal active learning: sharing solutions to elicit feedback is the most efficient method for an agent to reduce its own uncertainty. To ensure scalability, we introduce epistemic caching, which leverages the forgetting factor to dynamically prioritize resources for the active head of non-stationary knowledge distributions. Finally, we demonstrate how these accumulated belief states serve as verifiable reward signals for Reinforcement Learning from Human Feedback (RLHF) and high-quality data filters for Supervised Fine-Tuning (SFT). Simulation results validate that this uncertainty-driven strategy significantly outperforms random baselines in heterogeneous (Zipfian) environments, maintaining high adaptability to concept drift.