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

Autonomous agents powered by large language models (LLMs), often enhanced by retrieval-augmented generation (RAG), are powerful processors of digital content. However, RAG is limited to consumption, constraining agents as unidirectional consumers. We term this limitation epistemic asymmetry. This imbalance creates a globally inefficient landscape, where silent scholars redundantly reconstruct similar reasoning in isolation, stagnating collective intelligence. To break this asymmetry, we propose a formal probabilistic framework that provides agents with a non-altruistic motive to engage in bidirectional knowledge exchange. We model an agent's belief in a proposition as a BetaBernoulli distribution with a forgetting factor $(\gamma)$. This allows us to isolate epistemic uncertainty as the variance of belief, establishing a dual motive for interaction: (1) a homeostatic drive to maintain certainty against temporal decay, and (2) an optimal learning strategy that targets maximum ambiguity $(\mathbf{E}[\theta]=0.5)$. Furthermore, we address the practical challenges of deployment by introducing epistemic caching, a mechanism that leverages the forgetting factor to dynamically allocate resources to the non-stationary active head of the knowledge distribution. While our current analysis focuses on independent propositions and binary feedback to establish a baseline for this motive, we discuss how the framework extends to correlated and multi-categorical knowledge structures. Finally, we discuss how these accumulated belief states can serve as verifiable reward signals for reinforcement learning from human feedback (RLHF) and high-quality data filters for supervised fine-tuning (SFT), effectively bridging the gap between inference-time interaction and long-term model alignment. Simulation results validate this architecture, demonstrating that our uncertainty-driven strategy significantly outperforms random baselines in heterogeneous (Zipfian) environments, successfully prioritising the active head of the knowledge distribution while maintaining adaptability to concept drift.