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：我们探索了一种新的语义信息理论在资源采集智能体问题中的应用。语义信息被定义为通过传递熵测量的智能体$A$与环境$E$之间、对于智能体维持其生存能力$V$所必需的相关性子集。生存能力在此是内生定义的，而非使用效用函数等外生量。在我们的模型中，采集者的运动由其通过传感器检测单个资源单元存在的能力决定，而生存能力函数则是其预期寿命。通过反事实干预——对传感器添加噪声以扰乱智能体与环境之间的相关性——我们证明了噪声参数存在临界值$\eta_c$，当噪声超过该值时，采集者的预期寿命显著降低；反之，当$\eta < \eta_c$时，对其生存能力影响极小。我们称此边界为语义阈值，它量化了智能体实际需要用以维持理想存活状态的智能体-环境相关性子集。每个信息比特都会影响智能体在语义阈值上下维持生存的能力。通过使用采集者/环境参数建模生存曲线及其语义阈值，我们展示了相关性是如何具体实现的。我们的工作为基于语义信息的既有智能体研究提供了有用模型，并表明此类语义阈值可能有助于理解信息在使系统成为自主智能体过程中所起的作用。