We explore the application of a new theory of Semantic Information to the well-motivated problem of a resource foraging agent. Semantic information is defined as the subset of correlations, measured via the transfer entropy, between agent $A$ and environment $E$ that is necessary for the agent to maintain its viability $V$. Viability, in turn, is endogenously defined as opposed to the use of exogenous quantities like utility functions. In our model, the forager's movements are determined by its ability to measure, via a sensor, the presence of an individual unit of resource, while the viability function is its expected lifetime. Through counterfactual interventions -- scrambling the correlations between agent and environment via noising the sensor -- we demonstrate the presence of a critical value of the noise parameter, $\eta_c$, above which the forager's expected lifetime is dramatically reduced. On the other hand, for $\eta < \eta_c$ there is little-to-no effect on its ability to survive. We refer to this boundary as the semantic threshold, quantifying the subset of agent-environment correlations that the agent actually needs to maintain its desired state of staying alive. Each bit of information affects the agent's ability to persist both above and below the semantic threshold. Modeling the viability curve and its semantic threshold via forager/environment parameters, we show how the correlations are instantiated. Our work provides a useful model for studies of established agents in terms of semantic information. It also shows that such semantic thresholds may prove useful for understanding the role information plays in allowing systems to become autonomous agents.

翻译：我们探索了语义信息新理论在资源觅食智能体这一动机充分问题中的应用。语义信息被定义为通过转移熵测量的智能体A与环境E之间对于维持智能体生存能力V所必需的关联子集。与使用效用函数等外生量不同，生存能力在此被内生定义。在我们的模型中，觅食者的移动由其通过传感器测量单资源单元存在的能力决定，而生存能力函数为预期寿命。通过反事实干预——用噪声干扰传感器来打乱智能体与环境间的关联——我们证明了噪声参数存在临界值η_c，超过该阈值时觅食者的预期寿命会急剧下降。另一方面，当η < η_c时，噪声对生存能力几乎无影响。我们将此边界称为语义阈值，量化了智能体实际需要用于维持存活状态的那部分智能体-环境关联。每个比特的信息都会影响智能体在语义阈值上下持续存在的能力。通过用觅食者/环境参数对生存能力曲线及其语义阈值进行建模，我们展示了关联是如何具体实现的。我们的工作为基于语义信息研究已建立智能体提供了有用模型，同时表明此类语义阈值可能有助于理解信息在系统成为自主智能体过程中所起的作用。