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

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📝 Original Info

  • Title: The Silent Scholar Problem: A Probabilistic Framework for Breaking Epistemic Asymmetry in LLM Agents
  • ArXiv ID: 2512.20884
  • Date: 2025-12-24
  • Authors: Zan-Kai Chong, Hiroyuki Ohsaki, Bryan Ng

📝 Abstract

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.

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The emergence of large language models (LLMs) has ushered in a new generation of autonomous agent systems [17]. These agents exhibit exceptional proficiency in analysing extensive information from the internet, performing intricate multi-step operations, and integrating knowledge to respond to user queries [22]. Ranging from advanced personal assistants to automated research platforms, they mark a major advancement in artificial intelligence, serving as highly capable processors and interpreters of digital content.

However, despite their breadth of capabilities, these agents remain constrained by the static nature of their pretrained knowledge. Retrieval-augmented generation (RAG) has emerged as a significant step toward addressing this, enabling LLMs to query external web resources to enhance factual accuracy and mitigate hallucination [9], [8]. Often, the retrieved documents provide valuable, context-specific examples that the agent can use for in-context few-shot learning to improve its immediate response.

Yet, RAG, even when used for few-shot learning, only solves the problem of consumption. Contemporary agents remain architecturally constrained as unidirectional consumers of knowledge, with minimal mechanisms for reintegrating their synthesised insights into shared digital ecosystems. We identify this limitation as epistemic asymmetry, and it creates a critical failure mode for the agent itself.

Without bidirectional exchange, an agent cannot distinguish between aleatoric noise (environmental randomness) and epistemic ignorance (model deficiency), terms coined in [18]. Isolated from external correction, the agent is forced to train on its own unverified outputs, a recursive process that leads to model collapse. In this degenerative state, the agent’s belief distribution loses variance, and it becomes confidently wrong and incapable of adapting to concept drift [16].

Current agents lack the motive to break their asymmetry because they lack a formal model to quantify this reducible, epistemic uncertainty. Without a formal uncertainty model, an agent cannot distinguish between environmental noise (which it should ignore) and its own ignorance (which it should resolve). Consequently, they have no mechanism to understand why contributing back to the digital commons (e.g., public forums, Q&A sites, Stack Overflow, Reddit, etc.) would be beneficial. For an agent, posting a solution to a public problem and receiving feedback is a powerful, low-cost method to gain new data. This feedback is the very evidence needed to reduce its epistemic uncertainty, but current models are not equipped to quantify this value.

In this paper, we envision that the contemporary agents will evolve from silent scholars to becoming epistemic agents and actively engaging in bidirectional knowledge exchange. To ground this vision, we propose the formal probabilistic frame-work that provides their non-altruistic motive. We initially model the agent’s belief over its propositions as an unknown success rate using a Beta-Bernoulli model with a forgetting factor (γ). While this treats propositions as independent units of evidence, it provides a necessary simplification for our initial derivation of the equilibrium sample size (N eq ) and the mathematical foundation for more complex, interdependent knowledge representations.

This framework provides a non-altruistic motive: First, the forgetting factor ensures that certainty decays over time, effectively converting stale knowledge back into epistemic uncertainty. This prevents the variance from decaying to zero, establishing a persistent motive for continuous engagement. Second, our analysis indicates that the agent’s potential for learning is mathematically maximised at the point of highest ambiguity (E[θ] = 0.5). These findings provide the formallyjustified motive for an agent to break its asymmetry. Furthermore, we address the challenge of scalability by deriving an eviction policy that functions as epistemic caching. By leveraging the forgetting factor, the agent creates a dynamic working set of beliefs, ensuring the model remains computationally tractable despite the vast proposition space of realworld LLMs.

The remainder of this paper is organised as follows. Section II reviews related work in autonomous agents and active learning , and explicitly positions our framework against established paradigms such as online Bayesian updating and multi-armed bandits. Section III formalises our probabilistic framework, detailing the Beta-Bernoulli model used to represent an agent’s belief state and uncertainty. Then it provides a formal analysis of this model’s properties, establishing a non-altruistic motive of persistent uncertainty and maximum ambiguity. Section IV presents our experimental setup and results validating this framework. Section V discusses the broader implications for system robustness and model alignment, proposing mechanisms to mitigate re-calibration latency and distill

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Reference

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